Lattice Boltzmann Model for Axisymmetric Multiphase Flows

We develop a lattice Boltzmann equation method for simulating multi-phase immiscible fluid flows with variation of density and viscosity, based on the model proposed by Gunstensen {\em et al} for two-component immiscible fluids. The numerical measurements of surface tension and viscosity agree well with theoretical predictions. Several basic numerical tests, including spinodal decomposition, two-phase fluid flows in two-dimensional channels and two-phase viscous fingering, ar...

This study develops a computationally efficient phase-field lattice Boltzmann model with the capability to simulate thermocapillary flows. The model was implemented into the open-source simulation framework, waLBerla, and extended to conduct the collision stage using central moments. The multiphase model was coupled with both a passive-scalar thermal LB, and a RK solution to the energy equation in order to resolve temperature-dependent surface tension phenomena. Various latti...

In this work, we develop a phase-field-based lattice Boltzmann (LB) method for a two-scalar model of the two-phase flows with interfacial mass/heat transfer. Through the Chapman-Enskog analysis, we show that the present LB method can correctly recover the governing equations for phase field, flow field and concentration/temperature field. In particular, to derive the two-scalar equations for the mass/heat transfer, we propose a new LB model with an auxiliary source distributi...

In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface fore (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition la...

A new lattice Boltzmann method for simulating multiphase flows is developed theoretically. The method is adjusted such that its continuum limit is the Navier-Stokes equation, with a driving force derived from the Cahn-Hilliard free energy. In contrast to previous work, however, the bulk and interface terms are decoupled, the former being incorporated into the model through the local equilibrium populations, and the latter through a forcing term. We focus on gas-liquid phase e...

The existing lattice Boltzmann models for incompressible multiphase flows are mostly constructed with two distribution functions, one is the order parameter distribution function, which is used to track the interface between different phases, and the other is the pressure distribution function for solving the velocity field. In this brief report, it is shown that in these models the recovered momentum equation is inconsistent with the target one: an additional interfacial for...

In this work, we consider a general consistent and conservative phase-field model for the incompressible two-phase flows. In this model, not only the Cahn-Hilliard or Allen-Cahn equation can be adopted, but also the mass and the momentum fluxes in the Navier-Stokes equations are reformulated such that the consistency of reduction, consistency of mass and momentum transport, and the consistency of mass conservation are satisfied. We further develop a lattice Boltzmann (LB) met...

The effects of mid-range repulsion in Lattice Boltzmann models on the coalescence/breakup behaviour of single-component, non-ideal fluids are investigated. It is found that mid-range repulsive interactions allow the formation of spray-like, multi-droplet configurations, with droplet size directly related to the strength of the repulsive interaction. The simulations show that just a tiny ten-percent of mid-range repulsive pseudo-energy can boost the surface/volume ratio of the...

Spurious velocities arising from the imperfect offset of the undesired term at the discrete level are frequently observed in numerical simulations of equilibrium multiphase flow systems using the lattice Boltzmann equation (LBE) method. To capture the physical equilibrium state of two-phase fluid systems and eliminate spurious velocities, a well-balanced LBE model based on the incompressible phase-field theory is developed. In this model, the equilibrium distribution function...

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible multiphase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhanc...