Multiphase Flows with Moving Interfaces and Contact Line—Constitutive Modeling

Abstract

A thermodynamic analysis, based on the muller–Liu thermodynamic approach of the second law of thermodynamics, is performed to derive the expressions of the constitutive variables in thermodynamic equilibrium. Non-equilibrium responses are proposed by use of a quasi-linear theory. A set of constitutive equations for the surface and line constitutive quantities is postulated. Some restrictions for the emerging material parameters are derived by means of the minimum conditions of the surface and line entropy productions in thermodynamic equilibrium. Hence, a complete continuum mechanical model to describe excess surface and line physical quantities is formulated. Technically, in the exploitation of the entropy inequality, all field equations are incorporated with Lagrange parameters into the entropy inequality. In the process of its exploitation, the Lagrange parameter of the energy balance is identified with the inverse of the absolute temperature in the bulk, the phase interface, and in the three-phase contact line. Interesting results, among many others, are the Gibbs relations, which are formally the same in the bulk, on the interface and along the contact line, with the pressure in the compressible bulk replaced by the surface tension on the interface and by the line tension along the contact line, see (28.45), (28.87).