Diffusion in nonelectrolyte systems

9 Generalized Matrix Method for Diffusion in Nonideal Mixtures 

In nonideal mixtures, the thermodynamic nonideality of the mixture has to be considered. We still need to predict the concentration dependence of the mutual diffusion coefficient Dt] of a binary pair of nonelectrolytes. The concentration dependency of l)u in liquid mixtures may be calculated by using the Vignes equation or the Leffler and Cullinan equation. Besides these, we may also use a correlation suggested by Dullien and Asfour (1985), given by 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by 

The modified matrix of dimensionless mass transfer rate factors is defined as 

The total fluxes Nt are calculated as for ideal gases using the finite flux mass transfer coefficients defined by 

---