Biased diffusion in tubes of alternating diameter: Analytical treatment in the case of strong bias

Abstract

This paper is devoted to the effective transport coefficients of a particle in a tube of alternating diameter. Analytical expressions are derived for the effective mobility and diffusivity under strong bias conditions, i.e., in the limiting case where the external biasing force tends to infinity. The expressions give the transport coefficients as functions of the geometric parameters of the tube and the external force. They show that the effective diffusivity is a linear function of the square of the external force, whereas the effective mobility is independent of the force. The problem of finding effective transport coefficients in a tube of alternating diameter is too complex to be analyzed by conventional methods. Therefore, the expressions are derived in the framework of an intuition-based approach and validated by Brownian dynamics simulations. The obtained results extend a short list of available analytical expressions for the effective transport coefficients.