THE FICK AND LAGRANGE EQUATIONS AS A BASIS FOR THE MAXWELL-STEFAN DIFFUSION-EQUATIONS

Diffusion in multicomponent systems is described by equations derived by Maxwell in 1866 from the kinetic theory of gases and, independently , by Stefan in 1871 on the basis of hydrodynamic laws. These equations are called the Maxwell-Stefan equations. Their modern derivation is a matter of irreversible thermodynamics, or of statistical mechanics. I n the present paper, the Maxwell-Stefan equations are obtained from th e equation adopted by Fick in 1855 for diffusion in binary systems. In addition it is demonstrated that the Maxwell-Stefan equations can als o be derived from the classical Lagrange equations valid for a system of bodies undergoing energy dissipation. The energy dissipation in suc h a system is assumed to obey the dissipation function proposed by Lor d Rayleigh in 1873. (C) 1997 Elsevier Science Ltd. All rights reserved .