ON THE RELATIONSHIP BETWEEN THE EXACT AND LINEARISED SOLUTIONS OF THE MAXWELL-STEFAN EQUATIONS FOR THE MULTICOMPONENT FILM MODEL

Abstract

The exact solution of the Maxwell-Stefan equations for multicomponent mass transfer based on a film model is compared with the solution of the linearised equations. It is first shown that the formulation of the mass transfer coefficients for the two solutions can be written in identical form as the product of a square matrix of composition dependent low flux mass transfer coefficients and a square matrix of correction factors which accounts for the presence of finite rates of transfer. In the exact solution the low flux mass transfer coefficients are evaluated at a film boundary composition while in the linearised theory they are evaluated at the mean film composition. The comparison clearly shows the influence of the rates of transfer in modifying these mass transfer coefficients. It is the constituent molar fluxes which are important in the exact solution whereas it is the convective contribution to these fluxes alone which appear in the linearised theory. Despite these fundamental differences the molar transfer rates predicted by the two methods are usually in excellent agreement relative to the average absolute rate of transfer. It is argued that this will be the case in distillation examples where composition differences are small (the matrices of mass transfer coefficients are therefore almost equal) and the matrices of correction factors are closely approximated by the diagonal unit matrix. Further, in processes involving unidirectional mass transfer, such as condensation, the large differences between the respective matrices of mass transfer coefficients and correction factors frequently compensate for each other: As a result the errors introduced by linearising the equations are usually low, even in mixtures of high concentration and with high rates of mass transfer.