Critical Phenomena in an Immiscible Lattice-Gas Cellular Automaton

Abstract

A temperaturelike parameter is added to an immiscible lattice gas through the modification of the collision rule in a Monte Carlo manner. It is found that the lattice gas undergoes a phase transition from miscible to immiscible as the temperature is lowered. Critical phenomena similar to those of a thermal system are observed. The critical exponent p of the coexistence curve is found to be 0.3.

A three–dimensional lattice–gas model for amphiphilic fluid dynamics

“…It should be further noted that the inverse temperature-like parameter β is not related in the conventional way to the kinetic energy. For a discussion of the introduction of this parameter into lattice gases to reproduce critical behaviour we refer the reader to the original work by Chan & Liang (1990).…”

A lattice-gas model of microemulsions

“…This prescription was subsequently generalized by Chan & Liang (1990) (see also Chen et al 1989), who noted that the colour work, A can be thought of as a Hamiltonian function, H(s,s'), of the incoming and outgoing states; and they argued that this Hamiltonian should then be used to construct Boltzmann weights for choosing the outgoing state (see also Chen et al 1989). Specifically, if C(s) denotes the equivalence class of states with the same conserved quantities as state s, then one can define a partition function for each equivalence class,…”

Simulations of amphiphilic fluids using mesoscale lattice-Boltzmann and lattice-gas methods

“…The model was developed as an extension of the Rothman and Keller (RK) [21] model of binary immiscible fluids, including its generalization by Chan and Liang [22], to take into account the essential characteristics and interactions of amphiphiles. In the RK model [21] the lattice-gas particles are tagged with two "colours", to distinguish oil and water.…”