A mixture model for magneto-rheological materials

To model the response of magnetorheological (MR) materials, a continuum theory for a mixture consisting of a fluid continuum and a solid one is developed. In this mixture theory, the structure composed of the magnetizable particles in MR fluids is treated as a solid continuum. The aim of this paper is two-fold. Firstly, we adopt the extended irreversible thermodynamics (EIT) approach as the thermodynamic framework to formulate the general dynamic equations of MR mixtures. Introducing the concept of plastic deformation of the solid continuum, the mechanisms of dissipation are discussed and the evolution equations for the fluxes are derived. Secondly, by virtue of this derivation we study the propagation of an acoustic wave through the MR fluids. This study shows that there exist two longitudinal acoustic waves propagating along the direction of an applied magnetic field.