Symmetric Diffusion Equations, Barodiffusion, and Cross-Diffusion in Concentrated Liquid Mixtures
In models of diffusion in multicomponent mixtures, the current practice is to derive equations for an isobaric system. The equations are nonsymmetric in relation to the components of the mixture, and the concentration of solvent is assumed to be governed by the conservation of mass instead of its own corresponding diffusion equation. For concentrated mixtures, the solvent component is selected arbitrarily, which makes interpretation of the experimental data dependent on the choice of the interpreter. In this work, we derive a symmetric system of equations, made possible by the introduction of a spontaneously produced secondary pressure gradient. The effect of that pressure gradient is barodiffusion (barophoresis), defined by the force expressed as the secondary pressure gradient multiplied by the molecular volume. The model also considers the cross-diffusion (diffusiophoresis) that results from the hydrodynamic stresses associated with the local concentration-induced pressure gradient in liquid layers surrounding individual molecules. The resulting system of diffusion equations, which contains the secondary pressure gradient and component concentrations, is applied to a binary (nonionic) mixture of benzene and 1,2-dichloroethane. The steady-state system is placed in a uniform force field, and the effect of the secondary pressure gradient on the field-induced migration is discussed. Fluctuation dynamics in a system with no external force field is also discussed. The numerical results predict the establishment of lower concentration gradients compared to standard theory. Also, the predicted concentration dependence in the effective diffusion coefficient measured by dynamic light scattering is different compared to standard theory. Finally, experiments are proposed to further evaluate differences between the new model and the standard approach.
Schimpf, Martin and Semenov, Semen N.. (2004). "Symmetric Diffusion Equations, Barodiffusion, and Cross-Diffusion in Concentrated Liquid Mixtures". Physical Review E, 70(3), 031202-1 - 031202-10.