In addition, the deposition velocity was observed to increase with increasing roughness grade, albeit the increments with increasing surface roughness were not as significant as the influence of particle size on deposition. Surface Temperature: Warm vs. Cold As discussed in Section 3. In the presence of a temperature gradient, particles always move toward the direction of lower temperature. As a consequence, particles tend to preferentially deposit onto a cold surface over a warm one due to thermophoresis. Numerous experimental studies have examined the effectiveness of exploiting thermophoresis to minimize particle deposition on silicon wafers for microcontamination control [17 19].
However, experimental data for particle deposition on cold and warm surfaces with respect to an enclosed volume are sparse. The experiments performed by Thatcher et al. The deposition velocity predicted theoretically by Nazaroff and Cass [24,68] was also plotted for comparison. Depo sition velocities predicted theoretically by Nazaroff and Cass [24,68] for a vertical isolated flat surface are also plotted for comparison.
Each diamond symbol represents the average value obtained by 10 local surface extractions over the central portion of the cool or the warm wall from a single experiment. The asterisk denotes that the deposited particle mass was under the detection limit. Reprinted with permission from Thatcher et al. On the other hand, the measured deposition velocities to the cool and warm walls for larger particles 1.
Furthermore, for particles larger than 0. This observation is counterintuitive since the warmer surface is anticipated to enhance thermophoretic repulsion, thus reducing particle deposition. In summary, the deposition velocity determined experimentally in Thatcher et al.
In contrast, the deposition velocity to the warm wall obtained in the experiments appears to be much higher than predicted, particularly for increasing particle size. The discrepancy between experimental findings and theoretical predictions may be attributed to the fact that the existing model does not account for all the factors influencing particle deposition under the settings of the experiments. The surface-to-air temperature difference influences not only particle thermophoretic velocity, but also the near-surface airflow pattern, which further introduces more complexities toward the understanding of the deposition processes.
The complicated airflow pattern and flow instability in their chamber experiments are believed to play a role in contributing to the variations of the deposition velocity measurements. Other factors such as particle inertia and the effect of corners on airflow not being addressed in the model may be of importance to influence the deposition process. In the Presence of an Electric Field Electrostatic forces may play an important role in influencing particle deposition. When the interior surface of an enclosed volume has the tendency to acquire electrostatic charge e.
McMurry and Rader  demonstrated in their 60 m3 Teflon chamber experiments under natural convection that the enhanced deposition for 0. In another set of Teflon film bag L experiments, the deposition rates of singly charged particles could be significantly increased as compared to particles at Boltzmann distribution , as shown by the symbols V and ; in Figure 1.
For instance, a nearly 30 times deposition enhancement was observed for the 0. In addition, their experimental data indicated that the 9 As mentioned in Section 3. E electric field strength on the chamber interior surface and the parameter of airflow turbulence intensity respectively. Note that the experimental data exceeded predicted values for 0. Reprinted with permission from McMurry and Rader . The laboratory results agreed satisfactorily with their model, which incorporated electrostatic drift as an additional transport mechanism.
As explained in the model, deposition for particles larger than 1 mm and smaller than 0. Shimada et al. They found no difference in deposition rates for charged and uncharged particles when the surfaces were grounded.
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As the electric field strength increased, however, the enhancements of particle deposition rates were observed, as indicated in Figure 1. By directly collecting particle deposition mass onto vertical surfaces in a 1. The electrostatic attractions in Shimada et al. The first type, as will be discussed in Sections 7. One key challenge in this modeling approach lies in the determination of the near-surface particle eddy diffusivity, which is postulated to be related to the air turbulence intensity within the enclosure as well as the distance to the wall.
The second type of modeling Particle Deposition onto Enclosure Surfaces 33 approach, as will be described in Section 7. In this section, the modeling developments based on these two approaches for predicting particle deposition rates in enclosures are summarized, together with the available experimental investigations to compare against the modeling analyses as well as the limitations associated with these models.
Developments in Surface Contamination and Cleaning: Methods for Surface Cleaning
Homogeneous Turbulence Model Modeling efforts for studying particle deposition from turbulent flow onto enclosure surfaces were initiated in the early s. Corner and Pendlebury  developed the first theoretical model accounting for particle deposition onto the surfaces of horizontal and vertical orientations in a rectangular enclosure where the air was homogeneously turbulent.
Their model was derived based on the following key assumptions: 1 the air outside the boundary layer is homogeneously turbulent and aerosol concentration is uniform as illustrated in Figure 1. The particle concentration profile in the boundary layer can thus be solved from 34 Developments in Surface Contamination and Cleaning equations 21 and There is no a priori way to estimate the values of ke with available data; hence it is usually determined empirically by fitting experimental data into the theory.
Following the seminal work of Corner and Pendlebury , several additional model extensions have been proposed. Crump and Seinfeld  derived expressions for estimating particle deposition rate in an enclosure of arbitrary shape, and the analytical solutions for a spherical vessel were specifically formulated. They showed that, in an enclosure having only horizontal and vertical surfaces, the transport processes of gravitational settling and diffusion can be treated independently by vectorially summing the gravitational settling velocity to the deposition velocity associated with the diffusion process.
For the inclined surfaces of a sphere, however, their derivations indicated that these two mechanisms are always intimately coupled to each other and cannot be separated. They proposed that the value of ke can be evaluated from the fluid energy dissipation rate, instead of velocity gradient in the boundary layer as suggested in Corner and Pendlebury . Particle Deposition onto Enclosure Surfaces 35 To validate their own theoretical derivations, Crump et al. Based on the existing model developed by Crump and Seinfeld , McMurry and Rader  incorporated electrostatic effects as an additional particle deposition mechanism to evaluate the particle deposition rate in an enclosure.
Experiments were also performed to measure the deposition rate of neutral and singly charged aerosols in a L Teflon bag and a 60 m3 Teflon smog chamber respectively. The turbulence intensity parameter ke in their experiments was calculated by the average energy dissipation rate per unit mass of air, and the parameters k and n were obtained by fitting the experimental data. The experimental deposition rates compared well with the model calculations by Crump and Seinfeld  when the eddy diffusivity was assumed to be proportional to the 2.
In addition, more deviations from the model were observed for increasing particle size or flow turbulence intensity, and this is likely attributed to effects of enhanced particle inertia, which were not considered in the model. Cheng  measured the particle deposition rates of monodisperse particles ranging from 0. Both the chamber temperature and air velocity profiles under various turbulence conditions were measured. The turbulence intensity in the experiments evaluated using both methods, including the velocity gradient as shown in equation 24 and energy dissipation rate [23,75], gave reasonable estimates of ke as well as the particle deposition rates.
The symbol 3 refers to the turbulence energy dissipation rate and n is the kinematic viscosity of the fluid. Their analysis showed that, as particle size increases, an increasingly pronounced difference in deposition velocity is predicted for the vertical warm relative to the cool walls. The experimental findings in Thatcher et al.
In summary, the existing experimental data agree reasonably well with the theory of Corner and Pendlebury , including its extensions. However, there are still some issues that must be carefully examined before applying the model to various scenarios.
For example, can ke and n be determined in any particular enclosure, without resorting to fitting the results of sophisticated particle deposition experiments? These two parameters are key and vary with experimental conditions; they ultimately influence the magnitude of the particle eddy diffusivity 3p, which directly affects the calculation of deposition rate and flux to the surface. This is also supported by some experimental data [45,70,74]. Using this new expression has shown to yield good agreements with data from one experimental study .
However, it remains unresolved with respect to the evaluation method for n. Nevertheless, Crump and Seinfeld  noted that the choice of n value is of little importance from the standpoint of their theoretical derivations. Van Dingenen et al.
Developments in Surface Contamination and Cleaning - 1st Edition
Commonly known as the law of the wall, a turbulent boundary layer consists of three distinct zones according to the velocity distribution as a function of the distance perpendicular to the wall . The approach used by Lai and Nazaroff  to analyze particle deposition from turbulent flow is to examine the turbulent flow structure zone by zone, and to formulate particle transport equations for each zone, assuming 1 gravitational settling, Brownian and turbulent diffusion are responsible for the particle deposition processes; 2 constant particle flux in the concentration boundary layer; 3 particle eddy diffusivity is well represented by fluid turbulent viscosity; and 4 negligible surface roughness effects.
Across the boundary layer, the expression for the deposition velocity was then integrated for each zone. The deposition velocity was evaluated for vertical, upward, and downward horizontal surfaces, and the firstorder deposition rates were derived for rectangular and spherical cavities respectively. This approach is somewhat complicated but remains practical to use. Their model predictions compared well with published experimental data for deposition of 0.
It is expected that the analogy between heat and mass transfer should hold when particle inertia is insignificant.
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Lai and Nazaroff  performed laboratory experiments to measure deposition of 0. The experimentally measured particle deposition velocities for 9 mm particles were higher by a factor of 30 as compared to their own model predictions for friction velocities of 2. The chamber walls were grounded, thus electrostatic force was considered negligible.
For smaller particles, the integration must be carried out numerically. See the following for results: Particle diameter, dp mm Integral, I 0. Reprinted with permission from Lai and Nazaroff . For example, particle inertia and shear-induced lift force11 are postulated to be potentially important players to enhance transport of larger particles through the relatively thin boundary layers and lead to subsequent surface deposition. Lai  later incorporated the mechanism of particle inertia into the three-layer model, by adopting the commonly accepted electrical resistance analogy in atmospheric dry deposition modeling , to simulate supermicron particle deposition from turbulent flow to a vertical surface.
Treating the frictionvelocity as the fitting parameter and incorporating analyses accounting for surface roughness effects , the agreements between experimental data and modeling calculations were good for smooth surfaces, but less satisfactory for rough surfaces. The influence of electrostatic drift was considered as an additional particle deposition mechanism in the inertia-incorporated three-layer model by Chen and Lai .
The experimental findings involved with electrostatic effects in Lai  again demonstrated that the particle deposition is a complicated 11 A particle in a shear flow field may experience a lift force perpendicular to the main flow direction.
This life force arises owing to particle inertia and is important for large particles.
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