Coagulation of aerosol particles in the free-molecule regime: regime has been studied theoretically by converting the nr governing partial integrodifferential equation into a set oftwo ordinary differential equations. The approach asNffi (Y7rln2) sumes that the s u e distribution of an aerosol attains or can at least be represented by a time-dependent lognorwhere n is the particle size distribution functi0n, Nm is mal distribution function during the coagulation process. the total number of particles, r is the particle radius, andThe calculations haye been performed and the results rgm is the geometric Itlean particle radius. In the found to be in good agreement with results for previous parameters used by the self-preserving sue distribution theories. In addition, the following asymptotic size distrithe proposed distribution is written bution function is found as an alternative solution for the self-preserving particle size distribution function forBrownian coagulation of an aerosol in the free-molecule ( Y r l n 2 )

b The Kuwabara flow model in a system of multiple spheres is used to predict the collection of aerosol particles from flow through a packed bed. Diffusional and interceptional collection efficiencies are predicted by a theoretical procedure which was derived using a boundary layer approach accounting for the flow interference effects of neighboring collecting spheres in packed beds. The results were compared with available experimental data and satisfactory agreement was obtained.Packed beds have been used widely for many industrial operations such as absorption, adsorption, and distillation due to their large contact area between gas phase and solid media or between liquid and solid. Recently there has been increasing interest in employing the packed bed concept for removing aerosol particles. A major advantage of aerosol filtration by packed beds is that by selecting the proper bed media, both particulate and gaseous pollutants can be simultaneously collected, the particulates removed by filtration, and the gases removed by adsorption. The possibilities for using packed beds a t high temperatures and pressures also make their development more attractive.It is well known that in packed beds consisting of fine media and operating a t a low flow rate, small particles are collected primarily by Brownian diffusion. As particle size increases, direct interception and gravitational settling become important. Eventually, inertial impaction will dominate if particle size and flow rate are further increased.In filtration study, it is first necessary to understand flow field inside the filter media. For packed beds, the individual collectors or granules either have or can be assumed to have a spherical or nearly spherical shape. These individual granules or spheres are closely packed together and the mutual interference effects of neighboring spheres on the flow field have to be taken into consideration. However, most previous theoretical studies such as those by Fuchs ( I ) and by Friedlander ( 2 ) are based on the model of an isolated sphere collector. It is therefore necessary to employ an additional empirical correction factor when these results are to be applied to packed beds. Consequently, many theoretical studies of aerosol filtration that are based on an improved model have been reported recently (3-7).A single sphere efficiency may be defined as the ratio of the cross-sectional circular area surrounded by limiting streamlines of the flow approaching the collecting sphere to the projected area of the sphere. The limiting streamlines are such that all the particles passing within them will be collected by the sphere while all the particles outside the streamlines will escape it. With this representation, the concentration ratio of the particles collected inside the packed bed to those approaching it, or the overall efficiency of particle collection by the bed, can be shown to relate to the single sphere efficiency as follows:(1)where E = overall collection efficiency of packed bed, 7 = single sphere efficiency, L ...

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