Analytical estimate of percolation for multicomponent fluid mixtures

The size of a dense region of a particular constituent (L) 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-s(c)) and the attractive force between L-s(c), particles are much weaker than that between L 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-s(c) particles into the fluid mixture. In that case. dense regions composed of L-sc 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) less than or equal to0, 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-s(c) 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.