Simulation of static critical phenomena in non-ideal fluids with the Lattice Boltzmann method

TL;DR

This paper demonstrates that the Lattice Boltzmann method, combined with a Ginzburg-Landau free energy functional, accurately reproduces static critical phenomena of non-ideal fluids at their critical point, including critical exponents and finite-size effects.

Contribution

It introduces a simulation approach using the Lattice Boltzmann method to model static critical phenomena in non-ideal fluids, emphasizing finite-size scaling and conservation issues.

Findings

Correct reproduction of Ising universality class critical behavior

Determination of critical exponents via finite-size scaling

Analysis of finite-size effects and conservation issues

Abstract

A fluctuating non-ideal fluid at its critical point is simulated with the Lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order-parameter.