Deposition and Suspension of Large, Airborne Particles

Aerosol Science and Technology, 40:503–513, 2006 c American Association for Aerosol Research Copyright ISSN: 0278-6826 print / 1521-7388 online DOI: 10.1080/02786820600664152

Deposition and Suspension of Large, Airborne Particles Obatosin Aluko and Kenneth E. Noll Department of Chemical and Environmental Engineering, Illinois Institute of Technology Chicago, Illinois, USA

The focus of this paper is the experimental determination of size-resolved estimates of both deposition and suspension velocities for large, airborne particles (greater than 10 µm diameter). Measurements of particle dry flux onto the top and bottom surface of a smooth, horizontal, surrogate surface were divided by measurements of the concentration of airborne particles to provide estimates of deposition and suspension velocities in 14 size intervals between 5 and 100 µm diameter. Eddy inertial deposition efficiencies (η di ) were determined as a function of eddy Stokes numbers (Stke) larger than 1 and the results agree with the model of Slinn and Slinn (1980). The model was used to provide estimates of both the inertial and gravitational components for total upward and downward particle velocities. Experimental results for individual particle size intervals produced highly variable results. Much of this variation can be attributed to experimental errors associated with the nature of the atmospheric experiments and not to problems with the model. Upward large particle suspension velocities are similar in magnitude to downward deposition velocities at higher wind speeds and represent a counteracting process to deposition processes that cannot be ignored for accurate representation of the long-range transport for particles between 5 and 50 µm diameter.

INTRODUCTION The transport and fate of large particles in the atmosphere depend in part on their inertial properties. Particles in the 5– 100 µm size ranges are unique due to the importance of inertial properties relative to gravitational settling. Accurate deposition and suspension velocity models that include inertial effects for large particles after they have become entrained in the major circulation patterns are important in understanding the transport and fate of airborne particles. These velocities are difficult to assess for a variety of reasons, one of which is their large variability in time and space and the difficulty of representing their distribution. The atmosphere can be considered to be composed of four layers. The first layer is a thin viscous sub-layer influenced by

Received 31 August 2005; accepted 28 February 2006. Special thanks are expressed to Jui-Min Lin for sample collection. Address correspondence to Kenneth E. Noll, Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 W. 33rd St., Chicago, IL60616, USA. E-mail: [email protected]

surface roughness. The second layer is the constant flux layer, which is dominated by mechanical turbulence and in which shear stress and friction velocity are assumed to be constant (up to 100 m). The third layer is the atmospheric boundary layer that extends from 100 m to 1 km. The fourth layer is the “free atmosphere” that starts near 1 km. In turbulent flow, a complex secondary motion is superimposed on the primary motion of transport. The turbulence in the constant flux layer is characterized by eddies that transport particles from one layer to another with varying velocities. The eddy motion, which is erratic, can only be defined in terms of probability. Thus the principles of statistics are applied or field experiments are conducted to define quantitatively the effect of the turbulence, such as size of eddies, the vertical velocity fluctuations or the particle inertial velocity fluctuations Deposition and suspension velocities for large particles in turbulent airflow are difficult to quantify due to the interaction of the particles with the turbulent eddies in the airflow. The manifestation of the total effect of all forces acting on the particles produces an “effective” particle velocity. The forces include gravity, particle inertia, particle drag, eddy diffusion, Brownian diffusion, and electrical charge effects. It is the combined effect of all these forces that produce “effective” particle velocities in both the upward and downward direction in the atmosphere at any time. The purpose of this paper is to compare experimentally observed upward and downward large particle velocities with an empirical model suggested by Slinn and Slinn (1980). Measurements of particle flux in the open atmosphere onto a smooth, horizontal, surrogate surface are presented and compared with theory. The vertical particle velocities have been experimentally defined as the vertical particle flux divided by the average concentration of particles in the air. The large particle concentration was directly measured using a size selective rotary impactor. Experimental details for the flux plate and the rotary impactor have been previously reported and are summarized below. The empirical model is based on the eddy inertial deposition efficiency (ηdi ) that is determined as a function of dimensionless eddy Stokes number (Stke) larger than 1. The model is empirical in the sense that the parameterization used to represent the transport process is determined by comparison of model predictions 503

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O. ALUKO AND K. E. NOLL

with field observations. The model results and field observations demonstrate that deposition and suspension velocities of large particles are both important to a determination of variations in airborne concentrations and this can lead to longer atmospheric residence times than when only deposition is considered. EXPERIMENTAL DESIGN Experiments that focus on measurement of upward and downward large particle suspension velocities have been conducted for entrained atmospheric particles. These experiments were conducted in an urban area (Chicago, Illinois), removed from close by point sources of particles (site is located in the middle of the IIT campus and four blocks from the freeway) and at an elevation of 12 m so that large particles generated in the vicinity of the sampling site will be well entrained in the atmosphere before they were collected. The sampling site is 5.6 km south of the urban center and 1.6 km west of Lake Michigan. These measurements are compared with theory and incorporated into a particle suspension model that includes the effects of both particle settling velocities due to gravity and vertical velocity fluctuations due to inertial effects and allows estimation of the effective suspension velocity of large particles for use in transport models. The experimental methods used in this study have been previously described (Noll and Fang 1986; Noll et al. 1988; Noll and Fang 1989). The airborne concentration of coarse particles (>6.5 µm aerodynamic diameter) was measured with a Rotary Impactor simultaneously with the measurement of particle dry deposition fluxes to a smooth surrogate surface with a sharp leading edge, mounted on a wind vane. The deposition surface was designed to provide minimum airflow disruption and thus provides an estimate of the lower limit for dry deposition flux. The deposited particles were weighed and counted. Microscopic count data generated the mass distribution of particles collected on the deposition plate. The results demonstrated that 99% of the mass deposited on the plate was due to particles larger than 2 µm diameter (Holsen and Noll 1992). Because both the measured dry deposition mass and the measured airborne concentration were due to coarse particles, the two data sets were combined to evaluate the dynamics of atmospheric coarse particle deposition. Deposition Plate The deposition plate used for this study was similar to that used in wind tunnel studies (McCready 1986). It was made from polyvinyl chloride (PVC), 16 cm long, 7.6 cm wide, and 0.55 cm thick, with a sharp leading edge (less than a 10 degree angle) that was pointed into the wind by a wind vane. A 2 mm (0.002 inch) thick Mylar film with the dimension of 7.6 cm long and 2.5 cm wide was used as the collection surface. One film was placed on the upper surface of the plate; the second film was directly below the upper film on the lower side of the plate. A smooth surface produces minimum deposition velocities for surrogate collectors

under atmospheric conditions (Sehmel 1971; Davidson et al. 1985) and the greased surface prevents particle bounce. Rotary Impactor The coarse particle airborne concentration was measured with a Noll Rotary Impactor (Noll and Fang 1986). The Rotary Impactor collects large particles by moving four rectangular collector stages of different dimensions through the aerosol at high speeds, relative to expected wind speeds. The performance of the open face inertial impactor is a function of Stokes and Reynolds number. The collector widths and velocity of rotation are varied to achieve different collection efficiencies. For this study, the Impactor was operated at 320 rpm and the data from Stage A, which collected atmospheric particles greater than 6.5 µm aerodynamic diameter, was used to obtain total airborne coarse particle concentration. The mass median aerodynamic diameter (MMDa ) and standard geometric deviation are calculated for the coarse particle mass concentration distribution, based on the measurement of the mass on the four Impactor stages. Particles are impacted on coated Mylar film-strips. SAMPLING PROGRAM Thirty one atmospheric samples were taken from April to October 1992 (Table 1; Lin et al. 1994). Particle mass size distributions and downward and upward flux plate samples were collected simultaneously in two time periods: 8-hour daytime samples (approximately 0800 to 1600) and 16-hour nighttime samples (approximately 1600 to 0800). The collection of day and night samples allowed a wide range of atmospheric conditions to be evaluated because wind speeds during the day are generally higher than at night. Continental flow (westerly winds) and Lake flow (easterly winds) provided different sources and transport times for the collected particles. The downward flux plate data (on the upward facing plate surface) were previously used to evaluate the effect of wind speed on deposition velocity (Lin et al. 1994). Detailed information about count/mass conversion is described in Noll et al. (1988) and Lin et al. (1994). In the earlier work, the flux data for the upward facing plate surface was used to determine that dry deposition velocities for atmospheric particles in the size range of 5–100 µm in diameter were greater than those predicted by Stokes law and those predicted with the Sehmel-Hodgson deposition velocity model developed from wind tunnel experiments. In this study, we include new data from the upward flux plate (on the downward facing plate surface) (Lin 1991) for comparison to the downward flux plate data in order to evaluate the inertial deposition velocity. MODEL FOR DEPOSITION AND SUSPENSION VELOCITIES Particle downward (deposition) and upward (suspension) velocities were computed from simultaneous measurements of particle flux to the upper and lower surface of the flat plate surface

505

Night (10)

Day (21)

Lake (5)

Continental (10)

Lake (8)

Continental (13)

Sample category (n) 2 4 9 16 19 20 21 24 25 26 28 29 31 Avg. Dev. 1 3 6 8 10 11 12 15 Avg. Dev. 5 17 22 27 30 Avg. Dev. 7 13 14 18 23 Avg. Dev.

Sample ID 4.0 7.7 7.7 4.8 3.5 6.2 6.2 3.3 5.1 8.8 6.2 7.1 8.6 6.1 1.9 7.6 5.0 4.1 7.4 5.5 5.4 4.5 3.9 5.4 1.4 6.0 5.9 4.2 3.5 5.0 4.9 1.1 1.1 2.0 4.9 3.7 0.6 2.5 1.8

Wind Speed m/s 17.0 32.8 32.8 20.4 14.9 26.4 26.4 14.1 21.7 37.5 26.4 30.2 36.6 25.9 7.9 32.4 21.3 17.5 31.5 23.4 23.0 19.2 16.6 23.1 6.0 25.6 25.1 17.9 14.9 21.3 21.0 4.6 4.7 8.5 20.9 15.8 2.6 10.5 7.7

U∗ cm/s 2.1 9.5 15.7 5.5 2.7 5.3 3.5 4.1 4.2 10.6 5 5.3 6 6.1 3.8 2.8 1.9 2.9 7.7 7 1.5 3.7 4.3 4.0 2.3 5.4 3 2.6 1.9 2 3.0 1.4 0.8 1.9 1 1.9 1.4 1.4 0.5

Fdownward µg/s-m2 50 58 65 49 42 51 59 45 52 63 56 59 54 54.1 6.8 51 43 54 62 43 48 46 41 48.5 7.0 50 52 40 41 47 46.0 5.3 48 36 42 40 32 39.6 6.1

MMDFd µm

2.1 1.7 1.9 2 1.9

2 2 1.8 2.1 2

2 2 2.2 2 2 2 2.1 2.1

2.2 2.1 2.1 2 1.9 2.1 2 2 2 1.9 2 1.9 2.6

GSDFd 0.6 4.2 8.6 2.1 0.8 2.2 2.5 1.4 1.6 5.3 2.1 1.9 2.8 2.8 2.2 1 0.7 1 3.2 2.5 0.5 1 1.4 1.4 0.9 2.1 1.2 1.5 0.6 0.7 1.2 0.6 0.2 0.5 0.5 0.5 0.4 0.4 0.1

Fupward µg/s-m2 40 44 54 32 62 45 53 31 45 43 40 45 43 44.4 8.4 84 58 47 38 44 47 44 55 52.1 14.4 42 64 45 44 40 47.0 9.7 51 22 55 36 26 38.0 14.7

MMDFu µm

TABLE 1 Ambient particle concentration and dry deposition data by sampling categories

1.8 1.9 2 1.7 1.8

1.9 1.7 2 2 2.1

2.1 1.8 2 1.9 1.8 1.9 20 2.1

1.9 1.8 2 1.9 2.2 1.8 2 2.1 1.8 1.7 1.7 1.6 1.7

GSDFu 13.3 40.6 61.8 30.6 15.7 18.7 19.6 25.6 26.1 35 23.6 15.8 21.4 26.8 13.2 6.7 8.4 12.6 21.1 31.3 4.8 14.3 14.6 14.2 8.6 37.2 19.9 19.3 16.6 15.6 21.7 8.8 9.4 14.8 3 7.3 14.2 9.7 4.9

Conc µg/m3 25 41 55 21 21 40 30 22 24 34 22 25 25 29.6 10.3 27 21 21 33 22 33 24 29 26.3 5.0 26 23 24 19 21 22.6 2.7 19 19 25 23 18 20.8 3.0

MMDC µm

2.7 2.3 2.3 2.5 2.4

2.6 2.4 2.6 2.3 2.5

3.2 2.1 2.6 3.3 2.7 2.6 3.0 2.0

3.5 3.2 3.1 2.7 2.7 3.3 3.0 2.5 2.4 3.1 2.6 2.9 2.3

GSDC

506


and rotary impactor measurements of atmospheric concentrations of large particles as follows (Sehmel and Hodgson 1978): Fi = VIi Ci + Vgi Ci = [VIi + Vgi ]Ci

[1]

Fi is the particle deposition flux onto the upper or lower deposition plate for the size interval (i). Vgi , is gravity settling velocity, Ci is the measured atmospheric particle concentration from the rotary impactor for the size interval (i). The term Vgi Ci is associated with gravitational forces. VIi represents an additional velocity associated with the particle’s inertia (the particle “inertial velocity”). For the large particles considered in this study, both “eddy diffusion” and Brownian motion are not important compared to the inertial velocity. The effective particle downward (deposition) and upward (suspension) velocities for each particle size can be determined by dividing the simultaneous measurements of flux in each particle size interval by the ambient concentration in the interval. Specifically, Fdi Ci Fui Vui = Ci

Vdi =

[2] [3]

where Vdi and Vui are the particle velocities (cm/s) for particle size interval (i) to the upper and lower plate surfaces, respectively. Fdi and Fui are the particle mass flux (µg/m2 s) converted from the particle number count onto the deposition plate upper (downward flux) and lower (upward flux) surfaces and Q is the airborne mass concentration (µg/m3 ) for size interval (i) measured with the rotary impactor. Figure 1 provides an example of calculated velocities for the upper and lower plate surfaces for sample 25. The velocities result from both gravitational and inertial forces acting on the particles and are delineated by Equations (2) and (3).

The deposition and suspension velocities for each particle size, Vdi and Vui , are the turbulent particle mass transfer coefficients and can be determined from particle velocity measurements as follows: Vdi = Vgi + VIi (upper plate) Vdi = −Vgi + VIi (lowerplate)

[4] [5]

To evaluate the contribution of the inertial velocity, VIi , to these experimentally determined particle velocities to the upper and lower plate surfaces, Vdi and Vui , the contribution of the gravitational velocity Vgi , needs to be quantified. One can determine the experimental values of VIi and Vgi by adding and subtracting the two equations. In our observations, the deposition and suspension velocities consider the surface resistance of the quasi-laminar layer near the flux plate. Our results and those of other investigators (Kim et al. 2000; Slinn and Slinn 1980) suggest that for large particles in the atmosphere, it would be an acceptable approximation to assume that the velocities are rate limited by turbulent transport through the constant flux layer. These particles have large stop distances compared to the thickness of the laminar layer near the plate surface. This means that for large particles, there is an additional velocity toward the surface associated with the particle’s inertia and these particles easily penetrate the quasi-laminar layer and impact with the surface. Particle transport through the quasilaminar layer by eddy diffusion and Brownian motion is not important compared with particle inertial transport. Slinn and Slinn (1980) used data from the literature on jet collection efficiencies to develop an empirical expression for VIi : VIi = ηdi U∗

[6]

ηdi = 10−3/Stke

[7]

Vgi U∗2 gv

[8]

where

and Stke =

FIG. 1. An example of the deposition velocities derived from the measured ambient particle concentration and count converted mass deposition data with Equations (2) and (3) for sample #25. (The flux, mass data have been normalized in this figure.)

ηdi represents the particle effective inertial coefficient associated with the particle inertial velocity. Stke is the eddy Stokes number, g is gravity, and v is kinematic viscosity of air. Vgi /g is the particle relaxation time and therefore, Stke is related to particle momentum, where U∗ is friction velocity. The particle inertial velocity is a direct function of the degree of turbulence as measured by the friction velocity. The eddy Stokes number is an important parameter for evaluation of inertial velocities because it is a function of both particle momentum and friction velocity. It is also important that equations that use the eddy Stokes number such as Equation (7) satisfy the logical limit of unity for large particles and zero for small particles (Kim et al. 2000). Zero represents no inertial effects while one represents maximum inertial interaction between

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PARTICLE DEPOSITION AND SUSPENSION

the particles and the turbulence flow. The vertical turbulent velocity fluctuations that are associated with the particle’s inertial velocities have finite values that are related to the intensity of turbulence and may be defined by the friction velocity, and can be determined from the mean wind flow in the constant flux layer as follows: U∗ U= k ln(Z/Z0 )

[9]

where U is the mean wind speed, U∗ is friction velocity, κ is a constant, (The von Karman’s constant, approximately equal to 0.4), Z0 is the surface roughness, and Z is the height above ground where the wind speed is measured. U* and thus the inertial deposition velocity are larger for higher wind conditions compared to lower wind conditions. The equation has been found to be a very good approximation for quantifying the velocity profile in the turbulent region above many environmental interfaces far downwind of transitions in surface type. A common correlation for measured sea surface wind stress is U∗ = 0.037U where the average wind speed is measured at 10 m height above the water surface (Slinn and Slinn 1980). By application of this equation over land areas, it can be shown that vertical velocity fluctuations, as indicated by values of U∗ , are generally 3–10% of the mean wind speed depending on the surface roughness. COMPARISON OF PARTICLE STOP DISTANCE AND QUASI-LAMINAR LAYER THICKNESS The relaxation time T, and the stop distance Xo , can be used to characterize particle inertial impaction on the flux plate and are defined as (Noll 1999): T=

Vg g

Xo = TU∗ =

[10] V g U∗ g

[11]

Stke(ν) [12] U∗ The relaxation time characterizes the time that a particle requires to decrease its velocity by a factor of 1/e when subject to a new force, where e equals Euler’s constant. The stop distance is the distance a particle travels before it comes to rest when it is projected into a motionless fluid at the velocity U∗ . Particles with stop distances greater than the thickness of the quasi-laminar layer near the plate surface can easily penetrate the layer and be collected on the deposition plate. For comparison of the particle stop distance with the thickness of the laminar layer, we can consider the thickness of the quasi-laminar layer to be equal to the surface roughness height for the smooth collection plate (approximately 0.01 cm) (McCready 1986). Table 2 provides information on the stop distance as a function of eddy Stokes number using Equation (12). Based on the information in the table, the selection of a minimum value for the eddy Stokes number of 1 provides a stop distance that is equal to the thickness Xo =

TABLE 2 Stop distance as a function of eddy Stokes number Stke X0 (cm)

1 0.01

5 0.05

10 0.1

50 0.5

100 1

of the laminar layer. For particles with an eddy Stokes number larger than 1, it would be an acceptable approximation to assume that the deposition velocity is rate limited by turbulent transport through the constant flux layer because these particles have large stop distances compared to the quasi-laminar later. Because the boundary layer surface for the plate is considered to be small for large eddy Stokes numbers, the experimental velocities apply to airborne particles anywhere in the constant flux layer. Low friction velocities and small particle sizes produce eddy Stokes numbers that are less than one. One has to expect, therefore, that the flux under these conditions will be subject to significant resistance near the plate surface not considered in Equation (1) and therefore experimental velocities will be different than those in the constant flux layer. Three of the samples in Table 1 (7, 13, and 23) had eddy Stokes numbers that were less than one for all particle sizes due to low friction velocities and therefore were not considered in the evaluation process. As expected, for these 3 samples, the experimentally determined deposition velocities were significantly less than those predicted by Equations (7) and (8). For other samples, some of the smaller particle size intervals also had low friction velocities and were also excluded from the evaluation due to the resulting low stokes numbers. Also, negative values for the effective deposition velocities were obtained for some of the field observations and were also excluded from the evaluation process (∼5%). These negative values were obtained for the lower plate surface when Vg was larger than VI due to low friction velocities. COMPARISON OF MODEL PREDICTIONS WITH FIELD OBSERVATIONS To determine the magnitude of the experimental particle gravitational settling velocities and the particle inertial velocities in Equations (4) and (5) the equations can be subtracted and added. Experimental observations of Vgi , obtained by subtraction of Equations (4) and (5), were compared with theoretical values based on particle settling according to Stokes law in Figure 2. The particle size range between 5 and 100 µm diameter was divided into 14 intervals and each was assigned an appropriate Stokes settling velocity for comparison to the experimental data for the 28 samples in Table 1. A straight line was used to evaluate the data in Figure 2 to allow a visual demonstration of the variation between experimental data and Stokes law. Samples 7, 13, and 23 were not included in the evaluation due to low eddy Stokes numbers. Measurement errors associated with variations in particle density, shape, particle mass and particle count account for some of the variation shown in Figure 2. The correlation coefficient between the average data shown in the figure and the straight line is 0.88, demonstrating that the two values

508


FIG. 2. Comparison of the experimentally determined settling velocity (Vgi ) and theoretical Stokes settling velocity (VgT ), Average experimental settling velocity represented by the squares. The null hypothesis was accepted at the 95% confidence level for the data.

FIG. 4. Comparison of experimental inertial deposition velocity (VIi ) determined from adding Equations (4) and (5) with upward inertial deposition velocity (VIu ) from an equation similar to Equation (5) using theoretical Stokes settling velocity (VgT ) instead of experimental Stokes settling (Vgi ).

are similar. In order to avoid experimental errors as shown by the scatter of the data in the figure, theoretical settling velocities based on Stokes law settling were used in further evaluation of the inertial velocity and comparison with model predictions. Experimental inertial velocities were determined for 14 particle size intervals between 5 and 100 µm for each of the 28 samples in Table 1 by adding Equations (4) and (5). The experimental settling velocities were compared with inertial velocities to the upper (Figure 3) and lower plate (Figure 4) surfaces obtained using settling velocity determined from Stokes law as shown in Figure 2. The results demonstrate that values of VIi determined for the top surface are equal to VIi determined for the bottom surface. Using the null hypothesis that the means of the two normal distributions were equal, there was no significant difference in the two velocities at the 95% confidence level.

This supports the basic assumption that particles experience the same upward and downward inertial velocities near the top and bottom of the flux plate. From observed values of VIi and U∗ we were able to directly examine the relationship between the experimentally determined values of the particle effective inertial coefficient and eddy Stokes number using Equations (6) and (8). The inertial coefficients for specific size ranges determined from the experimental observations and calculated with Equation (6) were compared to the eddy Stokes number calculated with Equation (8) in Figure 5. The particle size range between 5 and 10 µm was divided into 14 intervals and each was assigned an appropriate value for ηdi and Stke. An exponential curve fit to the observed data that has the form of the relationship suggested by Equation (7), was obtained using robust regression (Venables and Ripley 1997)

FIG. 3. Comparison of experimental inertial deposition velocity (VIi ) determined from adding Equations (4) and (5) with downward inertial deposition velocity (VId ) from an equation similar to Equation (4) using theoretical Stokes settling velocity (VgT ) instead of experimental Stokes settling (Vgi ).

FIG. 5. Eddy inertial deposition efficiency determined from Equation (7) as a function of eddy Stokes number from Equation (8). Experimental settling velocity shown in Figure 1 was used in the calculations. Solid data points indicate data used in robust fit (see text).


509

and is shown in the figure. The equation that best fits the data for eddy Stokes numbers between 1 and 100 has a value of 3.3 for k: ηdi = 10−3.3/Stke

[13]

The equation has an upper limit of unity for large values of Stke as suggested by Slinn and Slinn (1980). Only eddy Stokes numbers of one or more were used in the analysis to assure a particle stop distance equal to the boundary layer as discussed earlier. The relationship between ηdi and particles Stokes number developed by Slinn and Slinn and presented in Equation (7) is also shown in Figure 5. The value of 3.3 for the experimental data is similar to k = 3 suggested by Slinn and Slinn. Therefore, this study provides experimental support for the use of the empirical relationship, between the inertial coefficient and eddy Stokes number suggested by Equations (6) and (8) to determination inertial velocities for airborne particles. Kim et al. (2000) obtained a value of 2.8 for k from simultaneous measurements of particle flux and airborne concentration in the open atmosphere using three different types of artificially generated particles in the size range 10–100 µm (also shown in Figure 5). This provides further verification of the general mathematical form for the dependence of inertial velocities on the eddy Stokes number and the use of Equations (6), (7), and (8). APPLICATION OF THE VERTICAL VELOCITY MODEL FOR DEPOSITION AND SUSPENSION OF AIRBORNE PARTICLES By adding and subtracting the gravitational settling velocity from the inertial velocity using Equations (4) and (5), one can obtain experimental deposition and suspension velocities to the upper and lower plate as a function of particle size and friction velocity. The comparisons between observed and modeled velocities using Equations (6), (7), and (8) are shown in Figures 6 and 7, respectively. Overall the model reproduced fairly well the observed velocities. Two noticeable features can be observed in these figures: first, vertical velocities are strongly dependent on particle size and friction velocity and vary from 1–100 cm/s for particles between 5 and 100 µm. Second, there is a large difference in the deposition and suspension velocities and in their variation with both particle size and friction velocity. Figures 6 and 7 show that even for relative small values of friction velocity, particles in the 10–100 µm size range can have inertial velocities that are comparable to gravitational settling and that the inertial velocities increase rapidly as the friction velocity increases. Also, the suspension velocities are quite similar to the deposition velocities for particles in the 10–50 µm size range for higher friction velocities. As shown in Figure 6, deposition velocities that include both inertial and gravity settling can increase by an order of magnitude from those that include only gravity settling for particles in the 10–100 µm size range (Noll and Fang 1989; Noll et al.

FIG. 6. Model calculated deposition velocities Vdi Equation (4) to the upper surface of the deposition plate as a function of particle size and friction velocity using theoretical Stokes settling velocities. Inertial velocity was determined from Equations (6), (7), and (8) with a k value of 3. Experimental data was determined from Table 1 and Equation (2).

2001). This is especially true for high wind speed conditions when there is significant additional turbulence as represented by large values of friction velocity. Based on this observation, one would expect that all large particles would rapidly settle out of the atmosphere. However, the suspension velocities shown in Figure 7 have a maximum in the 10–50 µm size range depending on friction velocity and their magnitude is quite similar to the deposition velocities. The large suspension velocities shown in Figure 7, will promote the ability of some particles in the 10–50 µm size range to remain suspended in the atmosphere (counteracting gravity) and this will lead to longer atmospheric residence times and transport distances for these particles. Not considering both the suspension velocity as well as the deposition velocities of large, airborne particles can provide a very inaccurate estimate of the carrying capacity of the atmosphere and therefore the availability of large particles for long range transport. Results for even larger particles (50–100 µm) that are characteristic of source area wind erosion do not have large upward velocities

510


FIG. 7. Model calculated suspension velocities Vui Equation (5) to the lower surface of the deposition plate as a function of particle size and friction velocity using theoretical Stokes settling velocities. Inertial velocity was determined from Equations (6), (7), and (8) with a k value of 3. Experimental data was determined from Table 1 and Equation (3).

except under very high wind conditions are therefore short lived and are generally not capable of being transported over long distances except under high wind conditions (Gillette et al. 1978). For particles larger than 100 µm, gravitational settling velocities can be used to estimate effective velocities because Figure 6 shows that inertial deposition velocities are small in comparison with gravity settling velocities. There are several well-documented cases where the atmosphere transport of Saharan large dust particles over distances of several thousand kilometers has been evident (Prospero et al. 1970, Jaenicke and Schutz 1977; Schutz 1979). These large particles are observed far from their source regions despite their very high dry deposition velocities. As an example, the dry deposition velocity of particles of 20 µm diameter with a friction velocity of 20 cm/s is near 7 cm/s [Figure 6 or Equation (2)] and implies a downward transport of about 6000 m/day that should prevent them from being transported long distances. Since these particles are found far from their source areas, suspension velocities could be providing a significant counteract-

ing process that allows some of them to remain suspended in the atmosphere. As another example, Dulac et al. (1991) measured an apparent downward transfer velocity of the order of 1 cm/s for transport of African dust over the western Mediterranean (based on column mass loading), while dry deposition and aerosol sampling yielded a much higher dry deposition velocity of 7.7 cm/s. He attributed the difference to vertical upward synoptic movements of air masses that lifted particles to higher attitudes, making them available for long range transport. This indicates that another important characteristic of the atmosphere that affects particle transport is the temperature structure of the atmosphere, along with atmospheric divergence and convergence conditions. During convective conditions, particles can be carried to higher levels and transported farther than their sizes would suggest. Consequently, large airborne particles may experience synoptic upward movements as well as those due to eddy fluctuations. A number of investigators (Prospero and Carson 1972; Gillete 1977; Jaenicke and Schutz 1977; Rahn et al. 1979; Noll and Fang 1989; Dulac et al. 1991) have elucidated the dynamic nature of the size distribution of large particles. The maximum in the mass size distribution for large particles has been demonstrated to be in the 10–50 µm size range depending on the distance from the sources and the degree of turbulence (Schutz 1979; Noll and Fang 1989). This is confirmed in Figure 8 where the MMD for the size distributions in this study are in the 10–50 µm size range and are shown to be related to the fiction velocity. There is a general shift to larger sizes for higher friction velocities. This is an indication of the ability of large particles to remain suspended in the atmosphere under higher turbulent conditions due to an increase in the suspension velocity. However a detailed evaluation of the mechanism for transport of large particles needs to consider horizontal transport by wind as well as sedimentation and suspension transport by vertical velocity fluctuations. This is because airborne size distributions are derived from the original source by processes controlled

FIG. 8. Comparison of mass median diameter (MMD) of atmospheric coarse particles as a function of friction velocities from Table 1.

511


TABLE 3 Sensitivity of ηdi , Vdi and Vui % change in ηdi

% change in Deposition Velocity Vdi

% change in Suspension Velocity Vui

da

10 µm

30 µm

100 µm

10 µm

30 µm

100 µm

10 µm

30 µm

100 µm

10% increase of U∗ k Zo ρp

38.5 −17.1 3.8 28.5

3.7 −2.1 0.4 3.7

0.3 −0.2 0.04 0.3

46.3 −15.1 4.3 26.5

11.5 −1.7 1.2 6.8

3.4 −0.1 0.4 14.2

60.2 −19.7 5.6 31.1

18.1 −2.7 1.9 −1.3

−9.9 0.2 −1.0 30.8

10% decrease of U∗ k Zo ρp

−35.6 20.6 −4.1 −35.6

−4.8 2.1 −0.5 −4.8

−0.4 0.2 −0.04 −0.4

−37.2 18.2 −4.6 −23.7

−11.7 1.7 −1.3 −7.4

−3.4 0.1 −0.4 −12.9

−48.4 23.7 −5.9 −28.1

−18.4 2.7 −2.0 −0.7

10.0 −0.2 1.1 −26.8

Initial value for U∗ = 30 cm/s. Initial value for k = 3. Initial value for Zo = 0.001 m. Initial value for pp = 1.0 g/cm3 .

by the interaction between emission, airborne transport, gravity settling, and vertical velocity fluctuations (Gillette and Blifford 1972).

tive error for concentration measurements for larger particles depends on the particle size (B Stage—65%, C stage—57%, D stage—11%).

SENSITIVITY ANALYSIS FOR THE LARGE PARTICLE DEPOSITION MODEL The sensitivity of eddy deposition efficiency, as well as deposition and suspension velocities to the experimental parameters used in this study are summarized in Table 3. These results are based on Equations (6), (7), and (8) and show that the experimental parameters are most sensitive to the friction velocities and that the sensitivities decrease with increasing particle size. As particle size increases, gravitation forces become increasing important relative to inertial effects and results are relatively insensitive to changes in all of the experimental parameters. The relative insensitivity of results to changes in the exponent k in Equation (7) is important because the experimental values were between 2.8 and 3.3 and we assumed a general literature value for k of 3. Figure 1 indicates that the flux to the upper and lower plate surfaces is controlled by particles at the large end of the size distribution where results are relatively insensitive to variations in the exact values of the experimental parameters. Experimental errors for individual particle size intervals contributed to the highly variable results as indicated by Figures 2 to 5. Based on the theory of error propagation, the maximum relative error for measurement of atmospheric particle concentration for the NRI A stage (6.5–11.5 µm size range) can be as large as 200% (Zhang 1998). Higher mass loadings produce smaller errors (typically 50–80%). The maximum rela-

CONCLUSIONS Size specific parameterizations for upward and downward large particle velocities in the turbulent atmosphere have been determined based on an extensive field-sampling program involving diverse sources (lake/land) and transport times (day/night). The results are compared with empirical models developed by other investigators. Overall, the modeled results are in accordance with experimental observations. As shown in Figure 6, deposition velocities that include both inertial and gravity settling can increase by an order of magnitude from those that include only gravity settling. For these particles, Stokes law is not adequate to describe deposition velocities, thus an enhancement term is required as suggested by earlier work (Noll and Fang 1989; Lin et al. 1994; Noll et al. 2001). Experimental results for individual particle size intervals produced highly variable results as indicated by Figures 2 to 5. Much of this variation can be attributed to experimental errors associated with the nature of the atmospheric experiments and not to problems with the model. However, it is clear that application of the model to the constant flux layer represents only a first-order approximation because the mechanisms of transport, deposition, and suspension are complex and thus the processes are not able to be modeled at the most fundamental level. Both modeled and observed results for higher wind speeds suggest that suspension velocities provide the opportunity for

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large, airborne particles to remain suspended and counteract gravity (Noll and Fang 1989). This can promote their ability for long range transport. Upward large particle velocities are similar in magnitude to downward velocities at higher wind speeds and represent a counteracting process to downward deposition processes that cannot be ignored for accurate representation of the long-range transport for particles between 10 and 50 µm diameter.

ABBREVIATIONS AND NOTATIONS Ci airborne coarse particle concentration in particle size interval i (µg/m3 ) da aerodynamic diameter (µm) de equivalent volume diameter (µm) particle diameter (µm) dp dPA projected area diameter (µm) F mass flux of deposited particle (µg/m2 s) Fi mass flux of deposited particle in size interval i (µg/m2 s) Fd mass flux of deposited particle to the top of the deposition plate (µg/m2 s) mass flux of deposited particle to the bottom of the Fu deposition plate (µg/m2 s) g gravitational acceleration (cm/s2 ) GSD geometric standard deviation of atmospheric coarse particle size distribution κ Von Karman’s constant (0.4) MMDa mass median aerodynamic diameter of atmospheric coarse particle (µm) SD dynamic shape factor Sν volume shape factor Stke eddy Stokes number T relaxation time (s) U average wind speed at height Z (cm/s) U∗ friction velocity (cm/s) Vd particle deposition velocity to the top of the deposition plate (cm/s) Vdi average particle deposition velocity to the top of the deposition plate in particle size interval i (cm/s) Vgi average particle gravitational settling velocity in particle size interval i (cm/s) VgT theoretical gravitational settling velocity (cm/s) VIi average particle inertial deposition velocity in particle size interval i (cm/s) VId downward inertial deposition velocity (cm/s) upward inertial deposition velocity (cm/s) VIu Vu particle suspension velocity to the top of the deposition plate (cm/s) Vui average particle suspension velocity to the bottom of the deposition plate in particle size interval i (cm/s) Xo stop distance (cm) Z height of wind speed measurement (m) Zo surface roughness (m)

Greek ηdi ν

particle effective inertial coefficient in particle size interval i kinematic viscosity of air (cm2 /s)

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