Theory of multiphase mixtures—A thermomechanical formulation

The paper presents a theory of mixtures with the nonzero interfacial area between the constituents of the mixture. The conservation laws are physically motivated by utilizing a volume averaging procedure and by the definition of a mapping transformation. It is shown that the theory constructed in this manner is consistent with the theory of mixtures with a vanishingly small interfacial area and that a second law of thermodynamics can be assigned for each phase of the mixture. The conservation laws are examined for invariance properties with the principle of the material frame indifference, and a particular constitutive assumption is discussed. Also presented in the paper are the conservation laws in the integral form and the jump conditions for the singular surfaces in the multiphase mixture.