Thermodynamic field theory of chemically reacting fluids in an interface. I. A two-dimensional theory of mixtures of chemically reacting fluids

Abstract

The aim of the present paper is to formulate a thermodynamic field theory in discontinuous media from which we can deduce all relevant interfacial relations. To give light into the theoretical investigations, we consider a mixture of chemically reacting fluids in an interface. The surface of the interface has an arbitrary smooth shape which is closed and dependent on time. This interface can be considered as a model for a membrane. The interface is influenced by an external force field and a radiation field. We study heat exchange and material exchange of this membrane with the bulk fluids. We discuss field equations, namely, a system of first-order differential equations and give a systematic investigation for constitutive equations of nonviscous fluids. Moreover, we discuss the transformation properties in space and on surfaces of the constitutive equations of interfaces. From the representation theorem we obtain isotropic representations for the constitutive equations. In part II, our main object is concentrated to such thermodynamic processes which do not violate the entropy principle on interfaces. We give a rigorous discussion of the entropy inequality and the constitutive equations.