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- W201640460 abstract "The original proposal for this work suggested two lines Of analysis that could be used to develop an hierarchical analysis of filtration. The first of these was semi-empirical and required the use of an angle-dependent rate coefficient to model the effect of particle inertia, while the second made use of a particle velocity decomposition that separated the velocity into an inertial part and a diffusive part. We have concluded that the semiempirical approach cannot lead to an efficient treatment of the filtration problem, and in this study we have dirrcted most of our effort toward the development of the velocity decomposition approach. Problems arise with the velocity decomposition method because the panicle tracking equation is hyperbolic in nature, and there are regions in the flow field where it is difficult to calculate the deterministic particle velocity. These problems can be avoided with an asymptotic analysis, and we have used this approach to determine single fiber efficiencies for small Stokes numbers. These efficiencies illustrate a minimum as a function of the particle diameter; however, the range of validity (in terms of the Stokes number) of the asymptotic method is uncertain. If the range of validity of the asymptotic expansion is suitable for the solution of practical problems, the current work on homogeneous filters should be expanded to included a broader range of values of the key parameters and then extended to include the case of heterogeneous filters. If the range of validity of the asymptotic method is not suitable for the solution of practical problems, the particle tracking problem must be resolved or we must move on to the use of Brownian dynamics. This approach is outlined, where we have indicated how Brownian dynamics may be incorporated into the method of volume averaging." @default.
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- W201640460 date "1993-07-01" @default.
- W201640460 modified "2023-09-25" @default.
- W201640460 title "Hierarchical analysis of filtration. Progress report" @default.
- W201640460 doi "https://doi.org/10.2172/10184956" @default.
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