Electronics cooling by means of electro-static actuated ... - CiteSeerX

Technical note TN-2005-00543

Issued: 08/2005

Electronics cooling by means of electro-static actuated liquid flow through micro channels Geert Van der Veken Philips Research Eindhoven

Philips Unclassified

c Koninklijke Philips Electronics N.V. 2005

TN-2005-00543


Concerns:

End Report

Period of Work:

2004-2005

Notebooks:

None

Authors’ address G. Van der Veken

[email protected]

Promotor: Prof. dr. ir. M. Baelmans

[email protected]

Supervisors: ir. H. Oprins

[email protected]

dr. C. Nicole

[email protected]

ir. L. van der Tempel

[email protected]

Acknowledgements: Special thanks is addressed to: My promotor: Prof. dr. ir. Martine Baelmans (KULeuven) My supervising assistant: ir. Herman Oprins (KULeuven/IMEC) . Philips Research Eindhoven: Clemens Lasance, Celine Nicole, Jean-Christoph Baret, Leendert van der Tempel, Eugène Timmerings, Theo Michielsen, Dirk Budinski, Milan Saalminck, Menno Prins, Dr. Ronald Dekker, Remco Pijnenburg and Martin Hack. c KONINKLIJKE PHILIPS ELECTRONICS N.V. 2005

All rights reserved. Reproduction or dissemination in whole or in part is prohibited without the prior written consent of the copyright holder.

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Title:

Electronics cooling by means of electro-static actuated liquid flow through micro channels

Author(s):

Geert Van der Veken

Reviewer(s):

Lasance Clemens; Baret Jean Christophe; van der Tempel Leendert; IPS Facilities

Technical Note:

TN-2005-00543

Project:

2003-297 System in Package Approach to Solid State Lighting (SiPLED)

Customer:

LIG New Business Creation Company Research

Keywords:

droplet electrowetting; micro channel cooling; Lumileds

Abstract: A conceptual cooling system for individual cooling of electronics is investigated in this master thesis. The aim is to derive theoretically and experimentally the cooling rate of this conceptual cooling system with integrated pumping. The used electrowetting system consists of a liquid droplet deposited on a conductive substrate and electrically isolated from this substrate by a dielectrical layer of 1µm thickness. Micro channels of 100µm ×100µm are etched in this substrate. Across the droplet an electrical field is applied, the so called electrowetting, to fill the micro channels with the droplet. The theoretically achievable cooling rate of this enhanced system is compared with the cooling rate by conduction through the conductive substrate. Problems are discussed that occur when trying to experimentally validate the theoretically calculated cooling rate. Also the droplet behaviour is examined under influence of temperature increase. Areas of future research concern the confining of the channelstructures and the achieving of a continuous flow rate.


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Conclusions: A model for the actuation principle of electrowetting was explored and a theory is developed to estimate the enhancement in liquid cooling that can be achieved by electrowetting. This theory revealed that this new cooling method will induce enhanced heat transfer above a critical frequency. This critical frequency is for the 100µm square microchannels about 0.25Hz. The calculated cooling rate amounts 156W for a block shaped filling, 198W for a sinusoidal filling and 1.56W or 15.6W/cm2 for a real filling length characteristic at a frequency of 1.47Hz. Experimental results of the calculated enhancement of liquid cooling could not yet been given, due to the experimental setup and measuring problems. However, because of the promising achievable cooling rates, cooling by electrowetting with integrated pumping should be subject of further investigations.

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Contents 1

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Introduction to electronics cooling 1.1 General . . . . . . . . . . . . . . . . . . . 1.1.1 Importance of electronics cooling . 1.1.2 Recent trends in electronics cooling 1.2 Overview of cooling systems . . . . . . . . 1.2.1 Air cooling versus liquid cooling . . 1.2.2 Liquid cooling . . . . . . . . . . . 1.2.3 Other types of electronics cooling . 1.3 Conclusion . . . . . . . . . . . . . . . . .

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Experimental setup 2.1 Introduction . . . . . . . . . . . . . . . . . 2.2 The test samples . . . . . . . . . . . . . . . 2.2.1 Production of the micro channels . 2.2.2 Experiment samples . . . . . . . . 2.3 The testing liquids . . . . . . . . . . . . . . 2.4 Experimental equipment . . . . . . . . . . 2.4.1 Actuation of the droplet . . . . . . 2.4.2 Measuring the droplet behaviour . . 2.5 Reproducibility of results . . . . . . . . . . 2.5.1 Preconditions for valid experiments 2.5.2 Reproducible applied voltages . . . 2.6 Conclusion . . . . . . . . . . . . . . . . .

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Actuation Principle 3.1 Introduction . . . . . . . . . . . . . . . . . . . . 3.2 Behaviour on a flat surface . . . . . . . . . . . . 3.2.1 Introduction . . . . . . . . . . . . . . . . 3.2.2 Energy analysis of electrowetting . . . . 3.2.3 Young’s equation . . . . . . . . . . . . . 3.2.4 Lippmann’s angle . . . . . . . . . . . . . 3.2.5 Lippmann curves on a flat substrate . . . 3.3 Behaviour on a structured surface . . . . . . . . 3.3.1 Cassie’s and Wenzel’s equation . . . . . 3.3.2 Contact angle of filling . . . . . . . . . . 3.3.3 Lippmann curves on a structured surface 3.4 Dynamics: Filling of the channel . . . . . . . . .


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Philips Unclassified . . . .

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43 48 50 50

Achievable heat transfer 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 General heat transfer equations . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Thermal and fluidic laws for single phase forced convection . . . . . 4.2.5 Thermal resistances . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Convective exchange laws from a thermal and hydraulic point of view 4.2.7 A first approximation for the achievable heat transfer . . . . . . . . . 4.3 Heat transfer by electrowetting of micro channels . . . . . . . . . . . . . . . 4.3.1 General expression . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Heat transfer for a given filling function . . . . . . . . . . . . . . . . 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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51 51 52 52 53 53 54 54 57 60 61 61 62 68

Heat experiments 5.1 Introduction . . . . . . . . . . . . . . . . . . 5.2 Fabrication of test samples . . . . . . . . . . 5.3 Temperature effect . . . . . . . . . . . . . . 5.3.1 Viscosity . . . . . . . . . . . . . . . 5.3.2 Temperature effect on surface tensions 5.4 Heat transfer measurements problems . . . . 5.4.1 Infrared camera . . . . . . . . . . . . 5.4.2 Thermocouples . . . . . . . . . . . . 5.4.3 Measuring the cooling rate . . . . . . 5.5 Conclusion . . . . . . . . . . . . . . . . . .

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Future work 6.1 Confined channels . . . . . 6.1.1 Introduction . . . . 6.1.2 Possible techniques 6.2 Liquid metals . . . . . . . 6.3 Conclusion . . . . . . . .

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Conclusion References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A Cleaning procedure A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Cleaning methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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B Matlab-file for filling length calculation B.1 Users info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.2 The Matlab-file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.4.1 Dynamic experiments 3.4.2 Model of filling . . . . 3.4.3 Model of emptying . . Conclusion . . . . . . . . . .

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Section 1

Introduction to electronics cooling This chapter gives a short overview of current cooling systems for electronic devices, which are commonly named as electronics. Starting with a first section, where an explanation is given about the importance of electronics cooling and where the recent trends in electronics cooling are indicated with use of two examples, namely Intel processors and LEDs. In a second section a more extensive overview of cooling systems is given, starting with a comparison between air cooling and liquid cooling, followed by a classification of liquid cooling and ending with some other types of liquid cooling systems, recently developed.

1.1 1.1.1

General Importance of electronics cooling

Individual electronic components have no moving parts and therefore they are not affected by wear. They are extremely reliable and it seems they can operate for many years, without interruption. This would be true, if these components could work at room temperature. In general [1], for CMOS device technology, power dissipation is proportional to the number of devices per chip (N ), the capacitance of the logic elements (C), the square of the operating voltage swing (V 2 ) and the operating frequency (f ): P ower ∝ N CV 2 f

(1.1)

The number of devices per chip N and the frequency f increase, while the capacitance C and the operating voltage V decrease but all these parameters scale different. Not cooling this dissipated power would lead to very high temperatures, which involve thermal stresses, change in metallographique structure of the materials and will eventually lead to failure of the device. According to the International Technology Roadmap for Semiconductors (ITRS), predictions in 1999, 2002 and 2004 for the heat generated by high-end devices-microprocessors and microcontrollers are shown in figure 1.1. In figure 1.2 are similar forecast shown for chip heat flux. For the predictions of 2004 it is stated that peak power consumption will jump by 25% (from 0.51W/mm2 to 0.64W/mm2 ) for high performance desktops in 2010, while peak power consumption for lower-end desktops will jump 80% in 2018 (from 0.6W/mm2 to 1.08W/mm2 ). c Koninklijke Philips Electronics N.V. 2005

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Figure 1.1: Power dissipation forecast of 1999, 2002 and 2004, according ITRS.

Figure 1.2: Chip heat flux forecast of 1999, 2002 and 2004, according ITRS. From these predictions two observations are important. First, it is clear that we will reach powers well above 100W per chip by the middle of the decade. Second, it is also clear that power dissipations are expected to rise as time goes on. The ITRS forecast of 2004 predicts a stabilizing power output, caused by the increased leakage current flowing through the devices. So far no decent cooling method is found to increase power density. New cooling techniques are necessary but any elegant technical approach will not see the daylight if it doesn’t meet the major design goals for any thermal management solution. These goals are performance, cost, physical size and reliability [2]. This last design goal will not only apply for the stand alone device, but must also be valid for the device in the whole package and in the current working conditions. 2



1.1.2

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Recent trends in electronics cooling

In current electronic devices power dissipation increases with each new design. It was already in 1965 that Dr. Gordon Moore, co-founder of Intel, postulated his "Moore’s law". His law predicted that semiconductor-transistor-density and their corresponding power outputs roughly double every 18 months. Although Dr. Moore made his predictions in 1965, history seems to validate the 40 years old prediction of Dr. Moore (illustrated in figure 1.3): Moore’s law is also relevant for power dissipation as expressed by equation (1.1).

Figure 1.3: Number of transistors per die as function of time. This figure validates Moore’s assumption of 1965. [3] Together with the density of the gates, the power also increases. Figure 1.4 illustrates that for Intel microprocessors both active and leakage processor power have increased. The reasons for this increase in power are twofold. A first reason is the increase of clock speed and second it is caused by the increase of the number of gates in the chip. The decrease of chip parts dimensions made it possible to increase the number of parts in a chip area. On the other hand, the power supply voltage has decreased and energy consumption of each part and of each MHz lowered. Nevertheless the overall energy consumption of every chip has increased, caused by the increase in clock speed and the increase in gates. The main reason for this overall energy consumption is the fast increase in leakage power, as pictured in figure 1.4. This leakage power is the greatest dissipation source in the chip and therefore the main reason to perform cooling.


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Figure 1.4: Evolution of the active and leakage processor power output of Intel microprocessors. [3] The same power increase is valid for other electronic devices such as LEDs (Light Emitting Diodes). Future generations of high light-output multichip LED modules for general and automotive illumination applications should contain in one package: multiple red, green and blue LEDs, as well as first-stage optics, sensing drive and control electronics. These systems in package require build-in thermal management systems to maintain reliability and performance of the package. An example of such a system in package is pictured in figure 1.5.

Figure 1.5: Example of a high light-output multichip LED module. The efficiency of a white LED today has reached 30 lm/W. It is projected to reach 75 lm/W by 2006 and 150 lm/W by 2012. These future LEDs will create a high power dissipation on a very small surface area. As a result of increasing junction temperature, LEDs can loose light output, and resulting in a decrease in luminous efficiency. Furthermore the emission spectrum of a LED shifts to higher wavelengths when the temperature of the junction increases. To maintain good working conditions of LEDs an adequate thermal design is needed. As an example of a current LED and as a proof that heat dissipation of such a diode is not negligible anymore some technical specifations of the LXHL-NW98 White Luxeon Star/O are given here; it reaches a luminous efficiency of 25 lm/W, dissipates 1.2W and has a junction temperature of 120◦ C. 4



1.2

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Overview of cooling systems

In this section a short overview of past and current cooling systems is given. In general two different types of cooling exist: active cooling and passive cooling techniques. Passive cooling techniques require no external power input to establish cooling, while an active cooling technique does need a power input. Furthermore air cooling is briefly compared to liquid cooling (both passive and active cooling). Finally a short overview of already existing liquid cooling techniques is presented.

1.2.1

Air cooling versus liquid cooling

Air cooling has always been preferred above liquid cooling of electronics. Although liquids have higher cooling rates than gases (see in table 1.1). The advantages of air cooling, such as simplicity, low cost, easy maintenance and high reliability, have made it always favorable over liquid cooling. Cooling

h

technique Natural convection Gases Liquids Forced convection Gases Liquids Boiling and condensation

[W/m2 .K] 2-25 50-1000 25-250 50-20000 2500-100000

Table 1.1: Convective heat transfer coefficients of liquids and gases [4]. In current applications a heat sink coupled with a fan is the most used cooling technique. Heat sinks create a higher heat transfer caused by the increase in contact area between the cooling fluid and the hot device. The major limits in air cooling systems are the high sound levels which go together with high airflows over the heat sink and the required space for the fan. Due to the strong increase of heat dissipation and due to further miniaturization, air cooling has reached its limits. This has stimulated the development of new and alternative cooling systems.

1.2.2

Liquid cooling

The higher convective heat transfer coefficients of liquids compared to air make it possible to allow a greater heat dissipation. Consequently liquid cooling is much more efficient than air cooling and becomes even more efficient when fluid is forced to move through channels with very small dimensions, according to Tuckermann and Peace [5]. Unfortunately liquid cooling has also some disadvantages, like risk of leakage, corrosion and an increase of weight in comparison with air cooled systems. In this section two different types of liquid cooling are explained: direct-contact and indirect-contact cooling.


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Direct-contact cooling

With direct contact cooling there exists a physical contact between the electronic component and the cooling fluid. Consequently there are no thermal interfaces involved, because there is no conductive part between the component surface area and the cooling fluid. The major advantage of the direct-contact cooling exists in the lower temperature difference between the component surface area and the cooling fluid in comparison with indirect-contact cooling. The disadvantages are the dielectrical and chemical characteristics of the cooling liquid, such as compatibility with component materials like silicon, gold, epoxy. Also the chemical inertia of the fluid is required. Moreover the cooling liquid has to be electrically insulated, so no electrical breakthrough can occur between the closely packed electrical wires of the electronic component. Substances that meet these requirements are the chloridefluorcarbonoxides (CFC’s). Due to their harmful influence on the ozonlayer, these substances may not be used anymore. They were replaced by the fluorcarbonoxides and others. However the main disadvantage is the expensive manufacturing of these materials. 1.2.2.2

Indirect-contact cooling

Indirect-contact cooling has no physical contact between the fluid and the hot component involved: on top of the component a heat exchanger is mounted, for example a microchannel cooler. Due to the extra interface and the increased distance between the hot spot and the fluid this method is inferior to direct-contact cooling, but much simpler to implement. In an earlier master thesis from Derkinderen and Theodorou [7] such a heat exchanger for electronic components is studied which works on the indirect-contact cooling technique. The maximal cooling rate in their heat exchanger was measured at 292W at a flow rate of 4l/min. This resulted in an average chip temperature of 53◦ C ±2◦ C, corresponding to a thermal resistance of 0.184K/W. A refinement of the heat exchanger of Derkinderen and Theodorou works on the same principle, but the liquid is forced into micro channels. Such micro channels are channels with hydraulic diameters of a few 100µm or less. They are made by anisotropic ion etching in a wafer, in order to build them in the electronic component. Such microchannel heat exchangers have already developed and tested at Philips Research by Aubry [8] and Pijnenburg [9]. Their micro channels had dimensions of 100µm width and 300µm of depth, which results in a corresponding hydraulic diameter of 150µm. These micro channels had a peak cooling rate of 428W at a flow rate of 1.11l/min of water. This resulted in a mean chip temperature of 55◦ C, corresponding to a thermal resistance of 0.12K/W. A more practical flow rate of 0.1l/min allowed a cooling rate of 300W, which resulted in a temperature of 120◦ C. These two liquid cooling heat exchangers are pictured in figure 1.6:

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Figure 1.6: Two different types of indirect-contact heat exchangers: the one on the left is from Derkinderen and Theodorou [7], the one on the right is from Aubry [8] and Pijnenburg [9]. According to the beneficial effect to cooling of forced convection through micro channels [5], future heat exchangers for electronics could operate based on this principle. Unfortunately the systems pictured in fig. 1.6 need a pump to maintain circulation. Such a pump give disadvantages, added power, added volume, risk of leakage and being subject to mechanical wear. A more reliable pumping technique would be preferable. Such potential possible future techniques of pumping a liquid through micro channels are already developed and one of them is discussed in this master thesis. The first technique is based on the Maxwell force. This is the force that is responsible for driving a dielectric between the charged plates of a capacitive. This technique is already discussed in a former master thesis by Hectors and Huybrechts [10], but is also subject of investigation for Oprins [11], Paik, Pamula and Chakrabarty [12],[13]. This technique of droplet manipulating is also being used for mixing of biological liquids [14] or for microreactor applications [15]. The movement of the droplet can be made by independently increasing or decreasing the voltage on the control electrodes, as is pictured in figure 1.7. The main advantage of this technique is that no extra space is needed, since the liquid droplets will be forced to move between the electronic components and the PCB, where the components are fixed on. A droplet can be controlled to move to local hot spots, pick up the dissipated heat and transport it towards a place where the heat can safely be transferred to the environment.


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Figure 1.7: Working mechanism of electrostatic actuated liquid droplets, according to Oprins [11]. The second technique discussed in this master thesis is based on the so called "electrowetting" effect. In electrowetting a droplet of conductive liquid is deposited on a thin dielectric layer. A voltage is applied between the droplet and an electrode patterned below the dielectric. The electric field applied across the dielectric layer results in a net energetically surface contribution which changes the wettability of the surface: the surface goes from hydrophobic to hydrophilic. As a result the wettability active control can be used to drive a droplet into micro channels. The dynamics of this system is still subject of investigation but has been described by Baret [16] and also explained in this master thesis. The technique of manipulating a liquid to change its surface energy coefficients is already known and applied in microlenses (see figure 1.8) or in displays [17].

Figure 1.8: Working principle and layout of microlenses based on manipulating the surface tensions of a liquid.

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1.2.3 1.2.3.1

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Other types of electronics cooling Thermosyphon

Figure 1.9: A pulsated two phase thermosyphon (PTPT) and a loop thermosyphon, with regards to the level differences of their components [18] A thermosyphon is an indirect-contact passive liquid cooling system, where the cooling fluid is forced to perform a phase transition during its cooling cycle. Tests on prototypes have already reached heat fluxes of 150W/cm2 [19]. Different lay-outs are present: the ordinary thermosyphon, the loop thermosyphon and the pulsated two phase thermosyphons (PTPT). The ordinary thermosyphon consists only of one interconnection between the evaporator and condensor. The vapor phase and liquid phase travels through the same tube. The difference with heat pipes (see next paragraph 1.2.3.2) lays in the fact that no use is made of capillary structures, but only gravity is used to bring back the liquid phase to the evaporator. The most important limitation in this design is the travelling speed of the liquid through the hot vapor phase, this limitation is relieved in the loop thermosyphon. The so called loop thermosyphons consist of an evaporator and a condensor, which are connected to each other in a closed loop system. In the interconnection tube from the evaporator to the condensor the heat carrier is only vapor. This vapor is transformed in the condensor back to the liquid phase which flows through the interconnection tube from the condensor back to the evaporator. This one is pictured on the right in figure 1.9. The working principle of an ordinary thermosyphon and of a loop thermosyphon is such that the heat flows from the heat source through an interface in the evaporator into the cooling fluid. The interface is usually structured which benefits the boiling speed. The cooling liquid is transformed in the evaporator to its vapor phase, which will, on its turn, be transformed back to the liquid phase in the condensor. The vapor phase will rise by its thermodynamic characteristics to the higher placed condensor, where the condensor liquid will flow back to the evaporator due to c Koninklijke Philips Electronics N.V. 2005

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gravity. Thus the main disadvantage of these first two types of thermosyphons is the necessity to place the condensor always above the evaporator which conflicts with all mobile and many stationary applications. This major disadvantage can be overcome in some other types of closed loop thermosyphons: some natural convection thermosyphons were realized where the condensor could be placed at different positions below the evaporator [18]. In the third type of thermosyphons, the pulsated two phase thermosyphon (PTPT), this disadvantage seems to be fully solved: the condensor could be placed at any position with regards to the evaporator. The working principle of the PTPT is slightly different from a loop thermosyphon, because an additional accumulator tank is positioned in the liquid line in order to force a periodic pulsation of pressure. These devices are characterized by a periodic heat transfer regime. An example is pictured on the left in figure 1.9. The main advantage of a thermosyphon is that no pump is needed, so no external energy has to be applied. Another advantage is the absence of moving parts in the system, which results in a high reliability. These two advantages are no longer valid for the PTPT, but this one has more design freedom than the other thermosyphons. The last advantage is the high flexibility that can be obtained: the evaporator can be very small and the interconnection tubes very long, so the condensor don’t have to be mounted just on top of the evaporator. On the other hand does a danger for leakage exist. 1.2.3.2

Heat pipes

A heat pipe is a simple heat exchanger that can transport considerable heat rates over a relatively large area, without moving parts nor energy consumption. A heat pipe belongs to the group of the liquid passive cooling techniques, with indirect-contact cooling. The most trivial type of a heat pipe is a closed cylindrical vessel, filled with a saturated liquid. The walls at the inside of the vessel are covered with a capillary structure, a so called "wick". As can be seen in figure 1.10, a heat pipe can be divided in three working areas: the left side is the evaporator, the right side is the condensor and in the middle there is an adiabatic section where liquid and vapor can flow. A cross-section in this adiabatic section has three different areas: a core filled with vapor travelling from the evaporator to the condensor, an outside boundary layer called the wick, where liquid flows back from the condensor to the evaporator and finally the tube wall. In this adiabatic section, no heat exchange takes place with the environment. The only places where heat is transferred through the wall of the vessel is at the evaporator, where heat is taken away from the heat source, and at the condensor, where the cooling fluid gives its heat to the environment.

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Figure 1.10: Schematic and working operation of a heat pipe [6]. Initially the wick is saturated with the liquid phase, while the core of the tube is filled with the vapor phase. If some heat is taken in by the evaporator, than the vapor pressure will locally increase and thus a pressure difference will exist over the length of the heat pipe. This difference in pressure is the force that drives the vapor through the inner core from the evaporator to the condensor. At the condensor the vapor changes phase and the condensed liquid can flow back to the evaporator by means of the capillary forces inside the wick, creating a closed loop system. The used liquid and pressure inside the heat pipe depend on the temperature at which the pipe is used. A heat pipe can also only work optimally in a narrow temperature region, due to the limit of the used liquid: the used liquid must go from its initial vapor phase to its second liquid phase and back. It’s clear that different types of fluid are used to cover all the temperatures needed. Boiling and condensation involve very high heat transfer coefficients. That’s why heat pipes can have thermal conductivity that is higher than those of an equivalent block of copper (k = 400W/mK) with the same dimensions. So if a heat pipe is attached to a heat source instead of a copper block, than will the heat transfer away from the heat source increase 100 or a 1000-time. Table 1.2 gives an idea of the dissipating power of various heat pipes. Outside diameter

Length

Heat removal

[cm] 0.635

[cm] 15.2 30.5 47.5 15.2 30.5 45.7 15.2 30.5 45.7

rate [W] 300 175 150 500 375 350 700 575 550

0.95

1.27

Table 1.2: Typical heat removal capacity of various heat pipes [6].


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The capillary force makes it possible to use a heat pipe in any orientation with regard to the gravitational force. Although the heat removal capacities of a heat pipe will be best when the capillary force and the gravitational force are in the same direction, or when the evaporator is at the bottom and hence the condensor at the top. The worst case scenario is when the capillary force and the gravity are in the opposite direction, so the condensor is at the bottom and the evaporator is at the top. That’s why heat pipes are very sensitive for change in orientation and thus once again not useful in portable devices. Figure 1.11 shows the variation of the heat removal capacity with a tilt angle from the horizontal.

Figure 1.11: Variation of the heat removal capacity of a heat pipe with tilt angel from the horizontal when the liquid flows in the wick against gravity [6]. This sensitivity to orientation is tried to overcome with loop heat pipes: these are two-phase heat-transfer devices with capillary pumping of a liquid. They posses all the main advantages of conventional heat pipes, but are capable of transferring heat efficiency for distances up to several meters at any orientation in the gravity field, due to the separation of the liquid and the gaseous phase. Therefore is the travelling speed of the two phases not longer limited by the counterflow of each other. The schematic diagram of the loop heat pipe is pictured in figure 1.12. The main difference with a regular heat pipe is that the condensor is placed outside the heat pipe, which allows wide variations in design embodiments and improves reliability. The liquid still flows through capillary pressure from the condensor to the evaporator. These heat pipes are used for cooling applications in space, because they are small, consume almost no power, they can transport a lot of heat and are not influenced by gravitational forces.

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Figure 1.12: Principle scheme of a loop heat pipe [20]. 1.2.3.3

Thermoelectric cooler

A thermoelectric cooler is an active cooling technique based on the Peltier effect. Caused by a temperature difference at the junction of two conductors, made out of a different material, when a dc current is passing through these conductors. A typical thermoelectric cooling device consists of two ceramic layers, wherein between several pairs of P-type and N-type of semiconductors are mounted. These thermoelectric pairs are electrical in series and thermal in parallel. A thermoelectric device can contain a few hundred pairs (figure 1.13).

Figure 1.13: Principle scheme of a thermoelectric cooling device [21]. Since the charge carriers move in a different direction in each leg, each carries heat away from the cold end. A thermoelectric cooler is a solid-state cooler and thus has many advantages over conventional heat exchangers. They have the advantage of not having moving parts, nor any type of c Koninklijke Philips Electronics N.V. 2005

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fluid. Therefore, they produce no noise and can be made very compact. However, one main problem overrules all the benefits: it has a low efficiency and more power is needed than the device can cool. In thermoelectric heat exchangers or generators, electrons serve both as entropy and charge carriers in solids. In linear approximation, the effectiveness of heat and electric power conversion only depends on a single dimensionless material parameter ZT (= the Figure of Merit. This parameter is similar to the coefficient of performance (COP) of any other thermodynamic system): ZT =

Π2 ρκT

(1.2)

In equation (1.2) is Π [WA−1 ] the Peltier coefficient, which is equal to the entropy flow divided by the charge flow carried by the electric current. The electrical resistivity is expressed as ρ [Ohm] and κ [WK−1 m−1 ] is the thermal conductivity. It is important to reduce the thermal conductivity and electrical resistivity as much as possible in order to have a better thermoelectric material, as can be seen from equation (1.2). Since electrons serve both as heat and charge carriers in solids, it is a difficult task to find a good thermoelectric material. Metals for example have high thermal conductivity, but low electrical resistivity. While semiconductors are more effective: they have a small band gap, which allows conduction. A common used material for thermoelectric cooling is Bi2 T e3 . Superlattice Bi2 T e3 alloys increase the figure of merit from 0.8 to 2.4. These thermoelectric coolers are used in optoelectronic devices as temperature stabilization. They can cool down below ambient temperature and they are used for sub-zero cooling such as portable refrigerators. Unfortunately cost-effective thermoelectric coolers are reaching their limits in newer applications.

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Conclusion

Liquid cooling is required in current and future electronics. The trend towards more need for cooling isn’t only valid for computer processors, but also for other electronic devices such as LEDs (Light Emitting Diodes). Forced air cooling can not dissipate the required heat amount in the future and other reliable cooling techniques need to be developed, based on liquid cooling. The classification of the different possible existing liquid cooling techniques are given and the advantages and disadvantages of different liquid cooling techniques, such as thermosyphons and heat pipes, are examined. Further a brief explanation is given of another used, but ineffective cooling technique, called thermoelectric cooler. While research of all these already existing cooling techniques continues, new techniques have to be considered. A very promising cooling technique is forced liquid cooling with indirectcontact. Several studies have already been performed using this technique ([7], [8] and [9]) where a pressure driven flow is forced through a cooling device or micro channels. Nevertheless these techniques establish high cooling rates, though they have some disadvantages such as added power, added volume, danger for leakage and subject to mechanical wear. Therefore cooling of discrete droplet handling might be a possibility. An early start in this area was given by Paik [12], Pamula and Chakrabarty [13], Oprins [11] and Hectors and Huybrechts [10]. In this master thesis a study is made towards the use of an existing droplet manipulation technique, called electrowetting, as a heat dissipator or heat exchanger. This technique is still an active cooling technique, based on indirect-contact cooling, but an electrostatic droplet manipulation technique is used, instead of a pressure driven flow.


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Section 2

Experimental setup 2.1

Introduction

The system used in the experiments consists of an arsenic-doped silicon wafer. Micro channels of 100µm ×100µm cross-section are created in the wafer using anisotropic ion etching, following the procedure of Lärmer and Schilp [22]. This process is explained in more detail in the following section 2.2.1. At the end of the etching procedure a SiO2 insulating layer is thermally grown to a thickness of 1µm. Finally, in order to create a hydrophobic surface -resulting in contact angles θ larger than 90◦ for water- an additional monolayer (approximately 2nm) of OctadecylTrichloroSilane (OTS) is deposited on top of the oxide layer, following the protocol of Sagiv [23]. Figure 2.1 shows the different layers in the cross section of the channel structure.

Figure 2.1: Cross section of the micro channel test structure. In the experiments a liquid droplet is placed on top of the channel structures and an increasing potential difference is applied across the liquid-solid interface via a platinum electrode (see section 2.4.1) immersed in the droplet and a copper wire glued on the side of the wafer. An AC electrical signal at a frequency of 10kHz is used. The dielectric layer acts as an insulator defining a capacitive impedance in the electrical circuit. The current flowing through the circuit is a capacitive current, thus no charges can cross the dielectric SiO2 layer. The droplet is conductive, so no electrical field is present inside the droplet. An electrical field exists only across the dielectric layer and this field forces the droplet to spread at a smaller contact angle. This characteristic to transform a hydrophobic surface in an apparent hydrophilic surface is used 16



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to pull the liquid into the micro channels [24]. By subsequently filling and emptying of the channels a pulsating liquid flow can be achieved. In this master thesis the filling of the channels is investigated from a heat spreading point of view. Locally generated heat from an electronic device, e.g. a LED, can be spread over a larger area by the pulsating liquid flow in the channels. This principle is illustrated in figure 2.2:

Figure 2.2: A liquid filament of the droplet fills the channels in order to spread the heat generated by a hot spot (Q). This hot spot could be situated under the droplet or under the channels. The dashed line is the liquid droplet with no potential applied, while the solid line is the liquid droplet with an applied voltage. In this chapter the experimental setup is explained, starting from the manufacturing of the wafer, followed by the fabrication of the electric connections, continuing in the explanation of the liquid compositions and finally concluding with the description of the actuation and measuring devices.


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2.2 2.2.1


The test samples Production of the micro channels

The micro channels in the arsenic doped silicon are created by anisotropic dry ion etching. This specific dry-etching process has been developed by Bosch GmbH and licensed to several equipment manufacturers, like STS. Most characteristic for this process is the alternation of short etch and sidewall passivation steps. During these steps (of typically 5 − 10s duration) silicon is first etched by fluorine radicals and ions until sidewall passivation approaches the point of breakdown. Next, the composition of the gas mixture admitted to the etch chamber is changed, the role of the ions suppressed, and other parameter settings adjusted such that a passivation layer starts to grow. The passivation layer at the bottom of the etch profiles is quickly opened by the re-admission of energetic ions -the only particles capable of giving direction to the etchand etching recommences until sidewall passivation approaches the point of breakdown again. Repetition of this etch/passivation cycle is continued until the intended depth is reached. Typical etch rates are in the range of 2 − 8µm/s.

2.2.1.1

Deposition step

First, the deposition precursor gas is dissociated by the plasma to form ions and radicals. A possible chemical reaction for this process is: C4 F8 + e− → 3CFx· + CFx+ + F · + 2e−

(2.1)

which undergo polymerization reactions resulting in the deposition of a polymeric layer: nCFx· → (CF2 )n (s)

(2.2)

Here the suffix (s) is used to emphasize the deposition of the solid-state passivation film. This passivating Teflon-like layer (CF2 )n is deposited on the surfaces of the silicon and the mask during this first step, as shown schematically in figure 2.3:

Figure 2.3: Deposition step [27]. 18


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Etch step

The second step is the etch step. The gases are then switched to allow etching. During this subsequent etch step, the SF6 firstly dissociates, which illustrates the formation of ion and radical species by electron (e) impact dissociation: nSF6 + e− → pSx Fy+ + qSx Fy· + rF · + 2e−

(2.3)

Next, the fluorine radicals and ions must remove the surface passivation layer from the bottom whilst the sidewall passivation is left intact. (CF2 )n (s) + F ·

ionenergy

−→

Cx Fy (ads) → Cx Fy (g)

(2.4)

The ion bombardment plays a critical role. The ions are accelerated in the direction perpendicular to the bottom of the micro channels, with use of a bias potential. It removes the passivation layer only on the bottom and not on the sidewalls. Now the fluorine radicals can proceed further with the silicon etching by adsorption (ads), followed by product formation and desorption as a gas (g):

Si + F · → Si − nF Si − nF

ionenergy

−→

(2.5)

SiFx (ads)

(2.6)

SiFx (ads) → SiFx (g)

(2.7)

Figure 2.4: Etch step [27]. Figure 2.4 shows this schematically. These two dry physical-chemical etch steps (silicon etching and passivation layer etching conditioned by ion bombardment) can be broken down into as many as six primary steps as illustrated in figure 2.5. The first step is the production of the reactive species in the gas-phase (1). In a blow discharge the gas dissociates to some degree by impact with energetic particles. This step is vital because most of the gases used to etch thin films do not react spontaneously with the film. In a second step, the reactive species diffuse to the solid (2) where they become adsorbed (3), diffuse over the surface and react with the surface (4). Finally, the reaction products leave the surface by desorption (5) and diffusion (6). c Koninklijke Philips Electronics N.V. 2005

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Figure 2.5: Primary process occurring in a plasma etch process [27].

The cycle including passivation and etching is repeated until the expected depth is reached. The directionality of the etching is controlled by the ion bombardment through its role of aiding the removal of the surface polymer. The etching is controlled by process time, the flow of the injected gas, the pressure, bias power, coil power and temperature. The wafer temperature during processing is maintained by helium cooling flowing over the backside of the wafer. This process is carried out in a so-called ICP plasma (Inductive Couple Plasma) and is referred to DRIE (Deep Reactive Ion Etching), see figures 2.6 and 2.7.

Figure 2.6: The ASPECT-HRE reactor [27]. 20



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Figure 2.7: Schematic of the ICP process chamber [27]

2.2.2

Experiment samples

The micro channels etched in the silicon, using the anisotropic ion etching of the previous section 2.2.1, are not yet ready to perform experiments. The micro channels are etched in a silicon wafer, which allows automatization and multiple channel structures to be etched in one wafer. In order to perform experiments on a single channel structure, these micro channels have to be cut out of the whole wafer. Afterwards these channel structures must be connected to the copper electrode, while the liquid droplet must be connected to the opposite potential. 2.2.2.1

Dicing or Wafer cutting

Different ways are possible to cut these micro channels from the wafer: cutting with laser, sawing and manually breaking along the breaklines. In order to avoid as much dust as possible during cutting, laser treatment is probably the best way. However two disadvantages exist in laser cutting. A first disadvantage of laser cutting are the local high temperatures in the silicon wafer along the cutting line, which can change the characteristics of the silicon. The second disadvantage of laser cutting is the cost: to generate a laser cut a lot of power must be used and some expertise on behalf of laser cutting is also mandatory. Another possibility for wafer cutting is sawing: this has the advantage of creating straight lines, but will also create a lot of dust. A possible way to avoid that dust will enter the micro channels, is covering the structure with a mask layer, which can be removed after the cutting and hence will also remove all the dust. Unfortunately the channel structures are covered with c Koninklijke Philips Electronics N.V. 2005

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an OTS-layer and to find an appropriate material, which sticks sufficiently to the OTS, is very hard (See also further in chapter 6). In addition the same level of expertise, regarding to laser cutting, is acquired to cut the wafer by sawing. The last possibility is manually breaking the wafer along the breaklines inside the silicon. On the one hand the breaklines pattern in the silicon is such that they are perpendicular to each other. On the other hand the micro channels are etched in the silicon parallel to the breaklines. It is not the best way to perform the cut, but it is certainly the easiest and the fastest. The cutting technique is described here: manually an imaginary breakline is drawn on the wafer, by making two incisions in the silicon at the boundary of the wafer with a diamond pen. The imaginary line between these two incisions is the breakline. When a momentum force is applied around the imaginary breakline, the wafer has the advantage of breaking along a natural breakline. Cutting is easy, but will create a lot of dust and can damage the channel structures. These procedure is schematically pictured in figure 2.8:

Figure 2.8: Schematic principle of breaking the arsenic doped silicon wafer.

2.2.2.2

Manufacturing the micro channels sample

Once the wafer is cut into different samples, the structures can be prepared to perform experiments. Nevertheless the manual breaking technique, discussed in 2.2.2.1, has created a lot of dust on the small channels. An intensive cleaning procedure (of approximately one hour and a half) will remove most of the particles. This procedure is explained in appendix A. To connect the doped silicon to one of the two potentials, the channel structures are glued on a glass plate. Between the channels and the glass plate is, apart from the glue, also some copper wire, which is wound like a coil around the glass plate. To make sure the copper wires make connection with the arsenic doped silicon, a conductive paint or conductive epoxy is applied. To make sure that no electrical current can flow between the two potentials, a second glass plate is glued underneath the first glass plate to prevent electrical connection of the copper wires with the ground. Another benefit of the second glass plate is a more stable and smooth surface underneath the channels. This is illustrated in figure 2.9 and 2.10: 22



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Figure 2.9: Micro channels sample: the channels are glued on two glass layers. A wound copper wire makes connection with the arsenic doped silicon. A droplet can be positioned on top of the channels and actuated through the electrode.

Figure 2.10: An example of a micro channels sample, an additional layer of conductive paint is applied.


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2.3


The testing liquids

Three types of liquids are used in the experiments. The first liquid is pure water, the second and the third are two mixtures of water, glycerol and salt. Some experiments have been done with pure water, but with these experiments no filling of the channels could be achieved. This is in agreement with the electrowetting principle which requires free charges in the liquid (See Berge [24], [25], [26], Verheijen and Prins [28]). The water used in the experiments was water for High Performance Liquid Chromatography (HPLC), with a molecular weight of 18, 02g, and thus only consists of dipoles. In an electric field the dipoles will orientate along the field lines, but no free charge carriers are positioned on the liquid-solid contact line. The free charge carriers are brought in the other two testing liquids by dissolving N aCl in the water. Water can dissolve 35ppm to 270ppm salt, which accords respectively to the saltconcentration of the sea and of the Dead Sea. Unfortunately, water has the property to evaporate very quickly during the experiments, even at room temperature. To prevent evaporation, glycerol is added to the salt water. Glycerol has the beneficial effect of keeping the water molecules in the liquid phase, but the poor solubility of salt in glycerol is an obvious disadvantage. The preparation of the mixtures consists than of two steps: first adding salt to the water, and than adding glycerol to the mixture of salt and water. The salt must be solved in the water, before glycerol is added to the water-salt solution. To maintain a good solvability of the salt and the glycerol in the water, the mixture must be stirred or placed in an ultra-sonic bath during the period between adding small amounts of the salt or glycerol. Adding too much salt to the water in the first step will lead to the sedimentation of the salt in the glycerol-water mixture. Finally two mixtures have been achieved: the first mixture consists of 46, 7% glycerol, 51, 6% water and 1, 6% N aCl. The second mixture consists of 74, 7% glycerol, 18, 7% water and 6, 5% N aCl. Both mixtures are expressed in weight percentage. The second mixture is used for heating experiments. The more glycerol in the solution, the lower the evaporation rate. Furthermore the first mixture has a conductivity of 3, 6mS/cm, the second mixture has a conductivity of 2, 9mS/cm. The higher the conductivity the more charge carriers can travel freely through the solution, towards the liquid-solid contact-line, thus the electrowetting becomes easier.

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Experimental equipment Actuation of the droplet

In order to perform the experiments the droplet has to be actuated. Actuation of the droplet is done by changing the electric potential of the liquid droplet. Three difficulties have to be solved: First how to create an electrical field, second how to make the interconnection underneath the SiO2 -layer and third how to make the interconnection from above in the liquid droplet. The required devices to establish the electrical field are shown in figure 2.11:

Figure 2.11: Actuation devices: (a) Oscilloscope (Tektronics TDS 3032B); (b) frequency generator (Agilent 33220A) and (c) amplifier (TREK 601C). The frequency generator (b) generates an input signal. This input signal can be almost anything: a sinusoidal wave, a square wave, a modulated wave,... The intensity of this signal is displayed on the frequency generator and expressed as a peak to peak value. The generated signal however is too small to create electrowetting and thus an amplifier (c) must be used. The amplifier used in these experiments has a amplification factor of 100. The output signal of the amplifier is monitored with the oscilloscope (a) by connecting the oscilloscope with the voltagemonitor-output of the amplifier. The oscilloscope displays the voltage output of the amplifier, yet only 100 times smaller. The advantage of the oscilloscope is the possibility to read out the RMS-value of the AC-signal. The second step in solving the actuation problem is to connect the high voltage output of the amplifier to the conductive arsenic doped silicon wafer and to the electrode in the droplet. The connection to the arsenic doped silicon has already been partially described in section 2.2.2.2. The copper wires of the prepared micro channels only have to be connected to one of the two potentials. This connection is made by splitting up the high voltage coaxial output into two separated wires mounted with clamps. The clamps are pictured in figure 2.12. One of the clamps can easily be attached to one of the copper wires. The other clamp is attached to the other connection, namely the electrode, which consists of a tiny steel wire soldered to an even tinier platinum wire. Only the platinum wire enters the liquid droplet.


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The positioning of an electrode inside a droplet of a few micro liters has to be done very accurately. First when the electrode enters the droplet, the total energy of the droplet may not change due to a fast movement of the electrode. This could result in a change in contact angle. Second the electrode may never touch the surface of the channel structures, because if so the electrode could scratch the surface and thereby damage the hydrophobic monolayer or dielectric layer. A three dimensional positioning mechanism offers the solution: three controllers with micro precision can move the mounted electrode in the three coordinates. This mechanism is pictured in figure 2.12:

Figure 2.12: The three dimensional movability of the electrode (a) above the fabricated micro channels (c). In order to view the movement of the droplet a vertical camera (b) is positioned on top of the micro channels (c), together with a beam-splitter (d) and a light source (e). The droplet is actuated with the clamps (f) and (g).

2.4.2

Measuring the droplet behaviour

The electronic equipment, pictured in figure 2.11, makes it possible to change the voltage easily across the droplet on top of the channels. With the fabricated and cleaned micro channels, described in section 2.2.2.2, and the electrode positioned in the liquid droplet, it is almost possible to start the experiments. Only one step has to be taken: the characteristics of the droplet have to be measured. The characteristics of the droplet behaviour are the filling length of the liquid inside the channels and the shape of the droplet, which can be measured through the contact-angle (see chapter 3). As already shown in figure 2.12 a vertical camera is positioned to examine the filling length of the liquid droplet inside the channels. Measuring the droplet behaviour by its shape can be accomplished by a horizontal camera. Both (horizontal and vertical) cameras are CCD-cameras, thus a computer is needed, with image processing software. The total experimental setup is mounted on an optical table, which reduces vibrations: the vertical camera and positioning table can be fixed on this table. Figure 2.13 shows the total experimental setup. The table, where the channels are positioned, can rotate around a vertical axis and adjust its height. The electrode is movable in three directions, as is the vertical camera. The horizontal camera is not fixed, which allows less accuracy, but great flexibility. 26



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Figure 2.13: The total experimental setup, with (a) the actuation devices; (b) a light source; (c) the beam splitter; (d) the vertical camera (three degrees of freedom); (e) the positioning table; (f) the horizontal camera and (g) the computer. The reason why the horizontal camera is not fixed, is the presence of a high-precision contact-angle measurement system from Dataphysics OCA at the Philips Research laboratory. This measurement system is almost the same as the one situated at IMEC, used by Hectors and Huybrechts [10]. The measurement is pictured in figure 2.14. The Dataphysics OCA is used to measure the contact-angle of the droplets on top of the silicon wafer.

Figure 2.14: The Dataphysics OCA high precision contact-angle measurement setup, with (a) the computer, (b) the horizontal camera, (c) the positioning table and (d) the dosage unit.


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2.5


Reproducibility of results

Measuring the contact-angle of the droplets on top of the channels and on a flat area of the silicon wafers is an accurate characteristic for measuring droplet behaviour. However some precautions must be taken, in order to measure exact contact-angles. Furthermore is also discussed how experiments are repeated to obtain an average value for similar experiments.

2.5.1

Preconditions for valid experiments

The first precondition, to measure exact contact-angles, describes the surfaces: these surface have to be clean, following the procedure described in appendix A. Any grease or dust can influence local surface tensions and thus influence the contact-angle of the whole droplet. The second precondition describes also the surface: the surface has also to be free of trapped charges. Trapped charges can be left in the boundary layer between solid and liquid. To remove the trapped charges it is sufficient to wait a considerable time before repeating experiments on exactly the same spot on the surface. Another possibility is to clean the surface with ionized nitrogen or to clean it following the procedure of appendix A. A third precondition is that no leakage current is flowing through the actuation chain: the two potentials must only be separated by the dielectric layer. Precaution must be taken with the copper wires: they curl and may touch the 3D-positioning mechanism, the beam-splitter and finally may contact the electrode. If one of these preconditions is not fulfilled the measured contact-angles will deviate. To meet the needs of these preconditions it is sufficient to position a liquid droplet on a clean spot on the surface. To perform an experiment on exactly the same spot on the surface as the previous experiment even more precautions have to be taken. The first and the second preconditions are still valid: no dust, grease, liquid or trapped charge should be left behind on the surface. Additional preconditions apply to the previous experiment: during this previous experiment no electrical breakdown of the SiO2 may occur. If breakthrough occurs the next experiment on the same spot will be influenced through the electrolysis that will occur. A second additional precondition is valid when electrowetting experiments are performed on the micro channels. During previous experiments, the liquid channels might be filled with liquid. In order to make new and valid experiments, which involves filling in the previously filled-in channels, the precondition is set that these channels have to be empty. All these precautions have to be taken very carefully and it seems that almost no steady state working mechanism could be achieved. Nevertheless when a modulated signal is applied and thus a fill-in and fill-out pattern is established a stable movement of the droplet can be accomplished. However, the reliability of the system is not yet determined. Open channel structures are influenced by the presence of dust-particles in the air and therefore the filling of the channels with liquid will stop after a while, but still operation times exceed already eight hours.

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Reproducible applied voltages

To obtain a predictable value of a contact-angle at a given voltage, multiple experiments have to be performed. One single experiment is obtained by increasing the voltage over the droplet and measuring the contact-angles at discrete voltages. In order to compare the same contact-angles it is logical that the contact-angles, corresponding to the same applied voltage, are averaged. Unfortunately voltage differences exist almost in each different experiment: it is very difficult to obtain exactly the same voltages for each experiment. Slight voltage differences influence the measurements of the contact-angles. E.g. for contact angle measurement at 50Vrms measurements are performed at a voltage between 49.8Vrms and 50.2Vrms

2.6

Conclusion

In this chapter an adequate and reliable experimental setup is explained. First the aim of subsequently filling and emptying the channels is briefly explained, such that a pulsating liquid flow can be achieved. This filling of the channels is investigated from a heat spreading point of view. Second the fabrication method of the arsenic doped silicon micro channels is explained. This process is referred to as DRIE (Deep Reactive Ion Etching). Furthermore the manufacturing of the experiments samples by wafer cutting is also explained. Third are written down the different liquid compositions which are tested in the experiments. Fourth is the actuation of the droplet achieved and the measurement techniques of the droplet behaviour are shown. Fifth and finally the measures are presented for gathering reproducible results.


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Section 3

Actuation Principle 3.1

Introduction

This paragraph explains the modification of the wetting properties of a conductive liquid in the presence of an electric field. This behaviour is used to drive a droplet of the liquid inside micro channels. First, the wetting properties of a droplet in an electric field on a flat surface are studied theoretically, starting from the overall energy equation, using standard models [24], and experimentally to characterize our system. Then the model is extended to the case of a structured surface. Finally the model is confronted to experiments

3.2 3.2.1

Behaviour on a flat surface Introduction

In this section the voltage induced spreading of a droplet on a solid surface is described. This behaviour is called electrowetting. The standard model involves the surface tension and electrostatic contributions to the free energy of the droplet. The shape of a drop is given by the minimization of the free-energy of the system. In the absence of external fields (gravity or electric field) the free-energy is a combination of surface energies and leads to two conditions: Young’s equation giving the contact angel of the droplet on the surface and Laplace’s equation giving the curvature of the interface as a function of the pressure in the droplet. In electrowetting the electric field contribution does not modify Laplace’s equation but only Young’s equation as previously described [24], [28]. The effect of trapped charges in the insulating layer is neglected. Finally the behaviour of a droplet on a rough surface is explained, combining the theory of Cassie [29] and Wenzel [30]. This leads to the filling model for the channels presented by Baret [16].

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Energy analysis of electrowetting

Electrowetting is defined as the modification of the wetting behaviour of a liquid on a surface as a result of an electrically induced change in interfacial tension between a solid and a liquid. The change in surface energy results in a change in the contact-angle. The contact-angle is defined as the angle between the liquid-solid interface and the liquid-vapor interface (see figure 3.1). The basic equations relating the contact-angle to the electrical field are derived by Berge [24], [25], [26]. (see paragraph 3.2.4). In the studied systems a liquid is placed on a dielectric solid layer, surrounded by a vapor phase. Across the droplet-substrate interface a potential is applied which induces an electric field through the insulating layer. A change in electric field causes a change in free energy of the system. The main voltage drop is across the insulating layer and the voltage drop in the liquid droplet can be considered as constant. Berge [24] has shown that the use of a dielectric insulator prevents a flow of current responsible for Joule heating (see paragraph 3.2.4). The systems used in the experiments consist of an insulator between two solid electrodes as shown in figure 3.1. The top electrode is a solid platinum electrode immersed in the liquid droplet. The bottom electrode is the arsenic-doped silicon wafer. On top of this conductive silicon a SiO2 insulating layer is thermally grown. The platinum electrode at the top and the conductive silicon are connected to a voltage source supplying and AC voltage U. For sufficiently conducting droplets the potential inside the droplet is uniform. Paragraph 2.3 describes the composition of the used liquid; in this case the free charge carriers are the ions of dissolved N a+ and Cl− .

Figure 3.1: Schematic representation of the contact-line in the presence of an applied potential difference. An infinitesimal increase in base area dA at a given voltage results in a change of free energy of the droplet.


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A liquid droplet on a horizontal solid substrate spreads until it has reached a minimum in free energy. This is determined by the cohesion forces in the liquid and the adhesion of the liquid with the substrate. The phenomena of surface and interfacial tensions are explained in terms of γ, the surface tension [Nm−1 ] or surface free energy [Jm−2 ]. When electric charges are present in the system the free energy and therefore the droplet equilibrium configuration is influenced by electrostatic forces. The thermodynamical system is defined as the droplet, the solid substrate, the platinum electrode and the voltage source. The system is considered at equilibrium at a constant applied potential. A change in free energy of the system can be expressed as an infinitesimal increase in base area, it is the contact area of liquid with the solid. An increase in base area causes a new charge distribution inside of the droplet. At equilibrium the droplet shape changes to a situation such that the free energy of the system is minimum. The minimization of the free energy is performed at a fixed volume. The method of variation is used to solve the problem given in equation (3.1): E = γSL ASL + γLV ALV + γSV ASV − λV

(3.1)

γSL , γLV and γSV are introduced as the surface tension or surface free energy for respectively the solid-liquid, liquid-vapor and and solid-vapor interface. Those surface free energies are multiplied with their corresponding surfaces. λ is the Lagrange multiplicator and V the droplet volume. Minimizing the free energy leads to two conditions: the equation of Laplace which says that the pressure λ is constant and relates to the mean curvature, and to Young’s equation (3.3). To express an increase of the droplet base or increase of the solid-liquid interface, expressed with dA, equation (3.1) can be written in its differential form without the lagrange multiplicator: dE = γSL dA − γSV dA + γLV dA cos θ

(3.2)

θ is the angle of contact between the liquid and the solid substrate at the three-phase line, as measured through the liquid phase, or equal to the earlier defined contact-angle.

3.2.3

Young’s equation

Equation (3.2) describes the change of free energy of the droplet. At equilibrium, the shape and the surface of the droplet is such, that the energy is minimal or whenever dE/dA = 0. Equation (3.2) becomes than: γSV − γSL cos θY = (3.3) γLV This is the equation that Young discovered in 1805 [31]. Young’s equation (3.3) relates the surface energies to the static contact-angles. The forces working on the liquid at the three-phase line in vector notation are shown in figure 3.2. 32



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Figure 3.2: Vector notation representing the forces on the liquid at the three phase boundary.

3.2.4

Lippmann’s angle

In this section the equation for electrowetting is derived using the principle of virtual work, according to the work of Verheijen and Prins [28]. In this section only the behaviour of a droplet on a flat substrate is described, in the next section the behaviour of a droplet on a rough surface is examined. The droplet on top of the substrate is assumed to be kept at a constant voltage with the platinum electrode, the bottom of the system is assumed to be at zero potential. Assuming this a charge density in the liquid exists at the solid-liquid interface, notated as σL . In general, the electrostatic energy density per unit area is given by: Z →− → U 1− = E Ddx A 2

(3.4)

where U is the applied voltage, A is the liquid-solid interface area, x is the distance between → − → − → − the layers and D the displacement, with D = 0 r E . If an increase in voltage is applied, than there is also an increase in the free energy of the system because there is a change in the charge distribution in the liquid. An increase of free energy results in an infinitesimal increase in droplet base and equation (3.4) can be written as: dU dA

= = =


1 dED 2 1 U d σL 2 t 1 0 r 2 U 2 t

(3.5)

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where the dielectric constant of the insulating layer r is introduced. The insulator thickness is given by d. The work performed by the voltage source per unit area is given by: dW dA

= U σL 0 r 2 = U t

(3.6)

Using equations (3.2) and (3.5). Taking dU/dA = 0, it is found that: γLV cos θ = γSV − γSL +

1 0 r 2 U 2 t

(3.7)

Substituting Young’s equation (3.3) into equation (3.7) yields the change in contact-angle θ as a function of the applied voltage. cos θ = cos θY +

1 0 r 2 U 2 γLV t

(3.8)

The electrowetting force per unit of length of contact line (Few [Nm−1 ]) that acts on the three-phase line and which is responsible for contact-angle change, is defined as: Few = γLV ∆ cos θ =

1 0 r 2 U 2 t

(3.9)

The equation for change in contact-angle (3.8), better known as the Lippmann equation, is the one derived in literature to describe electrowetting [24], [25], [26] and [28]. It predicts a quadratic increase of the electrowetting force (see equation (3.9)) with the applied potential U. Few is measured by the contact-angle: an increase of the applied potential means a decrease of the contact-angle. In the next section 3.2.5 of this master thesis the equation (3.9) will be validated for different liquids. According this equation (3.9) the electrowetting force depends also on the characteristics of the insulating layer (thickness t and dielectric constant r ), thus in order to get the highest possible force, the thickness of the insulating layer must be manufactured as small as possible.

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3.2.5

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Lippmann curves on a flat substrate

Figure 3.3: Lippmann curve for water-glycerol solution (74.7% glycerol, 18.7% water and 6.5% N aCl), tested in atmospheric conditions on a flat substrate at 23◦ C. The measurement error on the contact angle was ±1.5◦ to 3.2◦ .

Figure 3.4: Viscosity dependence of Lippmann curves for water, water-glycerol solution 1 (46.7% glycerol, 51.6% water and 1.6% N aCl) and water-glycerol solution 2 (74.7% glycerol, 18.7% water and 6.5% N aCl). All liquids are tested in atmospheric conditions on a flat substrate at 23◦ C. The measurement error on the contact angle was ±1.5◦ to 3.2◦ . To assess the electrowetting effect for droplets positioned on flat areas of the sample, the contact angle between the substrate and the droplet is measured as a function of the applied voltage. Tests are conducted for pure water and two mixtures of water, salt and glycerol. From figure 3.3, it can be seen that the curves satisfy Lippmann’s equation (3.8) well up to 50V, resulting in a quadratic behaviour. Above 50V a saturation regime is detected. From figure 3.4 it is concluded c Koninklijke Philips Electronics N.V. 2005

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that electrowetting curves are different for the different mixtures, mainly due to surface tension and conductivity differences. Water has far higher contact-angles than the two mixtures, thus a higher potential difference is required to decrease the contact angle. The voltage is limited by the breakdown characteristics of the SiO2 layer. This layer has been measured with a spectrometer and gives layer thicknesses of 760nm until 911.6nm. Together with an approximate breakdown voltage of ≈ 100V/µm for the silicon oxide, this results in a maximal potential difference over the droplet of ≈ 75V. There are no significant differences between contact angles and sizes of the droplet: a droplet of 5µl has almost the same contact-angles as a droplet of 10µl as can be seen in figure 3.5. In the experiments pictured in figure 3.5 not enough data have been gathered to calculate error bars but the same error bars are expected as in figures 3.3 and 3.4. For our purpose, considering the modulation of the contact angle achieved with different liquids, the water-salt-glycerol mixtures are the best suitable. The mixture consisting out of 74.7% glycerol, 18.7% water and 6.5% N aCl is the best to perform heating experiments due to the prevention of evaporation of the water by the glycerol.

Figure 3.5: Droplet size dependence of Lippmann curves for water droplets of 5µl and 10µl. All liquids are tested in atmospheric conditions on a flat substrate at 23◦ C Sufficient experiments could be performed on the water-salt-glycerol mixture of figure 3.3, thus error bars could be calculated, according to the upper and lower limit of a 95% reliability interval for a t-distribution function [33]. In figure 3.4 no error bars could be calculated for water and the first water-salt-glycerol mixture due to insufficient measurements, but it is assumed that the error bars of these liquids are the same as the one derived for water-salt-glycerol solution in figure 3.3.

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3.3 3.3.1

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Behaviour on a structured surface Cassie’s and Wenzel’s equation

The previous formulas are deduced for a droplet on a flat substrate. In this section it can be understood that the previous formulas are not longer valid and a different, yet similar, approach is required. First the definition of a rough surface is given and second the effect of a rough surface on the droplet behaviour is stated. 3.3.1.1

A structured surface

A structured or a rough surface can be defined as a surface that is characterized by inhomogeneities in surface flatness. In this definition any surface can be defined as a rough surface, because of the local asperities every surface has at nanoscale. The roughness of a surface will be determined by the relative sizes of the droplet to the asperities. In case of the microchannel structures a 5µl droplet on micro channels of 100µm width and 100µm of depth is used. In the literature many authors ([29], [30], [43], [35] and [36]) already have studied the influence of a rough surface on droplet behaviour. In the next section the theoretical formulas which describe the droplet shape are given. 3.3.1.2

Two states of minimal energy

According to Cassie [29] and Wenzel [30] there is a difference in contact angle for a droplet that’s positioned on top of the structured substrates and thus on top of micro channels ([43] and [16]). A deposited droplet can exhibit in two typical states of minimal energy. The droplet either sits on the peaks of the rough surface or wets the grooves. The droplet shape also depends on a material property, via the contact angle θY , and the geometric properties of the surface. This is illustrated in figure 3.6:

Figure 3.6: Two states of local minimal energy: the grooves are wetted and the droplet sits on top of the peaks of the rough surface. The apparent contact angle of the droplet that wets the grooves, θrw , is given by Wenzel’s formula [30]: cos θrw = r cos θY

(3.10)

where r is the ratio of the actual area of liquid-solid contact to the projected area on the horizontal plane and θY is the equilibrium contact angle of the liquid droplet on the flat surface, according to Young’s equation (3.3). c Koninklijke Philips Electronics N.V. 2005

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The apparent contact angle of a droplet that sits on the roughness peaks, θrc , is given by Cassie’s formula [29]: cos θrc = rw φs cos θY + φs − 1

(3.11)

where φs is the area fraction on the horizontal projected plane of the liquid-solid contact and rw is the ratio of the actual area to the projected area of liquid-solid contact. If φs = 1, than rw = r, in which case Cassie’s formula (3.11) becomes Wenzel’s formula (3.10). Determined by the geometric parameters of the surface roughness, the droplet will behave like Cassie’s equation (3.11) or like Wenzel’s equation (3.10). In case of the micro channels of 100µm on 100µm, when a droplet is positioned on top of the channels, the minimal energy is first described by the Cassie formula. When afterwards a potential is applied the second state of minimal energy is reached: the droplet behaves like a Wenzel droplet. The criterion for the first transition between wetting the peaks of the rough surface and wetting the grooves of the surface is described by Patankar [43] and Oprins [32]:

cos θr > −

1 1 + 2(d/w)

(3.12)

with d the depth of the channels and w the width of the channels. Following a two-dimensional approach, this formula can readily be understood by describing the energy contents Ed of the droplet wetting the peaks and the one of the groove wetting state Eg . Writing the energy change in between these states, one obtains: Eg − Ed = (w + 2d)σLS − wσLV − (w + 2d)σV S

(3.13)

As grooves will be wetted for Eg < Ed , and as cos θ = (σSV − σSL )/σLV , equation (3.12) is obtained. Evaluation of this formula for the squared micro channels leads to a wetting angle of 109◦ (see figure 3.9 and 3.10). The equations of Cassie and Wenzel ((3.11) and (3.10)) are very general and deduced for a symmetrical rough surface. Nevertheless two differences exists and have to be taken in to account during experiments. In figure 3.8 both differences are illustrated. The first one is the difference of the rough surface used by Patankar [37] and of the rough surface used by Philips to obtain cooling. The first rough surface is isotropic and consists of pillars, while the channel structures from Philips are anisotropic. These surfaces are illustrated in figure 3.7. Still the formulas of Cassie and Wenzel can be applied for channels but the major difference between an isotropic substrate and an anisotropic substrate is the difference in contact-angle: when a droplet is positioned on an isotropic substrate, like pillars, the droplet is characterized by a uniform contact-angle independent of the view-direction. When a droplet is deposited on an anisotropic surface, like channels, the contact-angle of the droplet depends on the view-direction. The contact-angle viewed in front of the micro channels (in the direction of the channels) is clearly larger than the contact-angle viewed from aside of the channels. 38



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Figure 3.7: Difference between an isotropic surface (a) and an anisotropic surface (b) The second major difference is the number of channels that can be filled underneath the droplet. In figure 3.8 it is clear that the contact-angle in front of the channels change as a function of the underlying channels. To control this variable in the experiments droplet volume and the properties of the droplet have to be kept constant.

Figure 3.8: The equilibrium droplet shapes as a function of the number of grooves on which it settles. The two figures on the left are for four groves, while the two figures on the right are for three grooves (figures for the two cases are not drawn on the same scale). According to Patankar [43].

3.3.2

Contact angle of filling

In the last section 3.3.1 it was written how the transition between wetting the top of micro channels and wetting the grooves of the channel can be explained. In this section the further filling of the channels or second transition will be explained using a similar derivation. For this case the energy change while filling the channel of a length dx is examined. The total energy of the system is written as equation (3.1) and here repeated as equation (3.14): E = γSL ASL + γLV ALV + γSV ASV − λV c Koninklijke Philips Electronics N.V. 2005

(3.14) 39

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The energy change during filling can be derived from this total free energy of the system and is written as equation (3.15), according to Baret [16]: 1 dE = γLS (w.dx + 2d.dx) + γLV w.dx − γSV (w.dx + 2d.dx) + CU 2 2

(3.15)

with C = (2d.dx + w.dx) 0tr The assumption is made that the channels are perfectly square: it means that also the top of the channel has no curvature, caused by the Laplace pressure inside the drop. Equation (3.15) can be rewritten as follows: γSL 2d γSV 2d 2d 1 0 r 2 dE = ( + 1) + 1 − ( + 1) + ( + 1) U γLV .w.dx γLV w γLV w w 2 γLV t with

d w

(3.16)

= A, the aspect ratio, equation (3.16) becomes:

γSL γSV 1 0 r 2 dE = (1 + 2A) + 1 − (1 + 2A) + (1 + 2A) U γLV .w.dx γLV γLV 2 γLV t

(3.17)

Or: dE γSL γSV 1 0 r 2 = 1 + (1 + 2A)[ − + U ] γLV .w.dx γLV γLV 2 γLV t

(3.18)

Together with Young’s equation (3.2), equation (3.18) can be written as: 1 0 r 2 dE = −(1 + 2A)[cos θY + U ]+1 γLV .w.dx 2 γLV t

(3.19)

Using Lippmann’s angle (3.20) or (3.8): cos θL = cos θY +

1 0 r 2 U 2 γLV t

(3.20)

The further filling of the channels occurs than when dE < 0. Equation (3.19) becomes than, together with the Lippmann’s angle (3.20): −(1 + 2A)[cos θL ] + 1 < 0

(3.21)

Filling occurs whenever: cos θL >

1 1 + 2A

(3.22)

This critical contact angle is referred as filling angle or the threshold angle, i.e. the contact angle of the threshold voltage. In case of the used micro channels structure (w = 100µm and d = 100µm) the evaluation of formula (3.22) leads to an apparent contact angle for filling of 70◦ (See figure 3.9 and 3.10): 40



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A cos θL

d 100µm = =1 w 100µm 1 1 = > 1 + 2A 3 ⇒ θL > 70◦ =

(3.23)

From figure 3.10 it is seen that a filling angle of 70◦ corresponds to a threshold voltage of 50V. Note that the formula for filling (3.22) is the negative of the formula for filling in the grooves under the droplet placed on top of the micro channels (3.12).

3.3.3

Lippmann curves on a structured surface

Figure 3.9: Lippmann curve for water-salt-glycerol solution (74.7% glycerol, 18.7% water and 6.5% N aCl), tested in atmospheric conditions on a structured substrate at 23◦ C. The measurement error on the contact angle is ±4.6◦ to 9.3◦


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Figure 3.10: Viscosity dependence of Lippmann curves for water, water-salt-glycerol solution 1 (46.7% glycerol, 51.6% water and 1.6% N aCl) and water-salt-glycerol solution 2 (74.7% glycerol, 18.7% water and 6.5% N aCl). All liquids are tested in atmospheric conditions on a structured substrate at 23◦ C. The measurement error on the contact angle is ±1.6◦ to 17◦ for pure water and ±4.6◦ to 9.3◦ for solution 2 From figure 3.9 and 3.10 one could conclude that no wetting, nor filling of the channels could be established. Only the water-salt-glycerol mixture 1 should fill the channels. However, filling the channels can be achieved with all three liquids. As already stated in the previous section 3.2.5, no filling of the channels with water could be achieved unless the voltage over the droplet is increased above the minimal breakdown voltage of 75V. According to figure 3.9 and 3.10, this same rule would be valid for the second water-salt-glycerol solution (74.7% glycerol, 18.7% water and 6.5% N aCl). Nevertheless in all experiments filling of the channels has been achieved with this second mixture. The reason why the wetting angle and the filling angle couldn’t be reached is due to the size of the droplet. No precision needles could be used to measure exactly the size of the droplet: the water-salt-glycerol mixture 2 was too viscous to flow inside the needles, thus the droplets had to be positioned manually on top of the channels. Although no influence of droplet size has been seen in the experiments of a flat area 3.2.5, there is a big influence of droplet size on contact angle measurement on the micro channels. Contact angles of large drops decrease not below the filling angle while contact angles of very small drops can even become zero due to complete filling in of the channels. Only the experiments with water-salt-glycerol mixture 1 gave decent results, but unfortunately insufficient experiments have been done to calculate error bars. The error bars are calculated according to the upper and lower limit of a 95% reliability interval for a t-distribution function [33].

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3.4

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Dynamics: Filling of the channel

In the previous shown experiments a contact angle modulation of a droplet on a flat substrate and on a structured surface has been illustrated by applying an electrical field over the droplets of a conductive liquid. The aim of this section is to investigate how fast a channel can be filled and again emptied. It should be preferential if this filling behaviour can expressed in an analytical formula which can be used later in section 4 to calculate the achievable cooling rate of the real system. Lippmanns equation (3.20) accounts for the energy contribution of the electrical field as an additional surface energy related to the solid/liquid interfacial energy, which decreases when the applied voltage is increasing. According to Baret [16], now the filling and emptying characteristics of the droplet in the channels are explained using capillary theory. Electrowetting is included in this capillary theory in order to investigate the morphological transitions expected from a theoretical point of view. However the ideal behaviour stops above a saturation voltage for which the contact angle remains more or less constant, the physics of saturation is still subject of investigation. First experimental results will be shown and afterwards the filling and emptying theory will be discussed, according to Baret [16].

3.4.1 3.4.1.1

Dynamic experiments Introduction to experiments

Baret [16] has studied the filling and emptying of the grooves as a function of the applied voltage, the frequency of the voltage source and the dimensions of the channels. According to his results, the frequency of the voltage source has an influence on the length of the liquid finger wetting the channel in the equilibrium state. Except right at transition, the equilibrium length is given by the length scale λ∞ . The equilibrium length is a result of electrical loss along the channel and is defined in equation (3.24) [38]: λ2∞ =

1 2T wd ω ρ0 r w + 2d

(3.24)

Where λ2∞ depends on three main factors, the dependence on the frequency of the voltage source ω = 2πf , a dependence on the electrical properties of the system ρ2T and a geometrical 0 r wd dependence representing the influence of the dimensions of the channel w+2d . The constants in this formula are: T being the threshold voltage (= the voltage for filling in the channels), ρ the resistivity of the liquid, 0 the dielectrical permittivity of vacuum, r the relative dielectrical permittivity of SiO2 , w the width of the microchannel and d being the depth of the microchannel. Equation (3.24) shows the frequency dependency of the equilibrium length; the lower the frequency, the longer the filling length. In the limit, when a DC-current is applied over a droplet, then this droplet completely fills the channel. Here a few examples of filling characteristics are given. Both filling and emptying are considered and the effect of a different input signal is also examined. In the case of filling, the voltage is applied by a step from zero voltage to a value larger than the threshold voltage. In c Koninklijke Philips Electronics N.V. 2005

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the case of emptying, a first positive step is applied to induce the filling and the opposite voltage step is then applied to obtain the emptying. The curves in figures 3.13, 3.14 and 3.15 are obtained by taking pictures with a vertical mounted CCD-camera above the micro channels (see figure 3.11). The acquisition period of the camera is 100µs. The achieved pictures (in bmp-files) and corresponding time mapping file, are read in by a Matlab file, which is given in appendix B, and are the raw data for the figures. Since these experiments require a lot of disk-space, no error bars could be calculated, due to a lack of experiments. The shown figures are just set up as example, a more extensive study concerning the filling behaviour has been performed by Baret [16].

Figure 3.11: Filling length as result of the applied voltage for a water-salt-glycerol droplet of 5µl on squared microchannels (100µm ×100µm).

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Filling of the channels

Filling experiments were performed by applying a step function of a 10kHz AC-signal from zero voltage to a value larger than the threshold voltage VT (see figure 3.12(a)).

Figure 3.12: Step function of a 10kHz AC sinusoidal signal from zero to a voltage V > VT (a) and from V > VT to zero (b). In figure 3.13 three different steps were applied. The frequency however was maintained at a constant value of 10kHz during all experiments. The power-law behaviour of the filling characteristics are analogous to the Washburn law [39] and [40], which is expected from Warren [41], Darhuber [42] or Romero [44]. The results, displayed in figure 3.13, show a power-law behaviour of the form L ∝ tα with t the time and α

Figure 3.13: Response of filling length of the liquid filament in the channel on a step of three sinusoidal signals with different step heights. The filling length increase with increasing step height. The power-law behaviour is close to α = 1/2, which is expected from a capillary point of view [44] as a characteristic feature for confined capillary flow in the limit of viscous flow [39],[40] and [45]. c Koninklijke Philips Electronics N.V. 2005

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The choice of an alternative wave, such as a square wave, instead of a sinusoidal wave, have its influence on the filling dynamics. It is clear from figure 3.14 that a signal with a sinusoidal carrier wave reacts faster on an applied step than the blocked wave. Though power-law behaviour is still close to α = 1/2.

Figure 3.14: Response of the filling length of the liquid filament in the channel on the same step of a sinusoidal signal and a blocked-wave signal. Apparently the sinusoidal signal reacts faster on a step, than the blocked-wave signal. Although insufficient of these experiments have been done to draw a general conclusion, nevertheless they can be used to estimate the liquid speed inside the channels. This speed, seen in figure 3.13, variants from less than 1 mm/s for a step of 53.6 Vrms to 2 mm/s for a step of 69.8 Vrms . This filling speed is an important parameter for cooling applications: the higher the speed the higher the convective heat transfer. 3.4.1.3

Emptying of the channels

Similar to the filling of the channels, a reverse or backward step can be applied on the actuated droplet in order to examine the draining or emptying dynamics of the channel. To generate such a backward step, first a positive step is applied to induce the filling and then an opposite voltage step is applied to obtain the emptying (see figure 3.12(b)). As can be seen in figure 3.15 the respons of the channels on a backward step is nothing like the filling characteristics. No power-law behaviour can be seen. Two phenomena can be seen: First, the previous applied voltage doesn’t influence the time to empty the channel. The higher the voltage, the faster the draining occurs. This could be explained because the pressure inside the droplet can not be negative, while during filling this pressure can rise positive. Second an apparent increase of the filling length occurs in the first second after the opposite voltage step. This apparent increase is due to the faster decrease of the droplet front than the decrease of the liquid front inside the channel as is seen in figure 3.16. The matlab-file in appendix B calculates the filling length as the difference in distance between the front of the droplet and the front of the channel. Thus the liquid finger doesn’t fill further the channel, it doesn’t move, only the droplet retracts, leaving the liquid finger behind. 46



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Figure 3.15: Respons of the filling length of the liquid filament in the channel on a potential drop. Remark an apparent increase of the length after the first second and then a steady emptying time, regardless the previous applied voltage.

The figure 3.15 tells more about the emptying speed of the liquid. This emptying speed seems to variate between 0 and 1.5 mm/s for a backward step of 61.5 Vrms and variate between 0 and 0.8 mm/S for a backward step of 53.5 Vrms .

Figure 3.16: Filling length of the liquid filament in the channel as result of the applied voltage drop for a water-salt-glycerol droplet of 5µl on squared microchannels (100µm ×100µm). Filling length increases first and then it decreases. c Koninklijke Philips Electronics N.V. 2005

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3.4.2


Model of filling

This subsection focuses on the dynamical aspects of the groove filling using electrowetting, according to the work of Baret [16]. The static experiments showed that the contact angle is a significant characteristic to describe the transition. The model based on capillary theory is extended to the dynamics using the same tools as in the theoretical description of filling capillary tubes (See Washburn [39] and Quéré [40]). Writing the excess of energy required to increase the length of a liquid finger at zero Laplace pressure by an infinitely amount dL, one finds based on interfacial energies: P dE P = PLV − cos θY (3.25) dLγLV LS LS P P where LS is the surface area per unit of length, which is wetted by the liquid, P and P LV the surface per unit of length of the liquid/vapor interface. Defining cos θT = LV / LS as the contact angle for which wetting is favorable, equation (3.25) can be rewritten as: dE P

= cos θT − cos θY (3.26) P In the case of a closed and circular capillary tube LV is zero thus cos θT = 0. The transition occurs at θT = 90◦ . In the case of a channel with a rectangular crosssection and aspect ratio A, one finds back the expression cos θT = 1/(1 + 2A). dLγLV

LS

In order to determine the dynamics of the filling the excess of capillary energy is balanced by the viscous dissipation. Once again in the case of a closed circular capillary the computation leads to: dE = γLV 2πr cos θY (3.27) dL In the case of rectangular micro channels, the expression of the viscous dissipation has to be calculated and depends a priori on the dimensions of the channel. The calculation has to take into account the free-surface boundary and a non-slip boundary condition at the solid/liquid interface. In order to determine the viscous dissipation, it is assumed for simplification that the free-surface is flat, thus that no curvature is present at the liquid/vapor interface, which corresponds to a situation where the Laplace pressure in the channel is constant and equal to zero. For the flow in a channel, the pressure forces balance the viscosity forces leading to: 8πηLL0 = −

∂2u ∂2u + 2 =a (3.28) ∂x2 ∂z where u being the speed in the direction y of the channel while x and z are the physical coordinates perpendicular to the flow and a is the pressure gradient constant along the channel. Such an equation has already been solved for the mechanical torsion of a rectangular bar [46] or for flow in a closed channel [47], thus here the same Fourier decomposition is used. Here however different boundary conditions have to be applied: u(x = ±w/2, z) = 0, u(x, z = 0) = 0 and ∂u/∂z = 0, which are going to select different modes in the Fourier decomposition. Rescaling x and z by w and u by u0 = w2 a/(η), one find: u(x, z) =

48

4 π3

X n=1,3,...

(−1)(n−1)/2 cosh(nπ(z − A)) cos(nπx)( − 1) 3 n cosh(nπA)

(3.29)



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The velocity profile can then be integrated in order to find an estimation of the flow rate: 2

Z

1/2

Z

A

u(x, z)dxdz = w2 u0 F (A)

Q = w u0 x=−1/2

(3.30)

z=0

Solving the second equality of equation (3.30) for an aspect ratio A = 1 gives: F (A)|A=1 ∼ = 0, 05

(3.31)

Q out of equation (3.30) is on the other hand equal to w × d × dL/dt. After all, the length of the liquid finger follows the differential equation: 2LL0 =

2γdch 1 + 2A ) (cos θ − cos θT ) × F (A)( η A3

(3.32)

With F (A)( 1+2A ) = G(A) being a geometrical constant associated to the laminar flow in A3 the channel of aspect ratio A. In the case of an aspect ratio of A = 1 this geometrical constant G(A) equals: 1+2×1 ∼ ) = 0, 15 (3.33) 13 The interpretation of equation (3.32) can be easily seen as follows: This equation (3.32) is nothing more than: G(A)|A=1 = F (A)|A=1 (

dL dt

=

if C te < 0

⇒

C te > 0

⇒

L

C te dL < 0 → Retracting dt dL > 0 → F illing dt

(3.34)

Integrating equation (3.32) leads to a square root behaviour similar to the Washburn law. L2 (t) = (cos θY − cos θT ) ×

2γLV dch G(A).t η

(3.35)

Electrowetting is included in this capillary theory through replacing Young’s contact angle by Lippmann’s contact angle in equation (3.35), given by equation (3.36): 2γLV dch G(A) × (cos θL − cos θT ).t η 1 L ∼ tα with α = 2

L2 (t) =

(3.36) (3.37)

This simple equation (3.36) is valid as long as the driving force of the invasion is constant: in the case of capillary rise this means until gravity counteracts the rising motion and stabilizes the liquid front at Jurin’s height. However in electrowetting, the counteracting force derives from the finite conductivity and from the loss of energy along the channel: λ∞ has been introduced in the static case and is the length scale over which the voltage penetrates the liquid finger. As long as the actual filling length L λ∞ , than the voltage along the channel is constant and defines only one contact angle and the liquid filament has to increase following the square root c Koninklijke Philips Electronics N.V. 2005

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law (equation (3.36)). The saturation to the finite length L∞ is represented by the increase of the contact angle at the tip due to decrease of voltage. When it reaches the threshold contact angle the wetting is not favorable anymore and the driving force is going to zero, which means that the relaxation to the equilibrium will involve an exponential decay.

3.4.3

Model of emptying

Although an extensive study has been done for the filling characteristics, the emptying characteristics haven’t yet been subject to the same detailed theoretical investigation. Further study has to be undertaken in this area to predict this de-filling behaviour. The best approximation so far concerning the emptying characteristic would be to simple reverse the Washburn-law, thus approximate the emptying with the same power-law behaviour as the filling. As is given in the experiments, these power-law doesn’t resemble the emptying characteristic, but a polynomial equation would be more precise. If the emptying characteristic is approximated by the power-law behaviour, than the time to empty the channels is underestimated, resulting in a shorter time, than the real de-filling time.

3.5

Conclusion

The electrowetting on a rough substrate is investigated after being tested on a flat substrate. Both models are described by the total free energy of the droplet at equilibrium, given by equation (3.1). This formula leads to Young’s equation (3.3), for a droplet on a flat substrate, and also Cassie’s (3.11) and Wenzels formula (3.10), for a droplet on a rough substrate. Berge [24] has indicated the influence of an electric field to the model of the droplet behaviour and has written it out in the Lippmann’s equation (3.7). Baret [16] has given the condition for the transition between wetting and non-wetting the channels in equation (3.12) and the condition for further filling in the channels in equation (3.22). The experiments performed here show that not only the contact angle condition on flat surface has to be reached but also that the meta stability of the droplet shapes on the structured substrate may influence the filling condition. This effect would have to be subject of further investigations on a theoretically and experimentally point of view to really determine the limit of meta stability of the droplet shape. Finally, Baret [16] has obtained a dynamic model for the filling characteristic: filling length follows a square root behaviour as a function of time. However, further investigation have to be undertaken to obtain a similar emptying characteristic. Nevertheless equation (3.36) can be used in the next chapter 4 to calculate the achievable heat transfer with a real filling function. The experiments shown in figures 3.13, 3.14 and 3.15 validate this equation (3.36) for the 100µm ×100µm micro channels.

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Section 4

Achievable heat transfer 4.1

Introduction

The aim of this masters thesis is to investigate if the subsequently filling and emptying the channels can be used as an enhanced heat spreader for current cooling techniques. In order to estimate the enhancement by liquid convection achieved by this electrowetting technique a comparative theory with thermal conduction has been developed by Oprins and Nicole [32]. The general heat transfer equations are still valid, but in this theory the effect of the pulsating liquid flow inside the micro channels is elaborated. In this chapter, first the general equations valid for heat transfer will be explained and applied on liquid cooling capabilities and pressure drop of a reference cooling system without micro channels. In a second section the effect of actuation of liquid in micro channels on the total heat transfer is taken into account. This reference cooling system is a silicon block with dimensions lb × wb × db presented in figure 4.1. At the right surface the block is heated up to a maximum allowed temperature Th . At the left surface liquid, flowing through an adjacent micro channel, extracts the heat from the system.

Figure 4.1: Schematic of the reference cooling system [32]. Achievable heat transfer of this reference system is compared with the enhanced cooling rate of a system with the same dimensions but with additional micro channels in the silicon block perpendicular to the adjacent channel (see figure 4.2). Here the definition is made of the micro dw channel fraction ν = ndch with d,w,db and wb as indicated on figure 4.2 and nch the numbers b wb of micro channels. Liquid passing by in the adjacent channel is forced by electrowetting to penetrate in the micro channels until a certain filling length L. c Koninklijke Philips Electronics N.V. 2005

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Figure 4.2: Schematic of a cooling system additional micro channels perpendicular to the adjacent channel.

4.2 4.2.1

General heat transfer equations Conduction

Conduction is described as the transfer of energy from the more energetic to the less energetic → particles of a material due to the interactions between the particles. The heat flux vector − q −2 [Wm ] is the heat transfer rate per unit area perpendicular to the direction of heat transfer, and is proportional to the temperature gradient, as given in equation (4.1): → − − → q = −k ∇T

(4.1)

With k [Wm−1 K−1 ] the thermal conductivity of the material. The thermal conductivity variate with different material, e.g. the thermal conductivity for water at 20◦ C this mounts kw = 0.6W/(mK). The thermal conductivity for Silicon is higher (kSi = 100W/(mK)), but can not be competitive with the coefficient of copper (kcu = 400W/(mK)). Thus copper is widely used as a heat conductive material. Equation (4.1) is known as Fourier’s law. The minus sign is a consequence of the fact that heat is transferred in the direction of decreasing temperature. The power flux P [W] is defined as equation (4.2): dQ P = = dt

Z Z

− → → q .− n .dS

(4.2)

S

In equation (4.2) represents dQ [J] the elementary quantity of energy handed over by an → arbitrary surface S, characterized by the local vector − n perpendicular to the elementary surface dS. 52



4.2.2

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Convection

The convection heat transfer mode consists of two mechanisms. In addition to energy transfer due to diffusion, energy transfer is accomplished by the bulk or macroscopic motion of the fluid (or gas). The fluid motion is associated with the fact that, at any instant, large numbers of molecules are moving collectively. Such motion, in the presence of a temperature gradient, will give rise to heat transfer. The molecules retain also their random motion, which leads to diffusion in presence of a temperature gradient. The total heat transfer is the superposition of energy transport by the random motion of the molecules and by the bulk motion of the fluid. It is customary to use the term convection when referring to this cumulative transport and the term advection when referring to transport due to bulk motion only. For micro-channel cooling, heat transfer due to convection between a fluid in motion and a boundary surface has to be considered. A consequence of fluid flow is the development of a region in the fluid through which the velocity varies from zero to a finite value u∞ , associated with the bulk flow. This region is known as the hydrodynamic boundary layer. Moreover, if the surface and fluid differ in temperature, there will be also a region of the fluid through which temperature varies from TS , the temperature of the surface, to T∞ in the outer flow. This region, called the thermal boundary layer, may be smaller, larger or the same size as the hydrodynamic boundary layer. If TS > T∞ , convection heat transfer will occur between the surface and the outer flow. The diffusion dominates near the surface, where the fluid velocity is low. In fact, at the interface between the fluid and the surface, the fluid velocity is zero an heat is transferred only by this mechanism. The contribution due to bulk fluid motion originates form the fact that the thermal boundary layer grows as the flow progresses. The heat is transported into this layer, swept downstream and eventually is transferred to the fluid outside the boundary layer. Convection flow can be classified according to the nature of the flow. In general two types of convection exist: natural convection and forced convection. Natural convection is defined as coolant fluid flow, induced by natural forces, due to density differences caused by temperature variations in the fluid. In contrast is forced convection defined as a coolant fluid flow, whenever the flow is caused by an external force. The heat flux due to convection [Wm−2 ], regardless the particular nature of the convection, is given by the following equation (4.3): q = h.(TS − T∞ )

(4.3)

Where h [Wm−2 K−1 ] is the heat transfer coefficient. Values of this heat transfer coefficient are already tabulated in table 1.1 of the Introduction chapter 1. This coefficient encompasses all the parameters which influence the heat transfer by convection. In particular, this coefficient depends on conditions in the boundary layer, which are influenced by surface geometry. It depends also on the nature of the fluid motion and thus on fluid thermodynamic and transport properties.

4.2.3

Radiation

Unlike conduction and convection, which requires a medium, radiation is an electromagnetic phenomenon and travels through vacuum with the speed of light. All surfaces emit thermal radiation and absorb or reflect incident radiation. The net heat flux rate from a surface equals the total energy emitted minus the total energy absorbed from the surroundings. A "black" surface (emission at a maximal rate and, correspondingly, absorption of all incident radiation) emits c Koninklijke Philips Electronics N.V. 2005

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energy at a rate proportional to the fourth power of the absolute temperature of the surface. If a black surface has area A and temperature T , its radiant emission is given by equation (4.4): Eb = σAT 4

(4.4)

Where σ = 5.699 10−8 Wm−2 K−4 is the Stephan-Boltzmann constant. Real surfaces are non-black and emit radiation at a rate less than maximum. A convenient way to express this is that they emit at a fraction of the black body rate, given in equation (4.5) E = σAT 4

(4.5)

The dimensionless parameter is called the emissivity of the surface and varies between zero and unity. Experiments show that varies the temperature and also with surface parameters, like texture, color, degree of oxidation and the presence of coatings. The analysis of radiant interchange between two or more surfaces can be a complex algebraic formula. A common special case is, when body 1 has a temperature T1 and constant emissivity 1 , and is completely enclosed by a large surface area A2 A1 , with temperature T2 and constant emissivity 2 . The net radiant heat transfer from the small body to the large enclosure is expressed in equation (4.6) and is independent of the enclosure size and emissivity. q1→2 = 1 σ(T14 − T24 )

4.2.4

(4.6)

Thermal and fluidic laws for single phase forced convection

In order to characterize heat transfer between two objects or places in contact, thermal resistance is introduced in analogy with electric resistance. It links the temperature difference between the two objects or places with the heat flux P [W]. The thermal resistance [KW−1 ] can be expressed as equation (4.7), with TA > TB : Rth =

TA − TB P

(4.7)

Further down this section the different existing thermal resistances will shortly be explained. At least three different thermal resistances exist: one for conduction, one for convection and one for radiation. In addition the overall thermal resistance is defined. Finally the convective exchange laws from a thermal and hydraulic point of view are given, with the famous dimensionless numbers: The Reynolds number, the Prandtl number, the Nusselt number and the pressure loss. These laws will be applied on a reference cooling system, according to Oprins and Nicole [32] explained in the introduction and pictured in figure 4.1.

4.2.5

Thermal resistances

As mentioned above at least three different thermal resistances exist: one for conduction Rth,cond , one for convection Rth,conv and one for radiation Rth,rad . In addition is given the overall thermal resistances Rth . 54



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Conduction thermal resistance, Rth,cond :

Two cases have to be distinguished about diffusion resistance: The heat flux is unidirectional and the heat flux is not unidirectional. A unidirectional heat flux is established, whenever a uniform heat dissipation is present in the system and the cross section of the heat transfer path is equal to the heat dissipation area. In the simple case of a single layer diffuser, the conduction resistance is expressed as equation (4.8): Rth,cond =

d kAcross

(4.8)

With d the diffuser layer thickness, k the thermal conductivity of the diffuser and Across the diffuser area (= the cross section of the heat transfer path). This formula can be used in more complex systems, according to the laws of the electrical resistance. Whenever the heat flux is multidirectional, this easy equation (4.8) is no longer valid and more complex formulas have to be used. This case appears when the heat dissipation area is smaller than the diffuser area or when the heat dissipation is not uniform. Contrary to what is believed by many designers, heat spreading is not a trivial issue. Consider the simple configuration shown in Figure 4.3

Figure 4.3: Simple example of heat spreading. A square source with zero thickness of size As is centrally located on a square plate of size A, thickness d and thermal conductivity k dissipating Φ W. The top and sides of the plate are adiabatic (insulated), the bottom sees a uniform heat transfer coefficient h (W/m2 K). The remarkable thing is that even for this simple configuration no explicit solution is known for the description of heat spreading. Song and Lee [48] found a set of approximate explicit formulae that are easy to implement in a spreadsheet. They showed that the errors stay within 5% or less for the majority of cases of practical interest. However, observing the exact implicit solution of the governing differential equations reveals the source of the complexity of heat spreading: it is not possible to separate the convection and conduction parts. In other words, changing the heat transfer coefficient changes also the value of the spreading resistance.


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In summary, heat spreading is a complex phenomenon that can be addressed by analytical formulae only for geometrically simple cases and for which no explicit solution exists. For situations where double-sided heat transfer plays a role, or multiple sources, or multiple layers, the problem becomes intractable from an approximate analytical point of view and we have to rely on computer codes. Implicit solutions are known for multi-layer cases with multiple sources and uniform boundary conditions, even when time is a parameter. User friendly software exists that is based on these solutions, with the additional advantage that no mesh generation is required [49]. For the reference cooling system, pictured in figure 4.1, the heat flux is unidirectional and uniform, thus the conduction thermal resistance can be calculated following equation (4.8) and results in equation (4.9): Rth,cond =

lb kSi wb db

(4.9)

In this equation are the parameters lb ,wb and db as pictured in figure 4.1, and is kSi = 100 W/(m.K). 4.2.5.2

Convection thermal resistance, Rth,conv :

Convection thermal resistance represents the heat exchange between a solid and the flow of an adjacent fluid. This convection thermal resistance can be expressed as equation (4.10): Rth,conv =

1 h.Acontact

(4.10)

where h [Wm−2 K−1 ] is the heat transfer coefficient for convection and Acontact is the contact area between the fluid and the solid. As mentioned above in 4.2.2, the heat transfer coefficient for convection depends on numerous parameters and is tabulated in table 1.1. Again for the reference cooling system, pictured in figure 4.1, the convection thermal resistance can be calculated, following formula (4.10). This gives equation (4.11): Rth,conv =

1 h.(4dch )wb

(4.11)

where dch and wb are again the parameters as pictured in figure 4.1. h is the heat transfer coefficient for convection and will be calculated in more detail further in this section 4.2.6.3. 4.2.5.3

Radiation thermal resistance, Rth,rad :

The heat dissipation by radiation can be expressed in terms of a heat transfer coefficient hr , which is defined by: Q = hr A(T − T∞ )

(4.12)

4 ) σ(T 4 − T∞ (T − T∞ )

(4.13)

With hr = 56



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Thus similar to the convective thermal resistance, also a radiation thermal resistance can be defined as: Rth,rad =

1 (T − T∞ ) = 4 ) hr A σA(T 4 − T∞

(4.14)

In a first approximation of calculating the cooling capacity of the system, is the heat transfer by radiation from the system neglected. This neglecting is based on the fact that in the further calculations always liquid cooling is applied at one side of the system. The conduction thermal resistance and convection thermal resistance are always parallel in these calculations and the sum of these two resistances is much lower than the radiation thermal resistance. Therefore the radiation thermal resistance is neglectable. 4.2.5.4

Overall thermal resistance, Rth :

By applying equation (4.7) to fluid cooling, the overall thermal resistance can be calculated with: Tj − Tin (4.15) P where Tj is the junction temperature, Tin the fluid inlet temperature and P the dissipated power of e.g. an electronic device. Since temperatures inside the device are not known and can’t be measured appropriately, nor a constant fluid flow can be accomplished, this formula (4.15) has no much sense. Rth =

4.2.6

Convective exchange laws from a thermal and hydraulic point of view

In this part, the liquid flow will be characterized with use of three dimensionless numbers: The Reynolds number, the Prandtl number, the Nusselt number. Finally also a formula for the pressure drop is given. 4.2.6.1

Reynolds number:

The Reynolds number is a dimensionless number and is given by formula (4.16): Re =

ρvDh µ

(4.16)

where ρ [kgm−3 ] is the density of the fluid, v [ms−1 ] is the bulk speed, µ [Pa.s] the dynamic viscosity and Dh [m] the hydraulic diameter of the channel. The hydraulic diameter can be calculated with: Dh =

4s p

(4.17)

with s and p respectively the area and the perimeter of the channel. For the reference cooling system of figure 4.1, this hydraulic diameter of the rectangular channel is calculated as Dh = dch and thus the Reynolds number becomes than: Re =

ρvdch µ

(4.18)

The Reynolds number defines the transition between laminar and turbulent flows. The transition value is well known for channels and mini-channels (Dh > 1mm), the flow is laminar for c Koninklijke Philips Electronics N.V. 2005

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Re < 2300 and becomes turbulent for Reynolds numbers above this value. However, in the case of micro channels, the Reynolds number for the transition is not well known. Tuckermann and Peace [5] studied the forced convection of liquid in microchannels (Dh ∼ 0.3mm) experimentally and found that fully developed turbulent convection was initiated at Re = 1000 − 1500 and the conversion from laminar to turbulent occurred at approximately Re = 300 − 800. 4.2.6.2

Prandtl number:

Flow can be fully developed either thermally and hydraulically. A flow is fully developed thermally (or hydraulically), when the fluid temperature (or velocity) profile, in a channel, no longer depends on its position along the channel. The Prandtl number, P r, gives information about the thermal and hydraulic development of the flow. This dimensionless number only depends on fluid properties and not on the channel geometry. The formula for the Prandtl number is defined as (4.19): Pr =

µCp k

(4.19)

This number represents the relative importance between the thermal and viscous effects. For instance, consider a fluid element with a characteristic size of 1, than the viscous diffusion time τν and the thermal diffusion time τκ can be expressed as:

τν

=

τκ =

1 ν 1 κ

(4.20) (4.21)

where ν [m2 s−1 ] is the fluid kinematic viscosity and κ [m2 s−1 ] is the thermal diffusivity of the fluid. Now follows for the Prandtl number: Pr =

µCp ρCp ν ν τν = = = k ρCp κ κ τκ

(4.22)

So, for fluids with a high Prandtl number (P r 1), the time to reach thermal equilibrium is longer than the time to reach viscous flow equilibrium, consequently heat diffusion processes initially determine the fluid motion. On contrary, for low Prandtl numbers (P r 1), thermal effects decrease and hydrodynamic laws lead the fluid motion. The Prandtl number for water is around 7. This implies that the viscous diffusion time and thermal diffusion time have the same order of magnitude. 4.2.6.3

Nusselt number:

The Nusselt number describes the heat transfer between the solid and the fluid and is given by the Nusselt correlation: N u = CRem P rn K

(4.23)

where C, m, n and K are dimensionless constants, depending on the geometry of the channel, Re is the Reynolds number and P r is the Prandtl number. For a fully developed laminar flow in a rectangular channel, as pictured in figure 4.1, these constants are: C = 2.98, m = n = 0 58



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and K = 1, according to table 3.2 from Van Den Bulcke [4]. Filling in these numbers in equation (4.23) equals the Nusselt number to N u = 2.98. This Nusselt number gives an estimation of the convective heat transfer coefficient h, following the equality for the heat dissipation q (4.24): q = hA∆θlm =

N ukf l A∆θlm Dh

(4.24)

where h is the convective heat transfer coefficient, A is the contact area of the fluid and heat dissipating surface, kf l is the conduction heat transfer coefficient of the fluid (kf l = 0.6 W/(m.K) for water), Dh is the hydraulic diameter and finally ∆θlm is the logarithmic temperature difference. This difference is defined as: ∆θlm =

(Tw − Tf l )i − (Tw − Tf l )o (T −T )

ln (Tww−Tffll)oi

(4.25)

where Tw is the wall temperature, Tf l is the temperature of the fluid and the indexes i and o represent respectively that the values are taken at the inlet and the outlet. To calculate an estimation of the convective heat transfer coefficient, h, it isn’t necessary to calculate this logarithmic temperature difference. Following the equality of formula (4.24), this gives: h=

N ukf l Dh

(4.26)

Or for the reference cooling system in figure 4.1 this convective heat transfer coefficient can be estimated as formula (4.27): h= 4.2.6.4

2.98kf l dch

(4.27)

Pressure loss:

Pressure losses between channels input and output can be calculated with: ∆p =

4ρCf Lv 2 2Dh

(4.28)

where Cf is the friction coefficient, v is the speed in the channel and L is the channel length. This pressure drop can be calculated for the reference cooling system from figure 4.1. According to Oprins and Nicole [32] this pressure drop is governed by: ∆p =

28.455µf l wb Vf l d2ch

(4.29)

with µf l the viscosity of the fluid (µf l = 1.005 10−5 Ns/m2 for water at 20◦ C) and Vf l the mean velocity. From equation (4.29) it can readily be seen that lowering the microchannel dimensions will drastically increase the pressure drop. For a velocity of 1 m/s the pressure drop equals approximately 300 Pa for the 1 mm microchannel and 0.3 bar for the 100 µm c Koninklijke Philips Electronics N.V. 2005

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microchannel. Therefore in the next section 4.3 we will explore how to cope with the demand for a low pressure drop, by using relatively large (pool) channels while keeping the high cooling rates of smaller micro channels (fingers).

4.2.7

A first approximation for the achievable heat transfer

To calculate the heat transfer by electrowetting of micro channels, an easier first approximation can be calculated following the above given equations. The system is already explained in the introduction of this section as the reference cooling system from figure 4.1. The system is thus a Silicon-block with dimensions lb xwb xdb . At the right surface the block is heated up to a maximum allowed temperature Th and at the left surface liquid flowing through an adjacent microchannel extracts the heat from the system. In a first approximation, the heat that can be extracted by the liquid is given by: Q˙ =

∆T Rth,cond + Rth,conv

(4.30)

In this equation (4.30) Rth,cond and Rth,conv can be replaced by the previous calculated equations (4.9) and (4.11). Doing so, equation (4.30) gives: Q˙ =

∆T lb kSi wb db

+

1 h.(4dch )wb

(4.31)

for a fully developed laminar flow through square micro channels the convective heat transfer coefficient, h, can be replaced by formula (4.27). It is clear that for typical dimensions in electronics cooling (dch ∼ = 100µm to 1mm, lb = ∼ wb = 10mm and db ∼ = 1mm, e.g.), the maximum heat transfer that can be extracted by the liquid is limited both by the heat transfer coefficient in the channel and by the heat conduction through the Si-block. Indeed, for water at 20◦ C with kf l = 0.6 W/(m.K) and kSi = 100 W/(m.K), the conduction thermal resistance amounts to 10 K/W, whereas the convection thermal resistance equals 14 to 56 K/W depending on whether all sides or only one side of the channel will be available for heat transfer. This means for this numerical example that the configuration would be capable to extract 0.76 to 2.1 W for a temperature difference of 50◦ C. Further it should be noted that the heat transfer to one microchannel is not increased by decreasing the microchannel dimensions, though the heat transfer coefficient will. However, decreasing microchannel dimensions would allow increasing the number of channels in the sample. Keeping the same amount of water cooled area, we would be able to increase the cooling inversed proportional to d2ch .

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Heat transfer by electrowetting of micro channels

In this section the cope with the demand for a low pressure drop is explored, by using relatively large (pool) channels, while keeping the high cooling rates of smaller micro channels (fingers).

4.3.1

General expression

In order to analyze the cooling capabilities of the elctrowetted system, first on the heat convection part of the system is concentrated, taking the temperature of the Si-block at a constant temperature Th . As such for sake of simplicity the effect of the thermal conduction is neglected. This effect can be accounted for by using formulae for fin efficiencies. Further a certain known filling of the channels is assumed as a function of time, expressed by L(t), the length of the filling. This function is taken to be a periodic function with period τ and symmetric around τ /2. If a small fluid volume dV = Af dx is followed, with mass dm = ρdV , in a Lagrangian way on its path through the micro channels. The heating of the fluid volume is than governed by: dm.cf l

dTf l = hf (TSi − Tf l )Pf dx dt

(4.32)

with Pf defined as the perimeter of the microchannel. For a fluid volume that enters the micro channels at time t, and consequently will leave it again at time τ − t, the temperature evolution can be written as equation (4.33), according Oprins and Nicole [32]: h P

Th − Tf l − f f (τ −2t) = exp ρcf l Af Th − Tc

(4.33)

Thus, the total heat that will be extracted by the liquid filling one channel during a period τ can be retrieved as: Z

M

cf l (Tf l − Tc )dm

Q = 0

Z

τ /2

ρVf (t)Af cf l (Tf l − Tc )dt

= 0

Z

τ /2

h Pf f l Af

− ρcf

ρVf (t)Af cf l (Th − Tc )[1 − exp

=

(τ −2t)

]dt

(4.34)

0

with Vf (t) = dL(t) dt the velocity of the fluid in the channel. Calculation of the maximum amount of heat, that could be rejected, in case the water temperature would reach the hot temperature Th at the end of the filling, leads to the expression (4.35): Qw,max = ρLmax Af cf l (Th − Tc )

(4.35)

Filling in this equation (4.35) in the general equation (4.34) gives a more handy equation (4.36): Q = Qw,max [1 −

1

Z

Lmax


τ /2

h Pf f l Af

− ρcf

Vf (t) exp

(τ −2t)

dt]

(4.36)

0

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4.3.2


Heat transfer for a given filling function

Three different filling functions are discussed in order to approximate the real filling function L(t). These functions illustrated in figure 4.4 are a block shaped filling function, a sinusoidal filling function and a parabolic shaped filling function which is the best approximation of the real filling function. The block shaped and the sinusoidal function have a constant filling length which is not the case for a real filling characteristic as is seen in section 3.4.1 of chapter 3, the parabolic shaped function approximates this filling length dependency to the filling period. The equation (4.36) is used to calculate the heat transfer for a blocked shaped filling function and a for a sinusoidal filling function. However the calculation of the heat transfer for the parabolic shaped filling functions uses equation (4.34), due to the fact that the maximum length can not be easily deduced from the filling function L(t).

Figure 4.4: Explored filling dynamics: (a) a block shaped and a sinusoidal filling function with constant Lmax [32], (b) a parabolic shaped function with a filling length depending on the filling frequency. For each of these filling functions the heat rate has been calculated for the system pictured in figure 4.2 and compared with the heat rate of the reference cooling system from figure 4.1. For the sake of comparison with the channel configuration, a perfect conducting material is assumed in this reference cooling system. Furthermore, it is assumed that only one side of the channel is in contact with the silicon block. This reference system would than be able to extract 0.89W. 4.3.2.1 A blocked shaped filling function For a block shaped function L(t), with a value of Lmax for ατ ≤ t ≤ (1−α)τ and 0 ≤ α ≤ 1/2, the velocity of the fluid in the channels equals: Vf (t) = Lmax (δ(ατ ) − δ((1 − α)τ ))

(4.37)

Combining equations (4.36) and (4.37) results in: h Pf f l Af

− ρcf

Q = Qw,max [1 − δ(ατ ) exp

h Pf τ − ρcf A fl f

= Qw,max [1 − exp

(1−2α)

(τ −2t)

]

] (4.38)

Typical limit situations can be explored. At one hand, for a perfect convection heat transfer situation (h → ∞), the heat exchange will be limited by the amount of fluid wetting the channels, resulting in a maximal cooling of Qw,max . Ont the other hand, when the heat capacity of 62



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the fluid is high, e.g. because of a high specific heat (cf l → ∞), the heat transfer Q is limited by the convection heat transfer and equals hP τ Lmax (Th − Tc )(1 − 2α). The cooling rate achieved by electrowetting for the block shaped filling function (4.38) with α = 0.25 can than be evaluated by equation (4.39): h P τ

− f f (1−2α) nch Qw,max Q˙ = [1 − exp ρcf l Af ] τ Adding in addition the convection heat transfer of the side channel results in:

(4.39)

h P τ

− f f (1−2α) νdch lch Qw,max Q˙ = ] + h(1 − ν)dch lch ∆T [1 − exp ρcf l Af Ach τ

(4.40)

With ν the fraction of the cross section of the silicon replaced by microchannels. Furthermore the following parameters are used: dch = 1mm, lch = 10mm, Af = 0.01mm2 , Pf = 400µm, Lmax = 1750µm and α = 0.25. Finally a temperature difference of 50◦ C is used. With these parameters it is possible to calculate the achievable cooling rate in function of filling period τ and microchannel fraction ν. The effect of the microchannel fraction is linear between the reference case of convection of the pool channel only and the hypothetic value for ν = 1. In practice the value of ν is limited to 0.5. In figure 4.5 the heat transfer equation (4.40) is shown with variable τ and ν.

Figure 4.5: Comparing of the cooling rate of the silicon block and the structure with the channels for a blocked shape filling function.


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From this figure 4.5 it is clear that the different curves do intersect at a critical filling period. For shorter filling periods, the heat transfer will be improved by inserting microchannels, for higher filling periods the electrowetting deteriorates the cooling. Based on formula (4.40), assuming: h f Pf τ (1 − 2α) 1 ρcf l Af

(4.41)

As is the case for the present example, the critical filling period can be calculated: ρLmax cf l (4.42) h For the sample under consideration, this critical filling period amounts up to 4.1s. Further it can be seen from figure 4.5 that the enhancement of the heat transfer can be drastically improved by lowering the filling period, or increasing the frequency (given a constant filling length Lmax would be achievable). In the extreme case of τ → 0, a cooling rate τcrit =

dch lch hf Pf Lmax ∆T Q˙ = h(1 − ν)dch lch ∆T + ν Af

(4.43)

can be achieved. For very short filling periods the cooling rate will reach the limit for high capacity of the fluid flow, as described in paragraph 4.3.2.1. For ν = 0.5 the maximally achievable heat transfer will equal 156W. 4.3.2.2

A sinusoidal shaped filling function

The heat transfer can also be evaluated for a sinusoidal function L(t) = Lmax sin(πt/τ ). When this filling function is assumed, the fluid velocity in the microchannel is given by: πt π cos (4.44) τ τ Based again on expression (4.36) the heat rejection for one microchannel during a period τ can be worked out as follows: Vf (t) = Lmax

π πt cos exp−β(τ −2t) dt] τ τ π 2 − 2πβτ exp−βτ = Qw,max [1 − ] π 2 + 4β 2 τ 2

Q = Qw,max [1 −

(4.45)

h P

With β = ρcff l Aff . Again the limit for perfect convection heat transfer equals Qw,max , whereas the limit for a high fluid heat capacity amounts to hP τ Lmax (Th − Tc )(2/π). The achievable heat rate of the sinusoidal filling function can be calculated, analog to the previous calculations of the cooling rate for a blocked shape filling functions. The same assumptions are made: a perfect conducting material is assumed and only one side of the channel is in contact with the silicon block, which is still able to extract 0.89W. Again a system with nch micro channels of 100µm equipped with electrowetting activation. Then equation (4.40) becomes with use of equation (4.45): νdch lch Qw,max π 2 − 2πβτ exp−βτ [1 − ] + h(1 − ν)dch lch ∆T Q˙ = Ach τ π 2 + 4β 2 τ 2 64

(4.46)



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Using the same constants as the block shaped function, again the comparison of the cooling rate of the silicon block and the structure with the channels is made, resulting in figure 4.6

Figure 4.6: Comparing of the cooling rate of the silicon block and the structure with the channels for a sinusoidal filling function. From this figure it is again clear that the different curves intersect at a critical filling period, given by formula (4.42) and equals to 4.1s. The difference with a blocked shape filling function is the increase in maximal achievable heat rate. For ν = 0.5 the maximally achievable heat transfer will equal 198W. 4.3.2.3

A parabolic shaped filling function

The parabolic filling function is used, because this corresponds the best to reality. In the parabolic shaped filling function, the filling characteristic is approximated with the equation (3.36) derived by Baret [16] in section 3.4.1. This parabolic equation take in account that the filling dynamics are no longer a function of the maximum filling length Lmax , but the filling length is a function of the characteristics of the used liquid, of the channel geometric and of the applied voltage step. The equation (3.36), once more repeated here as equation (4.47), was derived from the capillary theory from Washburn [39]: L2 (t) =

2γLV dch G(A) × (cos θL − cos θT ).t η

(4.47)

This equation (3.36) can be reduced to the filling length as a function of time, with G(A)|A=1 ∼ = 0.15: s L(t) =

0.3γLV dch (cos θL − cos θT )t η

(4.48)

This equation (4.48) can be more easily written as the filling length in function of a constant, K, and the square root of time, t: c Koninklijke Philips Electronics N.V. 2005

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√ L(t) = K. t s 0.3γLV dch with K = (cos θL − cos θT ) η

(4.49) (4.50)

The complete filling function during a period τ is described as follows: √ 0 ≤ t ≤ τ /2 ⇒ L(t) = K. t √ τ /2 < t ≤ τ ⇒ L(t) = K. τ − t

(4.51)

Equation (4.49) can be filled in the general equation for the the total heat, that can be extracted during filling of one channel (4.34), which leads to equation (4.52) τ /2

Z Q= 0

1 1 − exp−β(τ −2t) √ ρAf cf l (Th − Tc )K[ ]dt 2 t

With K equal to equation (4.50) and β =

hf Pf ρcf l Af .

(4.52)

This integral has been solved with

Mathematicar , leading to: p √ r exp−βτ π2 Erf i( βτ ) τ √ − ] Q = ρAf cf l (Th − Tc )K[ 2 2 β

(4.53)

With y = Erf i(x) the error function, defined as: Z x 2 2 expt dt (4.54) Erf i(x) = √ π 0 Note that here the equation (4.34) is used instead of equation (4.36) due to the relation of the filling length with the filling period. The cooling rate achieved by electrowetting with in addition the convection heat transfer of the side channel results in: p √ r exp−βτ π2 Erf i( βτ ) νdch lch τ ˙ √ Q= (ρAf cf l ∆T K[ − ]) + h(1 − ν)dch lch ∆T (4.55) Ach τ 2 2 β With the earlier defined constants: s K = β =

0.3γLV dch (cos θL − cos θT ) η

h f Pf ρcf l Af

(4.56) (4.57)

Solving the cooling rate equation (4.55) should provide us the same figures as fig: 4.5 and fig: 4.6, nevertheless is the imaginary error function not provided in Matlabr thus no valid cooling rate could be calculated from the analytical approach. However, in section 3.4.1 the real filling characteristics of a liquid filament along the channels are measured, these data points are used in the numerical calculation of equation (4.52). Equation (4.52) can be rewritten as: Z Q= 0

66

τ /2

K ρAf cf l (Th − Tc )(1 − exp−β(τ −2t) )[ √ ]dt 2 t

(4.58)



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√ is nothing else than the velocity of the liquid filament since In equation (4.58) the term 2K t √ L(t) = K t. This velocity can be derived from the filling length data with:

v(ti ) =

L(ti+1 ) − L(ti ) ti+1 − ti

(4.59)

With L(ti ) the filling length at time ti . The same parameters as for solving the cooling rate of a block shaped filling function and a sinusoidal filling function are used. The dependence of the heat transfer with τ and ν is shown in figure 4.7.

Figure 4.7: Comparing of the cooling rate of the silicon block and the structure with the channels for a parabolic filling function. Both curves in figure 4.7 show a critical filling frequency which is equal to τcrit = 0.2Hz. Above this critical filling frequency an enhancement in cooling rate is achieved with a maximal cooling rate of 1.56W at a filling frequency of 1.47Hz.


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4.4


Conclusion

In this chapter an estimation of the cooling rate is given, that can be achieved by electrowetting. In a first chapter the theoretical laws concerning heat transfer are briefly discussed and their relevance to a reference cooling system is indicated. This reference cooling system consist of a silicon block which is convectively cooled by a channel. This reference system would be capable to extract 0.76 to 2.1W for a temperature difference of 50◦ C, depending on whether all sides or only one side of the channel will be available for heat transfer. In a second chapter the cooling capabilities of the electrowetted system are analyzed. This electrowetted system has the same dimensions as the reference cooling system, but in addition liquid is forced by electrowetting to subsequently fill in and empty micro channels of 100µm ×100µm. Three different filling patterns are examined: a first filling pattern is a block shaped filling function, a second filling pattern is a sinusoidal function and a final third pattern approximates the real filling pattern by a parabolic function. The achieved cooling rate of these three filling functions is compared with the cooling rate of the silicon block, which amounts 0.89W. Cooling rate curves for the block shaped and the sinusoidal function intersect the cooling rate of the silicon block at the same critical filling period. For shorter filling periods than this critical filling period, the heat transfer will be improved by inserting micro channels, while for longer filling periods the electrowetting deteriorates the cooling. This critical frequency is for the 100µm square micro channels about 0.25Hz Maximal achievable cooling rates for block shaped and sinusoidal filling functions are respectively 156W and 198W, for very small filling periods. However the last filling characteristic takes into account a real filling characteristic. Numerical calculation of the cooling rate is zero for a filling period of zero, but gives a maximal cooling rate of 1.56W for filling a filling frequency of 1.47Hz. The maximal cooling rate induced by electrowetting seems nothing compared to the cooling rate of the reference system but flow velocity of the reference system amount 1m/s while flow velocity of the micro channels amount 1mm/s.

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Section 5

Heat experiments 5.1

Introduction

To validate the estimations of the enhancement in liquid cooling achieved by electrowetting, thermal experiments have to be performed. The estimations of the achievable cooling rate out of the previous chapter 4 were a complex task, but validating these estimations with experiments is not different. These thermal experiments on micro scale involve different aspects, which have to be solved for good experiments. This chapter describes the different aspects related to increase in temperature. In a first section of this chapter the test samples prepared for ordinary electrowetting experiments out of chapter 2 are transformed into test samples for heat experiments. This might be a trivial task, by mounting a heater to the surface, but nevertheless different aspects have to be taken into account. In a second section the temperature effect is examined. A first temperature influence is the effect on the viscosity, this influence is experimentally given. A second point of interest goes to the effect of temperature on the critical voltage, thus does the temperature benefit or deteriorate the filling characteristics of the droplet in the channels? This effect is measured for steady state conditions of a drop on a given temperature. In a third and last section the main problems, possible solutions and points of attention in making temperature measurements are given.

5.2

Fabrication of test samples

Making a test sample for an ordinary electrowetting experiment is already extensively discussed in subsection 2.2.2.2 of chapter 2. In order to perform the same electrowetting experiments at different temperatures the same experimental setup has to be used. However in addition an increase in temperature has to be established. This heating problem can be solved by just mounting a heater underneath the sample, next to the spot where the copper wires make contact with the conductive silicon (see figure 5.1).


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Figure 5.1: The test samples are embedded in an insulating material of polyurethane (Nestaanr PUR35C5). This polyurethane is very porous and looses easily tiny dust particles, therefore the polyurethaan is encapsulated in kitchen foil. The micro channels are glued on two glass layers in order to make connection with the copper windings. A heater is attached with thermal tape on the back surface of the channel structure. The heater is a KaptonT M from Mincor with a diameter of 12.7mm (HK 5537 R26.1 A). In between the heater and the channelstructure a thermocouple is positioned to measure precisely the temperature and a layer of Molycoter is applied to prevent encapsulated air. Mounting a KaptonT M heater from Mincor (see figure 5.2) involves no trapped air in between the heater and the silicon, otherwise a local increase in temperature could damage the heater. To overcome this problem a thermal paste (Molycoter ) has to be applied in between the heater and the silicon. Furthermore a thermal tape is needed to attach the heater: normal tape would loose while temperature rises. To measure the temperature at the heater more precisely, an additional thermocouple is immersed in between the heater and the silicon channel structure.

Figure 5.2: The KaptonT M heater HK 5537 R26.1 A from Mincor . The heater, the thermocouple, the copper wires have to be precisely positioned on the back surface of the silicon micro structures, while the available surface area does not exceed more than a few 100mm2 . The surface of the smallest available heater is almost as big as this surface and leaves only a few squared millimeters available for contact with the copper wires. The best way to solve this is to make the connection as tiny as possible, so just a few copper wires are sufficient to make connection. All the different parts are connected with glue or double faced tape.

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The whole test sample is then embedded in an insulating material of polyurethane. As reason is given here that the heat flux generated by the heater must brought to zero towards the bottom and the side walls. The only heat flux has to go upwards from the heater to the channel structure and no heat flux is allowed downwards nor sidewards. This is the best way to generate a uniform temperature inside the channel structure. On the top the channels are not covered by any insulating material, thus here a convective and radiative heat rate exist to the environment. However the polyurethaan has a great inconvenience: it is very brittle and looses tiny particles of its material during touching and handling. These tiny particles can dirty up the microchannels, so dust particles from this insulating material have to be evaded by wrapping up the whole polyurethaan shape in kitchen foil, before contact is made with the environment. The final thermal test setup is shown in figure 5.3 and is ready to perform experiments. Unfortunately, the time to build up this test setup is large, compared to the testing time. Time to build up is split up in cleaning time following the procedure of appendix A and assembling time. Cleaning time is approximately equal to 1h30min, while assembling times can reach easily another 30min. This rather long time to build up is the reason why not so many experiments could have been achieved.

Figure 5.3: The final thermal test setup: viewed from the top, the microchannels are embedded in the wrapped polyurethane. On the left a big red wire and a thermocouple are strangled together. These indicate the heater and the thermocouple underneath the channel structure. A tiny copper wire is also visible, indicating the droplet actuation. In addition thermocouples can be attached on top or underneath the channel structures to measure surface temperature. Actuation of the droplet can be achieved with the experimental setup explained in chapter 3, however the heat experiments requires three additional devices: a DC-power supply from δ electronics, a data-acquisition for measuring the thermocouples temperature from Fluke and a voltage meter to measure precisely the voltage across the heater. The different devices are pictured in figure 5.4.


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Figure 5.4: The additional experimental setup for heat experiments, consisting out of a DCpower supply, a data-acquisition for measuring the thermocouples temperature and a voltage meter.

5.3

Temperature effect

In this section the effect of the temperature on the droplet actuation system is investigated. This temperature effect involves in different ways the droplet behaviour in the pumping device and is necessary to know when further experimental investigation of cooling capacities wants to be done. These changing parameters are both of the liquid: First the viscosity of the liquid changes as a result of a temperature increase and second the surface tensions change as function of temperature. The change in viscosity has a result in the dynamic filling behaviour, as can be seen out of equation (3.36) in chapter 3. While the change in surface tensions will has its effect on the critical voltage or threshold voltage for filling in the micro channels

5.3.1

Viscosity

Viscosity is measured as a function of temperature with the Rheometric Scientific SR − 5000. Tests are done with a frictionless turnable cone mounted vertically. The cone, with a diameter of 40mm and an angle of 0.0408rad, is immersed in the liquid until a gap height of 0.056mm exist between the cone and the flat bottom plate. A schematic test setup is pictured in figure 5.5.

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Figure 5.5: A cone, immersed in the liquid until a gap height of 0.056mm, can turn without friction around its own axis. The cone angle amounts 0.0408rad and its diameter 40mm. An increasing torque and an increasing speed can be forced on the axis of the cone, while underneath the flat surface a heating element can increase the temperature. Two main tests are performed: one test with increasing the torque around the cone and a second test with increasing the axial speed of the cone. These tests are subsequently repeated at different temperatures for the water-salt-glycerol solution consisting of 74, 7% glycerol, 18, 7% water and 6, 5% N aCl. The results are given in figure 5.6.

Figure 5.6: The viscosity is measured following two test methods: an increasing torque test and an increasing rotation speed test. In the temperature range from 20◦ C to 60◦ C, viscosity lowers from 0.08 to 0.02 Ns/m2 . Viscosity of pure water amounts 1.005 10−5 Ns/m2 . c Koninklijke Philips Electronics N.V. 2005

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The result of this lower viscosity while increasing temperature can be seen out of equation (3.36) in chapter 3: the filling length will increase while viscosity lowers. Thus higher liquid temperatures will give lower viscosities and thus longer filling lengths.

5.3.2

Temperature effect on surface tensions

A second influence by temperature on droplet actuation characteristics is given by the change in surface tension due to temperature difference. In this subsection experiments on the test-samples are given, wherein the influence of contact-angle measurement on temperature difference is shown. First the influence on the Lippmann curves for a droplet on a flat substrate is shown and second the influence of a droplet behaviour on a structured microchannels surface is given. These experiments are performed by heating up the samples to a higher temperature and maintaining this temperature constant. 5.3.2.1

Contact angle measurement on a flat surface

The behaviour of a 5µl droplet of the water-salt-glycerol solution is positioned on a flat area, then electrowetting experiments were performed at different temperatures. The results are plotted in figure 5.7.

Figure 5.7: Lippmann curves for a water-salt-glycerol solution at 23◦ C, 28◦ C and 52◦ C on a flat substrate. Although the number of obtained experiments was not sufficient to calculate decent error bars, it is concluded that increasing the temperature has a significant effect on the contact angle: the contact angle decrease while temperature increasing, thus so the threshold voltage or critical voltage for filling in the microchannels will decrease. The reason for a change in contact angle could be given by formula (3.1). The total energy inside the droplet increases by increasing the temperature, thus the surface tensions will change. However it is not yet been clear how each of these surface tensions change as a function of temperature, further investigation is necessary here. 74



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Contact angle measurement on the microchannels

Similar to the electrowetting experiments on a flat surface, in this paragraph the experiments are made on a structured surface. These results for the water-salt-glycerol are shown in figure 5.8.

Figure 5.8: Contact angle measurements for a water-salt-glycerol solution at 23◦ C, 28◦ C and 52◦ C on the microchannels. Extracting results out of these experiments is not as easy as the results of the electrowetting experiments on the flat substrate. However similar behaviour is expected and can be seen in the temperature curve of 52◦ C: this curve is positioned outside the 95% reliability bars of the t-distribution from the experiments at room temperature and thus it can be concluded that temperature increase lowers the contact angle.


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5.4


Heat transfer measurements problems

In order to measure the heat transfer at micro scale different problems existed: The question is made, which the best suitable way is to measure temperature. First the use of an infrared camera is discussed and next the use of thermocouples is explained. Finally the major problem in heat transfer measurement is discussed: measuring the cooling rate.

5.4.1

Infrared camera

With an infrared camera the temperature gradients on a surface can be examined. First the working principle of an infrared camera is explained, according to Nevelsteen and Baelmans [50], and afterwards the problems arising with the use of an infrared camera are given. A IR camera works based on thermal radiation (see section 4.2.3 of chapter 4) which is defined as energy transport by electromagnetic radiation. This thermal radiation is generated by a system due to its temperature. The thermal radiation from a system on a given temperature depends on the spectral and angular distribution of the radiation. The mathematical formulas, which are the origin of equation (4.5), are based on Plancks law. This law gives the spectral distribution of the hemispherical emission of a black body given in formula (5.1) Eλ,T (λ, T ) =

C1 C 5 λ .(exp 2 /(λT ) −1)

(5.1)

With C1 and C2 known constants, λ the wavelength of the radiation and T the temperature of the body. Integration of Plancks law over the different wavelengths gives the law of StephanBoltzman, with Eb the total hemispherical emission of the black body. Eb (T ) = σT 4

(5.2)

A real body emits however less radiation than a black body at the same temperature. The ratio between the radiation of the real body to the radiation of the black body is defined as the spectral emissivity λ (λ, T ). This spectral emissivity is function of the wavelength of the radiation. An infrared camera takes images in a small wavelength band and thus can be assumed that this spectral emissivity is constant in this band, λ (λ, T ) = (T ). Furthermore, if a camera is mounted in a not too large angle from the surface at a temperature T , than this spectral emissivity is also independent of the viewing angle. Radiation which inclines on a surface will be partially reflected, absorbed or transmitted through the surface. The reflection coefficient ρ, absorption coefficient α and transmission coefficient τ give the ratio of the respectively amount of absorbed, reflected and transmitted radiation to the amount inclined radiation on the surface. When a temperature measurement is done with an infrared camera, not only the radiation of the examined surface is detected by the camera, but also reflection of other heat sources, atmospheric transmission τatm and absorption atm and reflection of radiation of the environment Tenv are detected. The basic equation for infrared thermography is given by formula (5.3): E = τatm (Eb (T ) + (1 − )Eb (Tenv ) + atm Eb (Tatm )) 76

(5.3)



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Given this information about the working principle of an infrared camera, this leads to the judgement that this temperature measurement device is most suitable for measuring the temperature of the micro channels. IR cameras with microscope lens can measure down to 2λ = 5 − 20µm spatial resolution. In comparison with the dimensions of the micro channels (i.e. 100µm), this accuracy is fair enough, but the available Agema 470 camera without microscope lens has a spatial resolution of about 1mm. Further advantage of an IR camera is that no contact with the dust sensitive micro channels has to be made. Too much radiation from the environment might disturb the measurements, due to the high reflection coefficient (ρ = 0.42) of the silicon channel structure, but this reflection coefficient can be lowered by depositing some bismuth on top of the silicon. Bismuth turns to black when reaching a layer thickness of 10µm. Given the microchannel dimensions of 100µm ×100µm this dimensions increase would give a negligible error. However covering the microchannels up with bismuth gives no guarantee that the electrowetting experiments still can be performed. Furthermore, covering with a 10µm layer of bismuth is not suitable for smaller structures such as nanochannels. Using lock in thermography may be a better option to overcome the reflectivity, as explained by Breitenstein and Langenkamp [51]. Surface temperatures of silicon can be measured by a long wave camera, whereas mid wave cameras integrate over the depth of the silicon in a hardly invertable way. Temperature measurement with the right infrared camera might be the best option, but unfortunately such a camera was not yet available and thermocouples, which are cheaper and yield a better temperature accuracy, were the best alternative.

5.4.2

Thermocouples

First the working principle of thermocouples is explained, according to Nevelsteen and Baelmans [50] and afterwards the problems are given with the use of thermocouples to measure temperatures of the microchannels. Thermocouples are widely used in temperature measurements because they are cheap, small and easy to mount. In addition they are reliable and reach high accuracy, if properly used. The different types of thermocouples amount a temperature range from −270◦ C to 2200◦ C. Thermocouples are based on the Seebeck effect. When joining two different materials a temperature gradient over the wires results in a net voltage difference (often called EMF: Electro Motive Force) that can be measured between the open ends. The measured EMF is a function of the temperature difference. The main problem with a thermocouple is that it always gives a signal, unless it is broken. One of the main error sources of temperature measurements with thermocouples are the errors at the reference junction. Further typical error sources of false EMFs are EMFs through inhomogenties in the wires, voltage induced EMF’s and galvanic EMF. Error current flows through the measurement devices, electromagnetic forces and AC-noice are the important sources of errors on measurements. If a thermocouple is used for measuring temperatures of the microchannels, than one has to take into account all these possible error sources. Errors at the reference junction are tried to minimize by dry calibration of the thermocouples with the Isotherm Isocal 6 Venus 2150B. All thermocouples gave a maximum error of approximately 0.5◦ C at 60◦ C. Furthermore measurement errors can occur when the electrowetting actuation is used during experiments. It is recalled c Koninklijke Philips Electronics N.V. 2005

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that a copper wire was winded as a coil to maintain contact with the silicon, as is explained in chapter 2. This coil could generate due to the existing leakage current an electromagnetic field and therefore disturb temperature measurements. More possible error sources are the presence of the heater and the presence of the AC-noise generated by the electrode. It has been seen in the experiments that all these error sources cumulated to a temperature increase of the thermocouples of 2◦ C, when the maximal electrowetting voltage of 70 Vrms was used. A few problems with thermocouples are taken from another point of view: the temperature inside the channels is not measurable, because the thermocouples are simply too big to enter the channels. Size of the thermocouples give also another problem: this relative size of the junction is rather big compared to the dimensions of the micro channel structure. A thermocouple attached to the surface will locally lower the temperature at the surface, due to a fin effect. This fin effect is even bigger when the thermocouple is mounted perpendicular to the surface, therefore it is beter to mount the thermocouple parallel to the surface. Several estimations concerning this decrease in temperature are given in literature, as an example is given here the correction formula (5.4), according to Azar [52].

(Tundisturbed − Tmeasured ) = φ =

φ φ+1 √ hDw kw 2ks

(5.4) (5.5)

With Dw the thermocouple diameter [m], kw the thermocouple wire conductivity [W/(mK)], ks the conductivity of the substrate [W/(mK)] and h the heat transfer coefficient [W/(m2 K)]. Although thermocouples give a lot of errors on temperature measurements, they can be used to measure global temperature. However they can not measure the temperature inside the channels or inside the drop, because the temperature measurement would be too much influenced by errors.

5.4.3

Measuring the cooling rate

A final step in temperature measurements would be to measure the cooling rate of an electrowetting actuated system, such as theoretically is investigated in chapter 4. However this could simply not be done yet, since no existing whole system is developed. For cooling rate measurements a subsequently flow of coolant is needed, but this can not be provided yet. A droplet can be positioned on top of the microchannels and can be driven in and out the channels, but the encapsulated heat in this droplet could not be transported to another area in the system. When a droplet is positioned on top of the channels and a heat flux is applied, than heats the droplet up in a few seconds. This time is to short to examine transient behaviour of the drop. Further investigation in this area is necessary.

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Conclusion

Different thermal experiments are performed in order to experimentally validate the theoretically achievable heat transfer, that can be obtained by an electrowetting actuated system. In an attempt an experimental test setup is built to perform isothermal experiments. The test setup allows electrowetting actuation, while a heater can heat up the silicon channelstructures to a stabilized temperature. With this thermal test setup successful electrowetting experiments could be performed at different temperatures. The electrowetting experiments are performed on a flat substrate and repeated on the micro channels. These experiments show that increasing temperature lowers the contact angle. An extrapolation of these results towards the influence of temperature on surface tensions could not be made. Further investigation in this area is still required. Furthermore the viscosity as a function of temperature of the used water-salt-glycerol mixture has been measured: at higher temperatures, a lower viscosity is measured. This viscosity change predicts longer filling lengths of the microchannels at higher temperatures. Unfortunately the achievable heat transfer could not be measured, due to measuring problems and problems with the system. Temperature is measured with thermocouples in between certain error bars, but no temperature could be measured inside the channels. Temperature measurement with an infrared camera seemed unfeasible. The biggest problem is related to the system: a subsequently replacing of a droplet by a new droplet could not be performed. In future investigation this must be achieved, in order to measure cooling techniques.


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Section 6

Future work In this chapter some future work on behalf of the electrowetting pump with integrated cooling. In a first section the confining of the channels is discussed in order to build a reliable system, which allows to measure the achievable heat transfer calculated in chapter 4. In a second section also a proposal of liquid metals is given as an alternative liquid for electrowetting based cooling.

6.1 6.1.1

Confined channels Introduction

The so far discussed open channel structure has two great disadvantages: dust particles can enter the channels and liquid can leak irreversibly. In order to minimize or even get rid of this problem, a closed channel structure has to be developed. The development of these confined channels is also necessary to implement this cooling technique in an electronic device. To maintain the reliability standards of these electronics no leakage nor any contact may occur between a conductive liquid and the present conductive paths. Contact may lead to shortcut and fatal breakdown of the device. Former developed liquid cooling techniques has always been the point of attention for costeffective solutions, due to possible high cost of leakage prevention. Many problems occur when repeatable heating up and cooling down of the cooling system is established. During these heat cycles the different system components induce stresses in the interconnect caused by the different thermal expansion coefficients of the different materials. The stresses will lead to crack formation. The device will loss its cooling rate, too high temperatures will be present in the components and in extreme cases even burn-out can occur. Therefore a maximum temperature difference can be deduced from the chosen materials, based on their maximum stress resistance and their difference in thermal expansion coefficients. These stresses can be reduced by choosing materials for the different components with almost the same thermal expansion coefficients. In case of the electrowetting cooling system the choice is made to make the channels from silicon. This has a great advantage on behalf of the thermal expansion coefficients: the arsenic doped silicon can be used for the channels, while the top of the channels can be made from non-conductive silicon. Using almost the same material will have the advantage that thermal expansion coefficients are almost the same and a higher reliability can be achieved for this liquid cooling technique. 80



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In this chapter some possible techniques to confine the channels are discussed. Unfortunately the cover could not be performed with a non-conductive type of silicon, because filling characteristics have to be examined and the only way to do this is by viewing from the top with a camera. Thus a transparant top layer like a glass plate, some plexiglass or ITO, has to be attached to the silicon.

6.1.2

Possible techniques

Two constraints have to be taken into account for choosing an appropriate top layer for the channels. The first constraint is already discussed: the top layer has to be made from a transparant material in order to examine the filling length of the channels. A second constraint is on behalf of the electrical characteristics of the layer: the top layer has to be non-conductive in order to create no voltage difference over the top of the channels and the top layer (see figure 6.1 (a)). The only voltage difference that may exist is over the bottom plate and the electrode, otherwise liquid can get trapped nearby or in between the top layer and the top of the channels.

Figure 6.1: Constraints of the interconnection between the top of the channels and the top layer: (a) non-conductive top layer, so no voltage difference over the top, (b) a hydrophilic surfaces trap the liquid by capillary forces, beter is a hydrophobic surface (c) or a completely closed channels (d). The second constraint describes the surface conditions of the top layer and the top of the channels: surfaces have to be hydrophobic and not hydrophilic (see figure 6.1(b) and (c)) so no liquid can get trapped by capillary forces between the top layer and the channels. Trapped liquid will certainly start to boil once a heat rate flows to the trapped liquid. A vapor phase is not wanted in this system due to the creating of hot spots. Hydrophobic surfaces will force the liquid to stay in the channels because a too high Laplace pressure would be needed to drive the liquid in the gap since this gap is much smaller than the micro channels. Besides two hydrophobic surfaces in the gap between the top layer and the microchannels another solution could be to completely close the channels (see figure 6.1(d)). As a result no liquid can get trapped in the gap but in contrary closing up a channel structure with channels of 100µm ×100µm or smaller is subject for further investigation. Some first attempts are made to completely close up the channels and explained in the next subsections. c Koninklijke Philips Electronics N.V. 2005

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Ideal confined system

The ideal configuration of a confined system for electrowetting pumping is pictured in figure 6.2.

Figure 6.2: Ideal configuration of a confined electrowetting pump. All surfaces inside the channels are hydrophobic and special electrodes are mounted along the whole length of the channels. The surfaces inside this ideal confined system are all hydrophobic. So whenever a droplet is deposited in the pool it will not fill in the channels unless a voltage is applied across the droplet. Furthermore can the platinum electrode of the experimental setup be replaced by thin gold electrode plates in each channel. Mounting this electrodes along the whole length of the channel has the advantage that no longer a potential difference along the channel exist and the liquid filament can fill the channel completely. Once the voltage drops back to zero the hydrophobic surfaces will force the liquid out of the channels. However, if this ideal confined channels has to be manufactured, one main problem arises concerning the bonding of the top layer with the microchannels. Different possible solutions are given in the next subsection.

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Bonding techniques

Bonding materials A and B together when A and B have different characteristics has always been a tough task and requires a lot of experience of chemical and material properties of both materials A and B and of the bonding material. Bonding silicon micro channels with a nonconductive transparant plate is not different. Research in a decent bonding mechanism for the microchannels with a glass plate is still continuing, so the given solutions are only provisional and have to be tested to be validated. Possible bonding mechanisms are: adhesive bonding [53] with a layer of glue or with BCB and anodic bonding [54]. Adhesive bonding is done by inserting a bonding material between the micro channels and the cover layer. This bonding material could be any glue based on acryl. The advantages of this method is that the glue is relatively cheap and its properties are very well known. However tests on the micro channels with the hydrophobic monolayer OTS on top gave problems: the glue did not stick to this hydrophobic surface and yet filled the glue completely the micro channels even when a small amount was used. A possibility would be to remove the OTS. Removal of this OTS layer was successful done by putting the channelstructures in a plasma oven. The areas which have to stay hydrophobic can be covered with a rubber cover made of PDMS. However, after this treatment the glue was applied on an OTS free area of the channel structures, yet filled the glue the micro channels due to capillary pressure. A solution could be to etch around the microchannels a buffer pool for the excess of glue. Another possibility to evade that glue enters the channel is to use another hydrophobic material like Montacellr which is used to make small lenses for DVD players etc. Another adhesive bonding material could be BCB. BCB is a heat curable (returns a polymer when heated up), solvent based, thermosetting polymer. Its main property is that it is sold as a fluid below 170◦ C but once it is heated up above this temperature its viscosity drops immediately to lower values and after adding a little more heat at this stage it returns to the solid state even when again a temperature of 170◦ C is reached. BCB is transparant in this solid state. The main advantage of BCB would be that it could bond cavities, thus no bonding material could obstruct the channels. However bonding BCB on the micro channels is not tested and problems still can rise with the hydrophobic monolayer on top of the microchannel which gave the most problems while bonding was tried to achieve with glue. A last possible bonding technique would be anodic bonding. Anodic bonding is defined as a bonding between two materials due to a high potential difference. The bond consist than only out material A and B and no additional bonding material is used. However, this technique is rather expensive and might lead to breakdown of the dielectric layer on the micro channels.


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6.2


Liquid metals

In an attempt to increase the heat transfer by electrowetting it is requirable to change one of the parameters related to the heat transfer. Since increase in average velocities of the liquid flow through microchannels is limited to a maximum velocity of 2mm/s another parameter has to be found to increase heat transfer. This parameter is simply replacing the liquid by another type like liquid metals. The main advantages of using liquid alloys over other liquids are: a much higher degree of thermal conductivity which is far superior than non-metallic liquids and they have much higher surface tensions than most non-metallic liquids which makes them suitable for electrowetting transport. Further research to liquid metals for use in electrowetting cooling has to be done.

6.3

Conclusion

The future of cooling by electrowetting looks bright, since the experiments revealed some deeper investigation in liquid behaviour and since the theoretical calculations promise an enhanced heat rate by electrowetting. However, the theoretical system needs still to be validated by means of experiments. To execute those experiments and even to implement this cooling technique in future devices to maintain the high standards of reliability different methods to confine the channels are discussed. A most promising confining method is based on adhesive bounding techniques: A glass plate can be glued on the silicon channelstructures when an additional cavity is etched all around the hydrophobic micro channels. Another future aspect to enhance cooling by electrowetting could be to investigate electrowetting behaviour of fluids with higher cooling capacities or which can work at higher temperatures. Metal liquids fulfil the demands of a higher thermal conductivity and higher surface tensions. Metal liquids are therefore proposed to be subject for further investigation.

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Section 7

Conclusion This master thesis describes experimentally and theoretically an electronics cooling technique. Cooling is investigated with an integrated pumping device based on electro-static actuated liquid flow through micro channels. The aim of this forced flow through microchannels is to achieve high cooling rates while downsizing dimensions. The application area of this cooling technique is not yet defined, but a possible way could be as an integrated heat spreader for LEDs in a system in package design. A first chapter gives a brief overview of the importance and the recent trends in electronics cooling. Current forecast predict stabilization of power density during the next decades because of the highly increasing leakage current in electronics. However the total output power has to increase, thus heat dissipation by the increased leakage current has to be kept as low as possible. The investigated system could give an answer to this heat problem. A model for the actuation principle of electrowetting was explored. The system consist of a droplet on top of a silicon substrate. On top of the substrate a dielectric layer is thermally grown, which electrically separate the droplet from the conductive silicon while applying a potential over the droplet to change its characteristics. A first model describes the droplet contact angle on a flat substrate being quadratic function of the applied voltage over the droplet. In a second model, a structured substrate is subject of investigation. These structures in the substrate are open micro channels of 100µm ×100µm. Droplet behaviour is such that increasing potential over the drop leads to a constant threshold voltage, where the droplet start to fill in the channels. This threshold voltage is function of the geometry of the structured channels. Finally also a dynamic model for the droplet is derived. Furthermore a theory is developed to estimate the enhancement in liquid cooling that can be achieved by electrowetting. This theory revealed that this new cooling method will induce enhanced heat transfer above a critical frequency. This critical frequency is for the 100µm square microchannels about 0.25Hz. The calculated cooling rate amounts 156W for a block shaped filling, 198W for a sinusoidal filling and 1.56W or 15.6W/cm2 for a real filling length characteristic at a frequency of 1.47Hz. Experimental results of the calculated enhancement of liquid cooling could not yet been given, due to the experimental setup and measuring problems. However a first investigation in droplet behaviour under influence of a heat rate could yet be experimentally obtained. Temperc Koninklijke Philips Electronics N.V. 2005

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ature rise of the liquid lowers the viscosity and changes the surface tensions, which results in lower contact angles, thus favorable electrowetting behaviour. Due to the promising achievable cooling rates cooling by electrowetting with integrated pumping can be subject of investigation in further research. However first a reliable system has to be built in order to perform experiments. A design proposal of such a reliable system is given by confining the channels. Still further research can be performed on these confined channels structures: not only in finding an adequate bonding method but also in examining the electrowetting characteristics of a confined system.

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References [1] R. HANNEMANN, Thermal control of electronics: perspectives and prospects, MIT, 2003 [2] C. LASANCE, Thermally driven reliability issues in microelectronic systems: statusquo and challenges, Microelectronics Reliability, 43, pp. 1969-1974, 2003 [3] G.E. MOORE, No exponential is forever...but we can delay forever, IEEE International Solid-State Circuits Conference, 2003 [4] E. VAN DEN BULCK, Warmteoverdracht, Cursustekst, Faculteit Toegepaste Wetenschappen, K.U.Leuven, 2001 [5] D.B. TUCKERMANN and R. F. W. PEASE, High-Performance Heat Sinking for VLSI , IEEE Electron Device Letters, Vol. EDL-2, No.5, pp.126-129, 1981 [6] Y.A. ÇENGEL, Heat transfer: a practical approach , Mc Graw Hill, ISBN 0-07115223-7, New York, 1998 [7] W. DERKINDEREN and N. THEODOROU, Numerieke modellering en experimentele verificatie van een warmtewisselaar voor selectieve vloeistofkoeling van elektronicacomponenten, Eindwerk, KULeuven, Dept. Werktuigkunde, TME/20022003/03EE-02 [8] A. AUBRY, Integrated microchannels cooling in silicon, Traineeship Report, Ecole superieure de physique et chimie industrielles, 2003 [9] R. PIJNENBURG, Integrated cooling in silicon, Eindwerk, Technische Universiteit Eindhoven, FTV/TIB 2004-02, 2004 [10] D. HECTORS and K. HUYBRECHTS, Vloeistofkoeling van elektronicacomponenten door middel van elektrostatisch aangedreven druppels, Eindwerk, KULeuven, Dept. Werktuigkunde, TME/2002-2003/03-EE-03 [11] H. OPRINS, B. VANDEVELDE, E. BEYNE, G. BORGHS, M. BAELMANS, Selective Cooling of Microelectronics using Electrostatic Actuated Liquid Droplets, Proc. of the 10th International Workshop on Thermal Investigations of ICs and Systems, pp. 207-212, 2004 [12] P. PAIK, V.K. PAMULA and K. CHAKRABARTY, Thermal effects on droplet transport in digital microfluidics with applications to chip cooling, International Conference on Thermal, Mechanics and Thermomechanical Phenomena in Electronic Sysc Koninklijke Philips Electronics N.V. 2005

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tems (ITherm), pp.649-654, 2004 [13] V.K. PAMULA and K. CHAKRABARTY, ooling of integrated Circuits Using DropletBased Microfluidics, ACM, April, 2003 [14] P. PAIK, V.K. PAMULA a.o., Electrowetting-based droplet mixers for microfluidic systems, Royal Society of Chemistry, Lab on a Chip, Vol.3, pp.28-33, 2003 [15] M. WASHIZU, Electrostatic Actuation of Liquid Droplets for Microreactor Applications, IEEE Transactions on Industry Applications, Vol. 34, No.4, pp.732-737, July/August 1998 [16] J.C. BARET, Morphological Transitions in Simple Electrocapillary Systems, PhD thesis, University of Twente (to be defended 2005) [17] R.HAYES and J. FEENSTRA, Video-speed electronic paper based on electrowetting, Nature, Vol.425, pp.383-385, September 2003 [18] F. FANTOZZI, S. FILLIPESCHI and E.M. LATROFA, Upward and downward heat and mass transfer with miniature periodically operating loop thermosyphons, Superlattices and Microstructures, 35, pp.339-351, 2004 [19] N. TENGBLAD and B. PALM, Flow boiling and film condensation heat transfer in narrow channels of thermosyphons for cooling of electronic components, Kluwer Academic Publishers, Dordrecht, 1997 [20] Y.F. MAYDANIK, Loop heat pipes, Applied Thermal Engineering, 25, pp.635-657, 2005 [21] X.C. XUAN, Investigation of thermal contact effect on thermoelectric coolers, Energy Conversion and Management, 44, pp.399-410, 2003 [22] F. LÄRMER and A. SCHILP, Method of anisotropically etching silicon, US Patent 5,501,893, March 26, 1996 [23] J. SAGIV, Organized monolayers by adsorption. 1. formation and structure of oleophobic mixed monolayers on solid surfaces, J. Am/Chem. Soc., 102(92), 1980 [24] B. BERGE, Electrocapillarité et mouillage de films isolants par d’eau, C.R. Acad. Sci. Paris, Ser.II, 317:p157, 1993 [25] M. VALLET, M. VALLADE and B. BERGE, Limiting phenomena for the spreading, Eur. Phys. J. B. II, pp.583-591, 1999 [26] QUILLET and BERGE, A recent outbreak , Current Opinion in Colloid and Interf. Science, Vol.6, pp.34-39, 2001 [27] A. ALAMI et al., Anisotropic Reactive Ion Etching of High Aspect Ratio Pore and Trench Arrays in Silicon for Integrated MOS Decoupling Capacitors, Nat.Lab. Technical Note 2003/00250 [28] H.J.J. VERHEIJEN and M.W.J. PRINS, Reversible Electrowetting and Trapping of 88



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Charge: Model and Experiments, Langmuir, 15,pp. 6616-6620, 1999 [29] A.B.D. CASSIE, Contact Angles, Discuss. Faraday Society, 3, 11, 1948 [30] T.N. WENZEL, Surface Roughness and Contact Angles, J. Phys. Colloid Chem., 53,p.1466, 1949 [31] T.N. YOUNG, Phil. Trans. Roy. Soc. London, 95(65), 1805 [32] H. OPRINS, C.C.S. NICOLE, J.C. BARET, G. VAN DER VEKEN, C. LASANCE, M. BAELMANS, On-Chip Liquid Cooling with Integrated Pump Technology, 21st IEEE Semi-Therm Symposium, 2005 [33] K. NEVELSTEEN and M. BAELMANS, Meetfouten: een inleidende tekst, Labo’s thermische systemen en energiebeheer, Leuven, Academiejaar 2002-2003 [34] N.A. PATANKAR and Y. CHEN, Numerical Simulation of Droplet Shapes on Rough Surfaces, Nanotech 2002, Vol.1, pp. 116-119, ISBN 0-9708275-7-1, 2002 [35] N.A. PATANKAR, Mimicking the Lotus Effect: Influence of Double Roughness Structures and Slender Pillars, Am. Chem. Soc., Langmuir, Vol.20, No.19, pp.8209-8213, 2004 [36] T. ONDA, S. SHIBUICHI, a.o., Super-Water-Repellent Fractal Surfaces, Langmuir, The ACS Journal of Surfaces and Colloids, Vol.12, No.9, pp.2125-2127, May 1996 [37] N.A. PATANKAR, Transition between Superhydrophobic States on Rough Surfaces, Am. Chem. Soc., Langmuir, Vol.20, No.17, pp.7097-7102, 2004 [38] J.C. BARET, R. SEEMANN, M. DECRE and S. HERMINGHAUS, Electro-actuation of fluid in open microchannels, Article in preparation [39] E.W. WASHBURN, The dynamics of capillary flow, Phys. Rev., 17(13):273, 1921 [40] D. QUÉRÉ, Inertial capillarity, Europhys. Lett., 39(5), pp.533-538, 1997 [41] P.B. WARREN, Late stage kinetics for various wicking and spreading problems, Phys. Rev. E, 69(04):1601, 2004 [42] A.A. DARHUBER, S.M. TROIAN and W.W. REISNER, Numerical Simulation of Droplet Shapes on Rough Surfaces, Nanotech 2002, Vol.1, pp. 116-119, ISBN 09708275-7-1, 2002 [43] N.A. PATANKAR and Y. CHEN, Dynamics of capillary spreading along hydrophilic microstripes, Phys. Rev. E, 64:031603, 2001 [44] L.A. ROMERO and F.G. YOST, Flow in an open channel capillary, J. Fluid Mech., 322, pp.109-129, 1996 [45] D. QUÉRÉ, E. RAPHAËL and J.-Y. OLLITRAULT, Rebounds in a capillary tube, Langmuir, 15, pp.3679-3682, 1999


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[46] S.P. TIMOSHENKO, Theory of Elasticity, third edition, McGRAW-HILL, New York, pp.309-313, 1970 [47] J.G. KNUDSEN, Fluid Dynamics and Heat Transfer, Robert E. Krieger publishing company, Huntington, New York, pp.101-105, 1979 [48] S. SONG, S. LEE and V. AU, Closed-Form Equations for Thermal Constriction/Spreading Resistances with Variable Resistance Boundary Condition IEPS Conference, pp.111-121, 1994 [49] THERMAN, www.micred.com [50] K. NEVELSTEEN and M. BAELMANS, Labo temperatuurmetingen, Labo’s thermische systemen en energiebeheer, Academiejaar 2002-2003 [51] O. BREITENSTEIN and M. LANGENKAMP, Lock-in thermography : basics and use for functional diagnostics of electronic components, Springer series in advanced microelectronics, 10, 2003 [52] K. AZAR, Thermal measurements in Electronics Cooling, CRC Press LLC, p.57, 1997 [53] F. NIKLAUS, Adhesive Wafer bonding for microelectronic and microelectromechanical systems, PhD thesis, Royal Institute of Technology, Stockholm, 2002 [54] A. BERTHOLD, Low-temperature wafer-to-wafer bonding for microchemical systems, PhD thesis, Technische Universiteit Delft, Deltech Uitgevers W.D. Meinema B.V., 2001

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Appendix A

Cleaning procedure A.1

Introduction

In this appendix the cleaning procedure of the microchannels will be explained. After cutting the microchannels out of the original wafer, the microchannels are dirty or grease can be left on the surface. The channels could be covered with cutting particles and dust particles, which can obstruct the filling of the channels. The cleaning procedure is also necessary after successful experiments: the channels are dirty, covered with dust and particles of the liquid, used in the experiments. Some trapped charges can be left at the surface and channels can be filled with the liquid.

A.2

Cleaning methodology

The cleaning method of the microchannels has the aim to remove small particles and grease of the surface and out the microchannels. An adequate procedure has to remove most of the dirt, but has to remain the hydrophobic layer of OTS intact. Though very reactive cleaning methods are not suitable, like Piranha clean: This is a cleaning of the wafer, for 10 minutes, in concentrated sulphuric acid (H2 SO4 , 96%) and hydrogen peroxide (H2 O2 , 31%) mixture at 90◦ C. This cleaning method is used, before the SiO2 -layer is deposited by wet oxidation on the etched silicon. The maximal reactivity that the OTS can resist is a hydrogen fluoride (HF , 50%) cleaning bath during 2min30”. A possible solution for cleaning is the following method: First blow with ionized nitrogen the biggest particles of the sample; next rinse the sample during 15 to 30 minutes in an ultrasonic bath of aceton; then blow the remaining aceton of the sample with ionized nitrogen; next rinse the sample again during 15 to 30 minutes in toluol; again blow the remaining toluol of the sample and out of the channels with ionized nitrogen; finally rinse it once again for 15 to 30 minutes in IPA (Isopropanol) and blow the remaining IPA of the sample and out of the channels. The reason for use of the ultrasonic bath (see figure A.1) is the disturbance of the boundary layer between the solid and the flow of the liquid. During rinsing usually a liquid is poured over the sample in order that the flow will carry the dirt particles. However this method has the no slip boundary condition at the liquid solid interface, thus the liquid has no speed and no dirt can be carried away in this boundary layer of the flow. The ultrasonic bath resolves this problem to agitate the molecules of the liquid by means of an ultrasonic wave. c Koninklijke Philips Electronics N.V. 2005

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Figure A.1: The ultrasonic bath Branson 3510. Three different bekers, containing aceton, toluol and isopropanol, are hanging in a large demi-water tank. Ultrasonic waves are generated in the demi-water tank and thus also in the three different cups. The three different cleaning liquids: aceton, toluol and isopropanol has these order, because of their characteristics. Aceton rinse the roughest particles, but has the disadvantage that it can’t hold the particles for a longtime in solution. Therefore the other two cleaning liquids are used: they rinse smaller parts and can hold longer particles in solution. The order of the liquids goes from heavy reactive to milder. These three liquids could also replaced by other liquids, like aceton, followed by ethanol and ended with toluol. The main reason for a choice of liquid is that they can solve temporary particles and the react with grease and oils.

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Appendix B

Matlab-file for filling length calculation Important: this matlab-file needs the "Image Toolbox", in order to use the commando’s "imcrop", "imshow",... This m-file computes the filling length of the liquid filament inside one single channel, as pictured in figure B.1. This program is developed by Baret [16].

Figure B.1: An electrowetted drop: the channel is filled in with liquid. A white line indicates the front of the drop and a black line indicate the front of the liquid finger. The distance between these two lines has been calculated as the filling length.

B.1

Users info

Basically this matlab-file needs two inputs: the first input are "runXX.rawmovie.YYYYY.bmp"files and the second input is a file named "runXX.rawmovie.bmp_time_mapping", with "XX" in both cases a number from "00" to "99" and "YYYYY" also a number. If the program wants to be ran, than a few adjustments have to be made in the m-file: First the BasisPathName has to be defined, second the filebeginnumber has to be filled in, third the fileendnumber has also to be filled in and finally the mmperpixel-value has also to be known, which can be obtained by examining one of the bmp-files very close (= counting the pixels of the file over a known distance). Then the program is ready to execute. Once executed, the program reads in the first bmp-file and allows an interactive interface with the user: the user has to draw a zoom window on a channel and has to define 6 points on the focussed channel. The first two points have to be defined inside the channel (one inside the drop and one a long way from the drop, but still inside the channel). The four points are split up in indicating two points above the channel and two points below the channel. The program will start reading in all the other "runXX.rawmovie.YYYYY.bmp"-files. The program draws two lines on the figures, one in front of the droplet and one in front of the liquid c Koninklijke Philips Electronics N.V. 2005

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finger in the channel. The absolute value between these two lines will be than the filling length, as is pictured in figure B.1

B.2

The Matlab-file

% extracting length as a function of time % Takes .bmp files and bmptimemapping file. c % JC Baret - march 2005 % Files should be named runXX.rawmovie.bmp % They must be in the folder named ’BasisPathName\RunXX\’ % You must enter the BasisPathName and the values % of the first (filebeginnumber) and last run (fileendnumber) % and the magnification ! clear all; close all; % Opening the file : Define the basis pathname where .bmp files are located BasisPathName=’C:\...’; filebeginnumber=...; fileendnumber=...; mmperpixel=0.2/36; %% Nothing should be changed after this point. flag = 0; for fileinx=filebeginnumber:fileendnumber %for all the files in the folder if fileinx< 10 RunNum=strcat(’Run0’,num2str(fileinx)); else RunNum=strcat(’Run’,num2str(fileinx)); end PathName=strcat(BasisPathName,RunNum,’\’); FileNameAuto=strcat(PathName,RunNum,... ’.rawmovie.bmp_time_mapping’); fidtest=fopen(FileNameAuto); if fidtest==−1 % if file does not exist else % if file exists fclose(fidtest); [FileName1, Time] = TEXTREAD(FileNameAuto,’%s%f’); N=length(Time);

strN=num2str(N);

start= 1;

last=N; time01 =start; Npoints=last-start;

Type= 1; time02 =start+1;

CalibOnImage= 0; flagright = 1;

time0 =(Time(time01 + 1)+Time(time02 + 1))/2;

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% Defining the region of interest FileName=strcat(PathName,FileName1start); A=imread(FileName,’bmp’); if flag== 0 % If it is the first time you run the program [A2,rect] = imcrop(A); imshow(A2); % Click on two points in the channels [AX1,AY1] = ginput(2); % Click on two points above the channel [AX2,AY2] = ginput(2); % click on two points below the channel [AX3,AY3] = ginput(2); flag= 1; else [A2,rect] = imcrop(A,rect); close all; end %of if it is the first time you run the program %Opening the output file : %ImageNumber && Time [s] && Length channel [mm] fid=fopen(strcat(BasisPathName,RunNum,’.dat’),’w’); %Loop on all the files of the folder waitbarh=waitbar(0,strcat(’Processing file ’, PathName)); for k= 1:Npoints %For all the files in the folder waitbar(k/Npoints,waitbarh); i = start + max(1,round((last-start)/Npoints*(k−1))); %opening file and recenter on the region of interest FileName=strcat(PathName,FileName1i); A0 =imread(FileName,’bmp’); A=imcrop(A0,rect); %Defining lines to get the position of the tip and contact line %Crossection in the channel [AlineX,AlineY,Aline] = improfile(A,AX1,AY1); %crossection above the channel [AcUpX,AcUpY,AcUp] = improfile(A,AX2,AY2); %crossection below the channel [AcDwX,AcDwY,AcDw] = improfile(A,AX3,AY3); %defining a threshold to detemine the boundary fluid / solid Threshold=(max(Aline)+min(Aline))/2; %find where the tip of the channel is: indx1 =find(filter([1 −1],1,(Aline>Threshold))== 1); %find the position of the contact line above and below the channel indx2 =find(filter([1 −1],1,(AcUp>Threshold))== 1); indx3 =find(filter([1 −1],1,(AcDw>Threshold))== 1); %determine the position in the image channelendX=AlineX(max(indx1)); channelendY=AlineY(max(indx1)); c Koninklijke Philips Electronics N.V. 2005

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clineX=(AcUpX( min(indx2) )+ AcDwX( min(indx3)) )/2; clineY=(AcUpY( min(indx2) )+ AcDwY( min(indx3)) )/2; %calculates channel length L=sqrt((channelendX−clineX)ˆ2 + (channelendY−clineY)ˆ2) ∗ mmperpixel; %display the images and position of the calculated points %(to check the results uncomment the next three lines) A(:,round(channelendX):round(channelendX)+1)= 0; A(:,round(clineX):round(clineX)+1)= 255; imshow(A); %Printing the results fprintf(fid,’%i %12.3e’,i,(Time(i)-time0)/1000000 ); fprintf(fid,’ %12.3e’, L ); fprintf(fid,’\n’); end %end of for all the files in the folder close(waitbarh); fclose(fid); end %(of if file exist) % close all; end % of for all the files in the folder

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