A THERMODYNAMICALLY CONSISTENT CONSTITUTIVE THEORY FOR FLUIDS

This work presents a general procedure, developed within the framework of thermodynamics of irreversible processes, to obtain constitutive r elations for fluids that verify automatically the principle of materia l objectivity and a local version of the second law of thermodynamics. In this constitutive theory the free energy is supposed to be a diffe rentiable function of a finite set of variables, some of them introduc ed to account for the interference of the microstructure with the macr ostructure. This phenomenological theory may allow a simplified macros copic description of microstructural physical mechanisms, relevant for certain classes of fluids. The choice of a particular objective time derivative and of two thermodynamic potentials is sufficient to define a complete set of constitutive equations. The theory comprises and ge neralizes a great number of constitutive equations found in the litera ture allowing a simple modeling of important phenomena such as normal stress effects and the dependence of viscosity on the rate of strain. Some basic features and possibilities of the theory are presented thro ugh examples concerning rigid-viscoelastic and viscoelastic fluids. (C ) 1997 Elsevier Science Ltd.