On the General Structure of Balance Equations of Flux on Non-Material Surfaces Bearing Surfacial Quantities with Application to Surfacial Electrodynamics

This paper is concerned with the formulation of the general structure of balance equations of a flux quantity on non-material surfaces (e.g., phase transition surface, interface, etc.) dividing two body parts and bearing surfacial quantities. The treatment based on the principles of continuum physics creates the possibility for interaction between fields of the three-dimensional continuum (body) and surfacial fields of the included two-dimensional continuum (interface). From a global formulation, local statements on the surface have been obtained by taking advantage of appropriate divergence and transport theorems. This localization leads to (1) two integral forms of the surfacial balance equations for (la) the surfacial fields and (lb) for the jump quantities on the surface, respectively, as well as to (2) required transversality conditions (proper boundary conditions) for the involving surfacial fields on the boundary surface. With these results, a rational description of surfacial electrodynamic statements has been obtained.