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A generalized Fokker-Planck equation for particle transport in random media

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  • Swailes, David C.
  • Darbyshire, Kirsty F.F.

Abstract

A transport equation is derived for the probability density function (pdf) that gives the phase-space distribution of a particle moving in a random medium: the motion of the particle is determined by a general second-order stochastic differential equation that models transport in a medium exhibiting correlated fluctuations in both space and time. The derivation makes use of cumulant expansions and functional calculus. The most general form of the transport equation requires closure, and a simple closure approximation is discussed. No closure approximation is necessary when the stochastic component of the particle equation of motion is a correlated Gaussian process, and results for transport in an unbounded medium are derived for this exact case. These results are consistent with other studies and serve to validate the model.

Suggested Citation

  • Swailes, David C. & Darbyshire, Kirsty F.F., 1997. "A generalized Fokker-Planck equation for particle transport in random media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 38-48.
    • Handle: RePEc:eee:phsmap:v:242:y:1997:i:1:p:38-48
    DOI: 10.1016/S0378-4371(97)00195-7
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    Cited by:

    1. Swailes, D.C. & Sergeev, Y.A. & Parker, A., 1998. "Chapman–Enskog closure approximation in the kinetic theory of dilute turbulent gas-particulate suspensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(3), pages 517-547.
    2. Aleksey Yu. Varaksin & Sergei V. Ryzhkov, 2023. "Mathematical Modeling of Gas-Solid Two-Phase Flows: Problems, Achievements and Perspectives (A Review)," Mathematics, MDPI, vol. 11(15), pages 1-20, July.

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