Mesoscopic continuum thermodynamics for mixtures of particles with orientation

Abstract

The aim of the present paper is a continuum theoretical framework for mixtures of different chemical components, including the possibility of chemical reactions. The molecules are assumed to have an orientational degree of freedom, i.e. they are needle-shaped or planar. In the first case the microscopic director is the orientation of the particle long axis, in the second case it is the unit vector normal to the disc. This orientation is introduced as an additional variable in the domain of the field quantities. On this enlarged domain, the mesoscopic space, balance equations are derived. Compared to usual continuum theory, additional fluxes in orientation space occur. These are constitutive functions, like internal energy, heat flux and stress tensor. The restrictions on constitutive functions imposed by the second law of thermodynamics are derived by the method of Liu. Therefore, this new approach is very promising, since microscopic features of the particles, discarded in traditional continuous thermodynamics, become now an important part in the understanding of chemical systems. In addition, the results presented here can be extended to the study of other complex materials such as alloys, ferrofluids, carbon fibers, etc.