Surface Conditions for the Liquid-Vapor System, Taking into Account Entropy Production Caused by Mass and Energy Transport across the Interface

Abstract

A general mathematical form of a surface condition is derived for any extensive physical quantity by considering a global balance equation. Because of the validity of both the conservation laws and the second law of thermodynamics, a distinct set of surface conditions must hold for any special discontinuous thermohydrodynamic system. This set of surface conditions is established for the classical liquid-vapor system to show that the whole set of surface conditions must be taken into account if mass and energy transport across the interface takes place. In particular, the surface density of entropy production is determined quantitatively and is written as the bilinear expression of mass and energy flux and their conjugated forces. It is shown that the form of the expression is independent of whether or not the surface tension is taken into account. The method presented for finding the production of entropy on an interface is of importance not only in connection with the classical liquid-vapor system but also in other branches of physics, for example in the physics of liquid helium II, in atmospheric physics, and in the theory of shock waves.