Generalized expressions for interfacial resistance to mass transfer in two-phase systems

Abstract

Interfacial resistance to mass transfer between two quiescent liquid phases is analyzed by modeling the solute molecules as Brownian particles and solving the associated Fokker-Planek equation for their distribution in phase space. As in previous work on this problem, the motion of the solute particles is assumed to be influenced by spatially varying diffusivity and potential energy functions in the immediate vicinity of the interface. The use of a Fokker—Planck equation, howeer, permits the investigation of systems in which the potential energy varies so rapidly with position that a description in terms of the simpler Smoluchowski equation is inadequate. An approximate analytical solution is obtained by expanding the velocity dependence of the phase-space distribution function in a series of orthogonal polynemials, the interfacial resistance then being given as an expansion in powers of a characteristic diffusivity. An evaluation of the first two terms in this expansion is seen to provide a convenient means of assessing the accuracy of results based on the Smoluchowski equation. A closed-form expression for the interfacial resistance is also derived for the case of arbitrary diffusivity by assuming the existence of a reasonably high potential energy barrier; this result is expected to be particularly useful for situations in which the series solution is only slowly convergent. Finally, the accuracy of these analytical results is determined by choosing appropriate (qualitatively correct) expressions for the potential energy and diffusivity functions and solving the Fokker Planck equation numerically, and the expected trends are thereby confirmed.