Equilibrium mass transfer coefficients for a dilute species diffusing between laminar counter flowing streams derived from the corresponding eigenvalue problem for the advection–diffusion equation

Abstract

The equilibrium mass transfer coefficients for a dilute species diffusing between two steady counter flowing fluid streams are derived from the eigenvalue problem for the laminar advection–diffusion equation. Both uniform and non-uniform velocity profiles are considered. A numerical method is first used to evaluate the limitations of the uniform velocity approximation and then to judge the accuracy of the derived approximate formulae. With a uniform velocity, the lowest order linear approximation is found to yield a fundamentally different formula to that based upon classical film theory. A key distinction is that the solutions enable the individual stream coefficients to be determined from experimental data, as opposed to the one overall value provided by film theory. The formulae are given in the form of fourth order polynomials in the driving force with high predictive accuracy only being achieved when all the terms are used.