Use of Fick's Law and Maxwell-Stefan Equations in Computation of Multicomponent Diffusion

摘要

Multicomponent diffusion has attracted the attention of chemical engineers both in view of its practical importance and complexity. Maxwell-Stefan equations (MSE) and generalized Fick's law (GEL) forms are used to describe multicomponent diffusion. A component has to be excluded to write a GEL form for a multicomponent system, and hence GFL cannot be defined in a unique way. The choice of the component to be excluded is arbitrary and can be difficult if all the components are present in approximately similar amounts. Solutions of mass balance equations in binary systems, where MSE and GFL become identical, are well known and conform to expectations. However, multicomponent systems do throw up surprises. One such, raised by Nauman and Savoca and reinforced by Price and Romdhane, is the difficulty of consistently combining mass balances with GFL forms where a component has to be excluded arbitrarily. Price and Romdhane refer to the instances where negative values are obtained for mass fractions when mass balances combined with GFL form were solved numerically. Their work pertains to polymer-solvent systems, and they attribute the physically unrealistic results mainly to inconsistencies in the approximations used to get away with measurement of fewer diffusiv-ities than the theoretical minimum. Nauman and Savoca suggest that neglect of concentration dependency of diffusion coefficients could also be an important source of error, and physically unrealistic results can be obtained for the "balancing" component, that is the component excluded in defining GFL. However, they also claim that numerical solution of unsteady-state mass balance equations in gas mixtures, where the composition dependency of GFL diffusion coefficients is exactly known, also results in negative mole fractions. What ever might be the source of the physically unrealistic results, these instances point to the convenience of defining GFL forms without having to arbitrarily exclude a component. It is also relevant to point out two advantages of GFL forms. One is that they are easily combined with mass balances and require lesser number of equations to be solved than when MSE are used. That GFL can be directly used with standard CFD routines is the other advantage.