Internal variables and the non-equilibrium thermodynamics of colloidal suspensions

Classical thermodynamics of irreversible processes is a valuable tool for t he study of suspensions, provided due care is devoted to the selection of i nternal variables. As a first example, the flow-induced anisotropic microst ructure appearing in many a suspension is usually depicted by a vector, the orientation and length of which are submitted to a statistical distributio n. We show how irreversible thermodynamics imposes restrictions on the time evolution of that structural internal variable (and consequently on the ti me evolution of its statistical distribution), and how this evolution is re lated to the elastic stress of the suspension. As a second example, we cons ider the possibility of a mean relative motion between the particles and th e suspending fluid. Upgrading that relative velocity to the status of an in ternal variable, we analyse the consequences concerning the transport of ma ss, momentum and energy providing a link with the two-fluid model of suspen sions, as well as with the well-known description of molecular mixtures. (C ) 2001 Elsevier Science B.V. All rights reserved.