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

Abstract

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.

Get full access to this article

View all access options for this article.

References

Albano

A.M.

and Bedeaux

, Non-equilibrium electro-thermodynamics of polarizable multicomponent fluids with interface, Physica A 147 (1987), 407–435.

Albano

A.M.

, Bedeaux

and Vlieger

, On the description of interfacial properties using singular densities and currents at a dividing surface, Physica A 99 (1979), 293–304.

A.M. Albano

Bedeaux and Vlieger

, On the description of interfacial electromagnetic properties using singular fields, charge density and currents at a dividing surface, Physica A 102 (1980), 105–115.

Wolff

P.A.

and Albano

A.M.

, Non-equilibrium thermodynamics of interfaces including electromagnetic effects, Physica A 98 (1979), 491–508.

Maugin

G.A.

and Daher

, Phenomenological theory of elastic semiconductors, Int. J. Eng. Sci. 24 (1986), 703–732.

Maugin

G.A.

and Eringen

A.C.

, On the equations of electrodynamics of deformable bodies of finite extent, J. Méc. 16(1) (1977), 1–47.

Daher

and Maugin

G.A.

, The Method of virtual power in continuum mechanics. Application to media presenting singular surfaces and interfaces, Acta Mech. 60 (1986), 217.

Daher

and Maugin

G.A.

, Virtual power and thermodynamics for electromagnetic continua with interfaces, J. Math. Phys. 27(12) (1986), 3022–3035.

Daher

and Maugin

G.A.

, Deformable semiconductors with interfaces: Basic continuum equations, Int. J. Eng. 25(9) (1987), 1093–1129.

10.

Maugin

G.A.

and Eringen

A.C.

, Electrodynamics of Continua, Vols I-II, Springer-Verlag, 1990.

11.

Moeckel

G.P.

, Thermodynamics of interface, Arch. Rat. Mech. Anal. 57 (1974), 255.

12.

Alts

and Hutter

, Continuum description on the dynamics and thermodynamics of phase boundaries between ice and water. Part I: Surface balance laws and their interpretation in terms of three-dimensional balance laws averaged over the phase change boundary layer, J. Non-Equil. Thermodyn. 13 (1988), 221–257.

13.

Gurtin

M.E.

and Murdoch

A.I.

, A continuum theory of elastic material surfaces, Arch. Rat. Mech. Anal. 57 (1975), 291.

14.

Grauel

, Feldtheoretische Beschreibung der Thermodynamik für Grenzflächen, in: Lecture Notes in Physics, Vol. 326, Springer-Verlag, 1989.

15.

Gurtin

M.E.

, Toward a nonequilibrium thermodynamics of two phase materials, Arch. Rat. Mech. Anal. 100 (1988), 275–312.

16.

Nadhdi

P.M.

, The theory of shells and plates, in: Handbuch der Physik, Bd VIa/2, ed. Flügge

, Springer-Verlag, Berlin, Heidelberg, New-York, 1972.

17.

Sadiki

, A. Elektrodynamik deformierbarer Phasengrenzflächen. Dissertation, Institut für Mechanik, Technische Hochschule Darmstadt, 1995.

18.

Dell'Isola

and Romano

, On the derivation of thermomechanical balance equations for continuous systems with a nonmaterial interface, Int. J. Eng. Sci. 25(11-12) (1987), 1459–1487.

19.

Dell'isola

and Konsiski

, Deduction of thermodynamic balance laws for bidimensional nonmaterial directed continua modelling interface layers, Arch. Mech. 45 (1993), 333–359.

20.

Sadiki

and Hutter

, Surfacial electrodynamics. Part I: Description of surfacial electric and magnetic fields at a dividing surface in a deformable body by considering its electric and magnetic quadrupole distributions. Int. J. Appl. Electromagn. Mech. 7 (1996).