PHASE-SPACE DIFFUSION EQUATIONS FOR SINGLE BROWNIAN PARTICLE MOTION NEAR SURFACES
Titel:
PHASE-SPACE DIFFUSION EQUATIONS FOR SINGLE BROWNIAN PARTICLE MOTION NEAR SURFACES
Auteur:
Peters, Michael H. Ying, Ruoxian
Verschenen in:
Chemical engineering communications
Paginering:
Jaargang 108 (1991) nr. 1 pagina's 165-184
Jaar:
1991
Inhoud:
In numerous physical processes involving the motion of micron and submicron sized particles near surfaces, such as the filtration of hydrosols and aerosols, the particle motion is the net result of the combined effects of fluid convection, external forces, particle inertia, Brownian particle motion, and particle-surface fluid dynamic interactions. The most general method of describing particle motion under the combined action of these effects is through the so-called Fokker-Planck equation. In the absence of particle-surface fluid dynamic interactions, the Fokker-Planck equation is well-known, and it has been applied in a general way to problems involving the adsorption or deposition of Brownian particles onto surfaces through a solution technique known as the Brownian dynamics simulation method. In this study, the Fokker-Planck equation for Brownian particle motion near surfaces is generalized to include particle-surface fluid dynamic interactions. The Fokker-Planck equation is shown to follow from the Liouville equation for the Brownian particle and n-fluid molecules present in the system, thus, establishing a firm theoretical foundation for the Fokker-Planck equation and the various other phase-space diffusion equations that follow from it. Based on diagonalization of the Fokker-Planck equation, its short-time behavior is also derived here which enables a generalization of the Brownian dynamics method for the study of particle motion near surfaces including fluid dynamic interactions. Additionally, a perturbation solution of the Fokker-Planck equation under the conditions of small, but finite particle Stokes number is also derived. These solutions are shown to agree with previously given representations of the Smoluchowski or convective-diffusion equation for Brownian particle motion near surfaces, as well as with inertial corrections to the Smoluchowski equation available in the literature. This latter equation is also generalized here to include particle-surface fluid dynamic interactions.
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