Fractionation by persistent random walk and two-coefficient diffusion law

Abstract

Random movement of microscopic particles in heterogeneous environments leads to fractionation phenomena, with the Soret effect being one of the most representative examples. This raises a fundamental question: what characteristics of random movement give rise to such fractionation phenomena? We investigate whether the persistence of a random-walk system has such a property and show that fractionation occurs only when the persistence is anisotropic. This is shown by investigating the convergence of a heterogeneous persistence random-walk system to a resulting anisotropic diffusion equation. Numerical simulations of the diffusion equation are compared with a Monte Carlo method and solutions to the recursive relations.