Phase-field modeling by the method of lattice Boltzmann equations

Abstract

In this paper, at first, a lattice Boltzmann method for binary fluids, which is applicable at low viscosity values, is developed. The presented scheme is extension of the free-energy-based approach to a multi-relaxation-time collision model. Various benchmark problems such as the well-known Laplace law for stationary bubbles and capillary-wave test are conducted for validation. As an appealing application, instability of a rising bubble in an enclosed duct is studied and irregular behavior of the bubble is observed at very high Reynolds numbers. In order to highlight its capability to simulate high Reynolds number flows, which is a challenge for many other models, a typical wobbling bubble in the turbulent regime is simulated successfully. Then, in the context of phase-field modeling, a lattice Boltzmann method is proposed for multiphase flows with a density contrast. Unlike most of the previous models based on the phase-field theory, the proposed scheme not only tolerates very low viscosity values but also emerges as a promising method for investigation of two-phase flow problems with moderate density ratios. In addition to comparison to the kinetic-based model, the proposed approach is further verified by judging against the theoretical solutions and experimental data. Various case studies including the rising bubble, droplet splashing on a wet surface, and falling droplet are conducted to show the versatility of the presented lattice Boltzmann model.

Multiphase lattice Boltzmann simulations for porous media applications

“…the leading order of the intermolecular forcing terms was reduced from O (1) to O(u) [87]). Although this model is more robust than most of the previous LBMs, it is restricted to density ratios up to approximately 15 [138]. The derivation and more details of the mean-field theory model can be found in [87].…”

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

“…Nevertheless, the model of Zheng et al was found to be restricted to density-matched binary fluids and unable to simulate multiphase flows with noticeable density differences [26]. The model of Lee et al has successfully reproduced some multiphase flows at large density ratio, but the numerical algorithm is complex and its computational efficiency may be low because the numerical implementation involves the discretization of many derivatives.…”

Pore-scale simulation of effects of coal wettability on bubble-water flow in coal cleats using lattice Boltzmann method

“…Then, a revised lattice Boltzmann equation to recover the CH equation is proposed by Zheng et al (2006), which has relatively high efficiency and stability. However, this model is proved to be restricted to densitymatched binary fluids (Fakhari and Rahimian, 2010). Recently, a modified new model considering the local density variation is developed by Shao et al (2014).…”