Microfluid Nanofluid (2005) 1: 280–283 DOI 10.1007/s10404-005-0033-z
SH O RT CO MM U N IC A T IO N
T. Stiles Æ R. Fallon Æ T. Vestad Æ J. Oakey D. W. M. Marr Æ J. Squier Æ R. Jimenez
Hydrodynamic focusing for vacuum-pumped microfluidics
Received: 3 November 2004 / Accepted: 10 December 2004 / Published online: 31 March 2005 Springer-Verlag 2005
Abstract Hydrodynamic focusing has proven to be a useful microfluidics technique for the study of systems under rapid mixing conditions. Most studies to date have used a ‘‘push’’ configuration, requiring multiple pumps or pressure sources that complicate implementation and limit applications in point-of-care environments. Here, we demonstrate a simplified hydrodynamic focusing approach, in which a single pump pulling at the device outlet can be used to drive hydrodynamic focusing with not only excellent control over the focus width and stream velocity, but also with minimal sample consumption. In this technique, flow can be either mechanically driven or induced simply through capillarity. Keywords Hydrodynamic focusing Æ Vacuum pumping
1 Introduction Owing to the small relevant length scales, microfluidics offers accelerated transport processes and the ability to manipulate smaller sample volumes than possible on the macroscale. These advantages make microfluidics platforms ideal for the investigation of processes involving expensive biological analyses and lend great promise as the basis for future sensing and analysis systems. In these techniques, small samples may be split for multiple T. Stiles Æ R. Fallon Æ T. Vestad Æ J. Oakey Æ D. W. M. Marr (&) Department of Chemical Engineering, Colorado School of Mines, Golden, CO, USA E-mail:
[email protected] J. Squier Physics Department, Colorado School of Mines, Golden, CO, USA R. Jimenez JILA and Department of Chemistry, University of Colorado and National Institutes of Standards and Technology, Boulder, CO, USA
parallel diagnostic tasks upon a single device, moving analytical processes out of the laboratory and into point-of-care situations. As such, portable handheld sensors capable of collecting samples from dynamic environments and providing immediate feedback may now be considered. The broad goal for microfluidics is the micro total analysis system (lTAS), in which a single sample drop (blood, saliva, etc.) could be split, mixed, and analyzed in a single, portable device. For a great number of potential microfluidic applications, particularly those focused on in-the-field or point-of-care use, minimization of the associated hardware can be vital for the practicality of a device. Applications motivated by high throughput or exceptional sample costs, such as drug screening and protein crystallization, intend to take advantage of the small sample volume requirements associated with microfluidic systems. We address both of these issues through the use of a hydrodynamic focusing technique that minimizes the sample volume and can be readily controlled with a single microfluidic suction pump. By varying the relative input channel flow resistances in vacuumpumped microfluidic networks, a hydrodynamically focused stream can be created and controlled. The required pressure drop may be generated conventionally with a pump or simply by capillary pumping, which exploits the importance of interfacial tension at the microscale. Under microfluidic conditions, where viscous effects dominate, the fluid dynamics are unique. The Reynolds number, defining the ratio of inertial to viscous forces, is extremely small, reducing the equations of motion to a simple, time-reversible differential form, known as the Stokes equation. These viscous-dominated flows are laminar in nature, time-reversible, and turbulent-free. Without turbulence to aid mixing, microfluidic flows rely entirely on diffusion to mix; in general, the time required to achieve mixing via diffusion can be expressed as smix=w2o/(p2D) (Knight et al. 1998), where D is the diffusivity and wo is a characteristic length corresponding to the width of the focused stream in our studies. The
281
square dependence upon the length illustrates that mixing limitations can be greatly overcome in microfluidic geometries by moving to smaller length scales. Previous efforts to achieve rapid mixing in microfluidics have achieved mixing times as fast as 106 s in hydrodynamic focusing configurations (Knight et al. 1998) and on the order of 103 s in droplets (Song and Ismagilov 2003). Due to the ease with which these systems can be imaged, microfluidic flow focusing has been used to study mixing in biological systems via infrared (IR) (Kauffmann et al. 2001), X-ray scattering (Pollack et al. 1999; Russell et al. 2002), traditional fluorescence (Pabit and Hagen 2002), and fluorescence resonance energy transfer (FRET)-based techniques (Lipman et al. 2003). These studies all employ hydrodynamic focusing, in which a sample inlet stream can be pinched or focused (Knight et al. 1998) with two side streams at a junction, as illustrated in Fig. 1a. The width and position of the center stream are solely the functions of the relative volumetric flow rates among the three inlets. This behavior is linear and the position of the inlet stream may be directed into a specific outlet position (Vestad et al. 2004) by simply altering the flow rate of the two side streams. Analysis and prediction of focusing behavior employs the fluidics equivalent of Ohm’s law, DP=QR, where DP is the pressure drop, Q is the volumetric flow rate, and R is the flow resistance, dependent on the fluid velocity profile. Assuming pressure-driven flows and no-slip boundary conditions, the Stokes equations can be solved (Brody et al. 1996) for channel geometries in the thin, Hele-Shaw limit (h/w fi 0) to yield a velocity profile independent of position across the channel width, w, and a parabolic velocity profile across the channel height, h, normal to the top and bottom channel walls. For square conduits, the flow resistance can be shown to be proportional to channel length L as R=12gL/h3w, where g is the fluid viscosity. With a linear relationship between the driving force, resistance, and flow, a simple circuit analysis (Fig. 1b) can be used to predict hydrodynamically focused flow profiles. For systems in which the inlet flows are pumped, predicting the focused stream width is particularly straightforward because the volumetric flow rates of the inlet streams are fixed. In this case, the width of the focus stream is accurately approximated by a ratio of the flow rates with: Fig. 1 a Illustration of hydrodynamic focusing. b Analogous circuit used to design and analyze the focusing network of a (Pi, Pf, Po are the pressures of the inlet, focusing stream, and outlet, respectively; Qi, Qf, Qo, and Ri, Rf, Ro are the associated flow rates and resistances, respectively)
wo Qi ¼ ¼ w Qi þ Qf
Qf 1 1þ Qi
where i, f, and o denote the inlet, sheath (focusing), and center (outlet) streams, respectively. For the design of vacuum- or capillary-pumped devices, one recognizes that Pi=Pf=atmospheric pressure. Under these circumstances, the hydrostatic head of the inlet reservoir is assumed to be uniform and negligible with respect to the total pressure drop. Also under these circumstances, the pressure drop across the network from the outlet to various inlets is identical and the relative flow rates and focused flow width is determined by the relative flow resistances as: wo 2Ri 1 2Li 1 ¼ 1þ ¼ 1þ w Rf Lf with equivalent channel cross-sectional geometries assumed throughout the network. One advantage here is the ease with which the relative resistance can be varied by modifying the length of the inlet channel during the fabrication process or through external actuation (Vestad et al. 2004).
2 Experimental We construct all of our devices in polydimethylsiloxane (PDMS) by first transferring the pattern of a shadow mask to a negative photoresist film (SU-8 50, MicroChem Corp., Newton, MA, USA) spun upon a silicon wafer to a depth between 50 lm and 80 lm. A two-part mixture of PDMS (Sylgard 184, Dow Chemical, Midland, MI, USA) is then poured and cured upon the silicon master to produce an optically transparent replica. This PDMS channel network is then sealed to a second, flat PDMS membrane to create our microfluidic flow cells. The center stream consisted of deionized water and fluorescently tagged colloidal tracer particles, while the focusing streams were composed of water only.
3 Results and discussion Figure 2 shows that longer inlet channels of increasing resistance result in smaller inlet flow rates and a tighter
282 Fig. 2a–d Focus stream width (entering from the left) can be readily varied with flow resistance of inlet channel. e: channel aspect ratio; filled circles: h/w=80/375=0.21 lm; open circles: h/w=50/ 525=0.10 lm (multiple data were obtained for this case, but the error bars were too small to be included). Note that model agreement improves significantly as the thin channel limit is approached
Fig. 3a, b With identical channel lengths in a and b, focus width is independent of the pulling flow rate and focus flow velocity, as indicated by colloidal tracer particles
focus. In this example, the inlet channel length was varied from approximately 15 mm to 50 mm, resulting in the predicted decrease in focus width. In addition to providing control of the focus width, this geometry requires the use of very small sample volumes. In general, the required sample consumption rate is given by woQo/ w, where Qo is the total volumetric flow rate of fluid drawn through the network. In this particular example, at the tightest focus, the sample consumption rate corresponds to 3 lL/h at Qo=1 lL/min. This includes an inlet channel volume of only 0.3 lL and is despite a focused stream velocity of 1,000 lm/s. As demonstrated in Fig. 3, and apparent from the expressions presented above, the focused stream width is independent of the applied pressure drop (as in the case of capillary-driven flow) or the specific overall flow rate Fig. 4 Focusing geometries can be used to study mixing at both short and long time scales within the same geometry (w=120 lm, h=100 lm, Qo=30 lL/min). The outlet channel length of 1 m (requiring 12 lL to fill) allows steady-state observation at times from 100 ms to 25 s after mixing
(as in the case of fluid withdrawal via syringe pump). The velocity of the focused stream, however, can be readily controlled by varying either of these experimental parameters. Because the focused stream velocity profile assumes the focusing streams to be at a steady state, the average velocity of the syringe-pump-driven flow is determined simply as vo=Qo/wh. In the case of capillary-driven or other fixed-pressure-drop-driven flows, the expression is given as: DPh2 2wf Li þ wi Lf vo ¼ 12g Li ð2wf Lo þ wo Lf Þ þ wi Lo Lf Such a microfluidic focusing geometry allows not only for rapid mixing but also permits simultaneous investigation of relatively long time scales. For biological processes that have multiple kinetic time scales for example, the ability to study the process over multiple orders of magnitude in time is extremely useful. Other applications, including bioassays, may require sample incubation after mixing but before observation, excitation, or further manipulation. An example of a geometry that allows for observation at both short and long times after mixing without sample translation is shown in Fig. 4. In this setup, an aqueous solution of fluorescent colloids is focused down to approximately 20 lm in width and, by extending the outlet by wrapping it multiple times around the inlet, both the short-time focusing region and long-time regions can be observed simultaneously. This particular geometry, with an overall
283
footprint of approximately 2.5·2.5 cm2 and an outlet channel length of 1 m, allows for observation at time scales ranging from 0.1 s to 25 s after mixing. As a result of the ability to fabricate narrow channels using soft lithography, extremely long outlet channels may be created in these microfluidic systems, allowing for studies to be of significantly longer times. Note that, despite the outlet channel length in this example, small sample volumes are sufficient for filling (12 lL in this example) and that one can achieve significantly longer residence times by employing narrower channels of smaller height. In fact, by using a vacuum-pumped geometry, the total required sample can be significantly reduced, related to previous focusing approaches by avoiding inlet pump or inlet tube filling. Here, only a sample reservoir is required at the inlet. Finally, the diffusion of the 0.28-lm colloidal tracers (D108 cm2/ s) should be noted as one observes the fluid streams at longer time scales. Analytic solution to Fick’s second law for diffusion normal to the flow direction is available (Carslaw and Jaeger 1959), making the first-order prediction of lateral concentration profiles down the outlet channel straightforward. In this work, we have presented the design and analysis for a new hydrodynamic focusing configuration that greatly minimizes the required sample volume and hardware associated with enhanced mixing in microfluidics. In addition, a circuit analysis method using limiting cases for thin-channel geometries has been presented that allows the prediction of focus profiles in multiple pull configurations with no fitting parameters. With the ability to readily predict flows, enhance mixing, use smaller sample volumes, and minimize associated
hardware, this approach will be useful to both clinical and point-of-care microfluidic device design. Acknowledgements This work was partially supported by NIH grant no. R21 EB0001722-01, NSF grant no. 0097841, and NASA grant no. NAG9-1364.
References Brody JP, Yager P, Goldstein RE, Austin RH (1996) Biotechnology at low Reynolds numbers. Biophys J 71:3430–3441 Carslaw HS, Jaeger JC (1959) Conduction of heat in solids. Oxford University Press, New York Kauffmann E, Darnton NC, Austin RH, Batt C, Gerwert K (2001) Lifetimes of intermediates in the b-sheet to a-helix transition of b-lactoglobulin by using a diffusional IR mixer. Proc Natl Acad Sci USA 98:6646–6649 Knight JB, Vishwanath A, Brody JP, Austin RH (1998) Hydrodynamic focusing on a silicon chip: mixing nanoliters in microseconds. Phys Rev Lett 80(17):3863–3866 Lipman EA, Schuler B, Bakajin O, Eaton WA (2003) Single-molecule measurement of protein folding kinetics. Science 301:1233–1235 Pabit SA, Hagen SJ (2002) Laminar-flow fluid mixer for fast fluorescence kinetics studies. Biophys J 83:2872–2878 Pollack L, Tate MW, Darnton NC, Knight JB, Gruner SM, Eaton WA, Austin RH (1999) Compactness of the denatured state of a fast-folding protein measured by submillisecond small-angle X-ray scattering. Proc Natl Acad Sci USA 96:10115–10117 Russell R, Millett IS, Tate MW, Kwok LW, Nakatani B, Gruner SM, Mochrie SGJ, Pande V, Doniach S, Herschlag D, Pollack L (2002) Rapid compaction during RNA folding. Proc Natl Acad Sci USA 99(7):4266–4271 Song H, Ismagilov RF (2003) Millisecond kinetics on a microfluidic chip using nanoliters of reagents. J Am Chem Soc 125:14613– 14619 Vestad T, Marr DWM, Oakey J (2004) Flow control for capillarypumped microfluidic systems. J Micromech Microeng 14:1503
