Abstract
A lattice Boltzmann model using the Shan-Chen prescription for a binary immiscible fluid is described, and the macroscopic equations obeyed by the model are derived. The model is used to quantitatively examine spinodal decomposition of a two-dimensional binary fluid. This model allows examination of the early-time period corresponding to interface formation, and shows agreement with analytical solutions of the linearized Cahn-Hilliard equation, despite the fact that the model contains no explicit free-energy functional. This regime has not, to the knowledge of the authors, been previously observed using any lattice Boltzmann method. In agreement with other models, a scaling law with the exponent 2/3 is observed for late-time domain growth. Breakdown of scaling is also observed for certain sets of simulation parameters.
- Received 6 December 2001
DOI:https://doi.org/10.1103/PhysRevE.66.016303
©2002 American Physical Society