Model of Mass Transfer Processes in a Mixture of Continua Consisting of One Deformable and Two Liquid Component

Abstract

The proposed mathematical model is based on the theory of a mixture of interpenetrating continua: deformable (polymer) and two liquid continuums. The governing equations of the model are obtained as consequences of the laws of thermodynamics and the requirements of their invariance to Galilean transformations. Equations describing the motion of liquid components are formulated in coordinates related to the polymer component of the mixture. The need for such a choice arises as a result of the fact that only a polymer can be deformed. When solving problems, it is required to find polymer deformations and investigate the movement of solvents relative to it, including the release of solvents through the polymer boundary into the external environment.Material considered in this mathematical model is capable of working under conditions of finite deformations. The expression of the free energy of the mixture takes into account the energy of interaction of the molecules of the mixture with each other (polymer and two solvents).