The typical approach to multicomponent mass transfer calculations assumes that the multicomponent diffusivities are constant. The errors which result because of this assumption have been accepted because of the complexity of the calculations resulting when diffusivity as a function of concentration is included. The influence of this assumption, previously not demonstrated, has now been determined for two physical situations—a stagnant film and a rigid drop (a solid sphere, or liquid drop in which there is no internal circulation). Multicomponent diffusivities, concentration profiles, and mass fluxes have been computed to compare results for constant, and for concentration-variable, diffusivity. Results include the cases of flux operating against the concentration gradient and non-zero flux of components with no imposed gradient. The technique used to estimate mass transfer rates in multicomponent mixtures considers the effects of multicomponent interactions (friction) among molecules and also the thermodynamic correction to these interactions based on the Maxwell–Stefan (MS) formulation. A program written in Mathcad was used to carry out the calculations. The coupled differential equations which represent solute balances were solved numerically applying a central finite difference scheme and the Crank–Nicholson method. The resulting system of equations in matrix form were solved with a program also generated with Mathcad. Results show that concentration-variable diffusivity may give significantly different (as much as 80%) component mass transfer flux values, when determined for high fluxes and large imposed concentration differences. However, even in this regime, it may be possible to formulate suitable constant ‘average’ diffusivities to produce results which are much closer to those predicted with concentration-dependent diffusivities.
- multicomponent mass transfer
- concentration-variable diffusivity
- film model
- rigid drop model
- liquid-liquid extraction