Theory of Diffusion in Simple Liquid Mixtures

A method is presented for obtaining the diffusion coefficient in terms of functions of molecular properties for a liquid system of monatomic molecules near equilibrium. The approach considers the reduced probability density functions Wn(r1···pn) for n molecules (n = 1, 2, and 3) in the limit of a steady state. By operating on the complete probability density function WN with the conventional Liouville operator and by integrating over the phase space of N − n molecules, we write the time dependence of Wn in a form not explicitly involving Wm for m > n. The reduced probability densities and the average vector forces are developed as a power series in a small parameter λ. Starting with singlet functions corresponding to a gradient in the density of a binary isothermal solution at constant pressure and the corresponding flux of molecules, we determine a singlet momentum‐dependent force which maintains the flux and gradient stationary in time. The force can only be consistent with a certain class of pair proba...