THE MASS FLUX BOUNDARY-CONDITION AT A MOVING FLUID-FLUID INTERFACE

The dissolution of organic chemicals into ground water aquifers represents a mass transport process of considerable complexity. The rate of dissolution can depend on the manner in which the organic material is distributed, on the nature of the mechanical and chemical heterogeneities associated with a particular aquifer, and on the equilibrium relations for the individual chemical species. One aspect of this problem that has not been considered in detail is the flux boundary condition at the organic phase-aqueous phase interface, and it is the nature of this boundary condition that is explored in this paper. At a moving fluid-fluid interface, one must make use of the species mass jump condition for a singular surface, the appropriate form of the Stefan-Maxwell equations, and the mass average momentum equation in order to develop a general form of the mass flux boundary condition. In this paper we show that the molar flux condition for species A at the beta-gamma interface can be expressed as c(A)(v(A) - w). n(gamma beta) = -Sigma(beta=1)(B=N-1)H(AB)cD(Bm)del x(B) . n(gamma beta)- H(AN)M(N)(-1)rho(v - w). n(gamma beta) in which H-AB represents a matrix of coefficients that depend on the binary diffusion coefficients and the concentration at the interface. We have used M(N) to represent the molecular weight of the Nth component, and it is the last term in the above relation that is ignored in the traditional models of the interfacial flux.