A mesoscopic approach to diffusion phenomena in mixtures
  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. 
A.Palumbo, C. Papenfuss and P. Rogolino