Lattice Boltzmann model of immiscible fluids

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 twophase 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.

Multiphase lattice Boltzmann simulations for porous media applications

“…Among them, five representative models are the color gradient model [79][80][81], the inter-particle potential model [82][83][84], the free-energy model [85,86], Fig. 1 Single phase flow in a segmented, μCT image of a Dolomite sample including a a rendering of the pore volume (i.e.…”

“…There are two recoloring algorithms widely used in the literature, namely the recoloring algorithm of Gunstensen et al [79] and the recoloring algorithm of Latva-Kokko and Rothman [92], which are hereafter referred to as A1 and A2, respectively. In A1, the distribution functions f R † i (x, t) and f B † i (x, t) are found by maximizing the work done by the color gradient,…”

Multicomponent lattice-Boltzmann model with interparticle interaction

“…The early stages of phase separation can be expected to have some arbitrariness. In addition, these models have other problems such as the anisotropy of the surface tension (14,12) and difficulties in dealing with components with different densities. Appert et al (15) suggested another LGA model to simulate a liquid-gas type of phase transition.…”

“…A Boltzmann equation version was formulated later. (12) The same idea was used to achieve a low diffusivity in the simulation of partially miscible fluids (13) with LBE method. In these models, a repulsive force between the two fluid components is most intense in the interfacial zone where the "color gradient" is large.…”

Pore-scale mass and reactant transport in multiphase porous media flows

“…This choice leads to a continuum mathematical formulation described by the Cahn-Hilliard theory (Cahn & Hilliard 1958). A second class of models is based on first principles for the microscopic interaction between the two fluids (Gunstensen et al 1991;Shan & Doolen 1995). These models converge to the continuum mass and momentum conservation for a slightly compressible multi-component mixture of fluids (Shan & Doolen 1995).…”