Physics of Fluids
Brownian motion processes, Molecular dynamics, Multiphase flow -- Mathematical models, Stochastic partial differential equations
A phenomenological theory is developed for Brownian motion in a flowing incompressible fluid. The Brownian particles are regarded as an ideal gas subject to a position- and time-dependent force field that represents interactions with the host fluid. This approach immediately leads to deterministic partial differential equations of motion for the Brownian particles. These equations are then examined in the limit of large friction, in which they imply an expression for the diffusional mass flux of Brownian particles. This expression is a sum of terms representing concentration, forced, thermal, and pressure diffusion. Comparisons are made with earlier work, and with the corresponding expression for the molecular diffusion flux of one component in a binary ideal gas mixture. The Brownian and molecular diffusion fluxes are found to be identical in form, with the Brownian particle volume fraction corresponding to the molecular mole fraction.
J.D. Ramshaw, "Brownian motion in a flowing fluid," Phys. Fluids 22, 1595 (1979)