Virtual power and thermodynamics for electromagnetic continua with interfaces

Abstract

This paper presents a systematic and rational formulation of the electromagnetic theory of deformable and fluent bodies swept out by singular surfaces that may carry their own thermodynamics (interfaces). The treatment is based on the principle of virtual power for finite velocity fields, which is so formulated that, when combined, for real velocity fields, with the first principle of thermodynamics in global form, it yields directly the so-called energy theorem both in the bulk and at the singular surface. Then the corresponding rates of entropy production are deduced after introduction of the second principle of thermodynamics. The various alternate expressions of the ponderomotive force, couple, and electromagnetic energy, obtained in the bulk from the Lorentz theory of electrons are developed across the singular surface by means of the generalized transport and Green–Gauss theorems. Finally, an extension of the constitutive theory (well established in the bulk) is given to account for surface phenomena in the case of an electromagnetic fluid. Thermodynamical restrictions are discussed, and comparisons are made with previous works.