Particle deposition, rates

In the general case, when arbitrary interaction profiles prevail, the particle deposition rate must be obtained by solving the complete transport equations. The first numerical solution of the complete convective diffusional transport equations, including London-van der Waals attraction, gravity, Brownian diffusion and the complete hydrodynamical interactions, was obtained for a spherical collector [89]. Soon after, numerical solutions were obtained for a panoplea of other collector geometries... 

To analyze the dynamic behavior of gas-solid pipe flows, the most common and easiest system to consider is a dilute gas-solid pipe flow which is fully developed and is subject to the effects of electrostatic force and gravitational force. The fully developed flow here refers to the situation where the velocity profiles of both gas and particles are unchanged along the axial direction. The system of this nature was analyzed by Soo and Tung (1971). In this section, the analysis of Soo and Tung (1971) is presented. It is assumed that no particles are deposited on the wall surface of the pipe (or the particle deposition rate is zero). Moreover, the pipe flow is considered to be turbulent, as is true for most flow conditions. 

Using a one-dimensional Monte Carlo analysis to estimate population exposure and dose uncertainty distributions for particulate matter, where model inputs and parameters (e.g. ambient concentrations, indoor particulate matter emission rates from environmental tobacco smoke, indoor air exchange rates, building penetration values, particle deposition rates) are represented probabilistically with distributions statistically fitted to all available relevant data. 

The nature of the current density dependence of particle codeposition is the most disputed aspect in the mechanism of composite plating (Section IV). In the simplest case the particle deposition rate is not affected by the current density, either because of particle mass transfer limitations or a current density independent particle-electrode interaction. Since the metal deposition rate increases with current density, this results in a continuously decreasing particle composite content. In other cases the particle-electrode interaction has to be current density dependent. An unambiguous explanation for this dependence has not yet been found, but it is apparent that the metal deposition behavior is involved. 

Despite these successes, important process parameters, like bath agitation, bath constituents and particle type are disregarded. The constants k, 0 and B inherently account for these constants, but they have to be determined separately for every set of process parameters. Moreover, the postulated current density dependence of the particle deposition rate, that is Eq. (2), is not correct. A peak in the current density against the particle composite content curve, as often observed (Section III.3.H), can not be described. The fact that the peak is often accompanied by a kink in the polarization curve indicates that also the metal deposition behavior can not be accounted for by the Tafel equation (Eq. 4). Likewise, the (1-0 term in this equation signifies a polarization of the metal deposition reaction, whereas frequently the opposite is observed (Section 111.3,(0 It can be concluded that Guglielmi s mechanism... 

Kariapper and Foster derived a simple model considering the effect of several process parameters. The particle deposition rate is again defined as a Langmuir adsorption isotherm, where the measure of the particle cathode interaction k depends on ... 

Taking N as the number of particle collisions with the cathode suitable for particle incorporation, which is affected by the agitation rate, the particle deposition rate is given by ... 

In the intermediate current density range the particle deposition rate due to H+ reduction is at its limiting value VpJ -, whereas the contribution of the metal reduction is similar to that of H+ in the low current density range. Consequently, the equation for Vp in this range is given by ... 

Next the difficulties in obtaining a good description of the particle electrode interaction are noticed. For non-electrochemical systems several particle surface interaction models exist of which the perfect sink , that is all particles arriving within a critical distance of the electrode are captured, is the simplest one. However, the perfect sink condition can not be used, because it predicts a continuous increase in particle codeposition with increasing current density, which contradicts experimental observations. Therefore, an interaction model based on the assumption that the reduction of adsorbed ions is the determining factor for particle deposition is proposed. This electrode-ion-particle electron transfer (EIPET) model leads to a Butler-Volmer like expression for the particle deposition rate ... 

In what follows, the equation of diffusion derived in Chapter 2 is generalized to take into account the effect of flow. For point particles (dp = 0), rates of convective diffusion can often be predicted from theory or from experiment with aqueous solutions because the Schmidt numbers are of the same order of magnitude. There is an extensive literature on this subject to which the reader is directed. For particle diffusion, there is a difference from the usual theory of convective diffusion because of the special boundary condition The concentration vanishes at a distance of one particle radius from the surface. This has a very large effect on particle deposition rates and causes considerable difficulty in the mathematical theory. As discussed in this chapter, the theory can be simplified by incorporating the particle radius in the diffusion boundary condition. 

A duct 4 ft in diameter with a 90 bend has been designed to carry particles In the range I < dp < 20 which adhere when they strike the wall. Before construction, it is proposed to carry out bench scale experiments to determine the particle deposition rate in the bend. The model is to be built to 1/10 scale, and the same aerosol will be used as in the full-scale system, Show that it is not pos.siblc to ntainlain both Stokes and Reynolds number similarity in the full-scale and model systems. If Stokes similarity is to be preserved, calculate the Reynolds number ratio for the model to full-scale systems. Why is it more important to preserve Stokes than Reynolds similarity in such experiments ... 

The particle deposition rate is independent of po.sition on the surface as long as the boundary layer is laminar. By attaching an electron micrograph grid to the surface, a sample can be collected for examination under the electron microscope. If the atmospheric concentration is 10 particies/cm, determine the sampling time necessary to have 10 particles in an area 100 on a side. The speed of rotation is 20,000 rpm and the temperature is 20"C. To simplify the calculation, assume the particle size is 0.05 fim. (For an application of this method,. see Pasceri and Friedlander, 1965),... 

Scranton, M. 1., W. R. Barger, and F. L. Herr (1980). Molecular hydrogen in the urban troposphere measurements of seasonal variability. J. Geophys. Res. 85, 5575-5580. Sehmel, G. A., and S. L. Sutter (1974). Particle deposition rates on a water surface as a function of particle diameter and air velocity. J. Rech. Atmos. 8, 911-918. 

Park, H.M. and Rosner, D.E., 1989b, Combined inertial and thermophoretic effects on particle deposition rates in highly loaded dusty gas streams. Chem. Eng. Sci. 44, 2233 - 2244. 

The dynamic model of Figure 7 can be used to illustrate the impact of water depth on the response of the sediment to changes in trace element supply. The effects on the sediment composition are illnstrated of five year episodes of doubled trace element supply rate (Fig. 8a), doubled particle deposition rate (Fig. 8b) and doubled (Fig. 8c), for different combinations of water depth and initial Ka-... 

The insensitivity of the sediment record of deep lakes to changes in trace element supply, does not mean that the trace element concentration profile in the sediment cannot show sharp changes. A change in the particle deposition rate will cause an instantaneous change in sediment composition through dilution. However, for deep lakes, particularly for low Kd values, this dilution effect is reduced by the high water column trace element inventory (Fig, 8b). This means that in deep lakes it is important not to infer external trace element supply simply using sediment trace element accumulation rates. 

Particle transport through boundary layers in the presence of thermophoretic and electric forces is complex but predictable [5]. For coarse particles, thermophoretic and electric forces can usually be ignored. For fine particles, they can be very important. If the material to be tested is expected to exist in the field at >10°C cooler or warmer than the ambient, or if the surface is expected to be >100 V above or below ground potential, these effects need to be considered. Cool surfaces increase the particle deposition rate while warm surfaces decrease it (analogous to condensation but for different reasons). Experience has shown that surfaces biased at a few hundred volts can collect fine particles at >5 times the rate of grounded surfaces. 

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