Continuum modelling of electrorheological fluids

Abstract

A thermodynamical continuum modelling is proposed for electrorheological fluids. This theormodynamical approach tries to describe the response of an electrorheological fluid in the solid phase (which means with an applied adequate electric field) under mechanical solicitations. Thermodynamic formulations distinguish the contributions due to reversible and irreversible process. In an electrorheological fluid the microstructure generated by the application of an electric field introduces parameters whose the evolution of which influence the behavior. These parameters will be defined as internal variables, or hidden variables, in the formulation of thermodynamics. They are used for the description of dissipative effects. The choice and the number of pertinent parameters are crucial and need to be selected according to the nature of microscopic mechanism and experimental observations. The presence of fibrous structures in the E.R. fluid, when an electric field is applied, is an observed fact. In the theory of thermodynamics with internal variables, the introduction of internal variables doesn't modify, by hypothesis, the balance equations. Nevertheless, the experiments show the existence of hysteresis phenomenon due to the reorganization, at the microscopic level, of the particle that compose the fibers. In order to describe these phenomena, we introduce two internal variables following an idea of Kiryushin.