A mesoscopic approach to diffusion phenomena in mixtures

TL;DR

This paper introduces a mesoscopic framework for analyzing diffusion in mixtures by extending the field variables to include component velocities, deriving balance equations and evolution equations that generalize Fick's law.

Contribution

It develops a mesoscopic approach to diffusion, deriving new balance and evolution equations for fluxes that extend classical diffusion laws.

Findings

Derived differential equations for diffusion fluxes

Generalized Fick's law through mesoscopic equations

Connected mesoscopic variables with extended thermodynamics

Abstract

The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the velocities of the components. Balance equations on this enlarged space are the equations of motion for the mesoscopic fields. Moreover, local distribution functions of the velocities are introduced as a statistical element, and an equation of motion for this distribution function is derived. From this equation of motion differential equations for the diffusion fluxes, and also for higher order fluxes are obtained. These equations are of balance type, as it is postulated in Extended Thermodynamics. The resulting evolution equation for the diffusion flux generalizes the Fick's law.