A mesoscopic approach to diffusion phenomena in mixtures

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.

Macroscopic Internal Variables and Mesoscopic Theory: A Comparison Considering Liquid Crystals

“…The mesoscopic concept has been applied to various kinds of materials with an internal structure, like solids damaged by micro-cracks [56][57][58][59][60][61][62][63], dipolar media [64], mixtures [65,66], granular materials [67], magnetorheological fluids [68] and fiber reinforced concrete [69,70]. Three different applications will be sketched in the following.…”

Mesoscopic Approach to Electromagnetic Mixtures

“…Equations (17) and (19) belong to the first kind of surface balance equations. Moreover, inserting the two specifications (16) and (18) into Eq.…”

“…(17), (19), (21), and (22), constitutes the set of mesoscopic balance equations for EM fields. (17), (19), (21), and (22), constitutes the set of mesoscopic balance equations for EM fields.…”

“…Multiplying the five mesoscopic balance equations (17), (19), (21), (22), and (24) by one x, and then integrating the results over the manifold M immediately give rise to the set of the first-moment EM equations Multiplying the five mesoscopic balance equations (17), (19), (21), (22), and (24) by one x, and then integrating the results over the manifold M immediately give rise to the set of the first-moment EM equations…”

“…To date, several authors have proposed applications of the mesoscopic approach to the description of material properties adopting di¤erent mesoscopic variables. Mesoscopic variables can be not only a quantity characterizing the specific geometric feature of a material, but also a kinematic quantity such as the velocity field [19]. Mesoscopic variables can be not only a quantity characterizing the specific geometric feature of a material, but also a kinematic quantity such as the velocity field [19].…”