Symmetrization of interface dynamics equations

Abstract

The system of conservation laws governing heat and mass transfer processes in a continuous medium is obtained in a symmetric form on the basis of the successive application of fundamental thermodynamic principles. This approach involves reformulating the problem in intensive thermodynamic variables such as the temperature and chemical potential. The equations of capillary fluid mechanics and phase transitions with moving free boundaries are analysed in detail. The unsteady motion of a drop driven by buoyancy forces in an unbounded ambient fluid with dilute surfactants is investigated where the LeChatelier principle is established for an arbitrary surfactant. The general procedure for construction of self-similar solutions for the thermodiffusive Stefan problem with piecewise constant matrices of coefficients is described