Classical Fluids in Constant External Fields and the Generalizations of the Ornstein-Zernike Relation

Abstract

We consider the equilibrium of pure and binary fluids in constant external fields by directly setting up the appropriate distribution functions of Statistical Mechanics. The equilibrium density gradients are obtained in terms of the partial structure factors a_ij and by connecting these results with the usual thermodynamic equilibrium conditions we obtain elementary proofs of all the expressions, for the a_ij in terms of thermodynamic quantities, usually derived by Fluctuation Theory. We also derive a general form of the Nernst-Einstein relation between mobility and diffusion constant.

The results for the density gradients are exemplified by brief discussions of fluids in gravitational fields and electromigration in a binary alloy.