Constitutive equations for multiphase mixtures of fluids

Constitutive equations for a multiphase mixture of fluids are presented. The mixture is assumed to consist of a single non-uniform temperature and no change is allowed. The theory is based on the conservation and balance equations of multiphase mixtures proposed by Dobran, and the constitutive assumption allows for the effects of temperature gradient, density gradients, velocity gradients, velocities and accelerations. A linearized form of the constitutive equations is presented for an arbitrary number of phases, and restrictions on the constitutive assumption are investigated by the second law of thermodynamics. The theory yielded a significant number of results and they are compared with previous investigations.