Lattice Boltzmann model of immiscible fluids

TLDR

The model, based on the Boltzmann equation of lattice‑gas hydrodynamics, incorporates features of a previously introduced discrete immiscible lattice‑gas model and appears straightforward to extend to three dimensions. The study introduces a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model is a lattice Boltzmann numerical method for simulating immiscible two‑phase flow, demonstrated by a preliminary simulation of flow in a two‑dimensional microscopic porous‑medium model. The derived theoretical surface‑tension coefficient agrees excellently with simulation values, and a preliminary application demonstrates the model’s ability to simulate flow in a two‑dimensional microscopic porous‑medium.

Abstract

We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduced discrete immiscible lattice-gas model. A theoretical value of the surface-tension coefficient is derived and found to be in excellent agreement with values obtained from simulations. The model serves as a numerical method for the simulation of immiscible two-phase flow; a preliminary application illustrates a simulation of flow in a two-dimensional microscopic model of a porous medium. Extension of the model to three dimensions appears straightforward.