Analytical estimate of percolation for multicomponent fluid mixtures.

Abstract

The size of a dense region of a particular constituent (L(s)) in a nonuniform distribution of particles generated in a multicomponent fluid mixture can develop under certain conditions. If both the attractive force between an L(s) particle and a particle of the other constituents (L(c)(s)) and the attractive force between L(c)(s) particles are much weaker than that between L(s) particles, then the percolation due to the growth of the dense region of L(s) particles can hardly be affected by the addition of L(c)(s) particles into the fluid mixture. In that case, dense regions composed of L(c)(s) particles can be formed passively. To derive these results, it is assumed that such a dense region is an ensemble of particles bound to each other as particle pairs that satisfy the condition E(ij)+u(ij)(r)</=0, where E(ij) is the relative kinetic energy for i and j particles and u(ij)(r) is the pair potential. The percolation in the fluid mixture can be estimated analytically. According to the pair connectedness function P(ij)(r) derived for evaluating the percolation, the probability that an L(s) particle is located near another L(s) particle can be insensitive to the addition of L(c)(s) particles. The magnitude of P(ij)(r) can be maximized for a pair of i-j particles interacting with the most strongly attractive force having the largest value of the effective ranges in a fluid mixture system. These particles can contribute to making the phase behavior of the fluid mixture complicated.