A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

Abstract

A multicomponent multiphase (MCMP) pseudopotential lattice Boltzmann (LB) model with large liquid-gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid-fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid-fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid-fluid and fluid-solid interaction strengths, but weakly affected by the time step ratio. The density ratio analyses show that the liquid-gas density ratio is dependent on both the fluid-fluid interaction strength and the time step ratio. For the liquid-gas flow simulations without solid phase, the maximum liquid-gas density ratio achieved by the present model is higher than 1000:1. However, the obtainable maximum liquid-gas density ratio in the solid-liquidgas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid-liquid-gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young's equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie's law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid-gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.

Contact Angle Measurement on Curved Wetting Surfaces in Multiphase Lattice Boltzmann Method

“…The lattice Boltzmann (LB) method is widely used as a very effective numerical approach for simulating complicated fluid flow. ,− The LB method is derived from the concept of cellular automata and kinetic theory, and it is excellent in modeling multiphase fluid flows including interface dynamics − and phase transitions. , Using the multiple relaxation time, both computational accuracy and numerical stability are enhanced: f i ( x + e i δ t , t + δ t ) − f i ( x , t ) = prefix− boldM − 1 · boldS · [ m − m ( eq ) ] + F i where M represents a transforming matrix that converts between the distribution function f and the velocity moment m linearly, and m = M · f , where boldf = ( f 0 , f 1 , ... , f 8 ) for the two-dimensional nine-velocity model, m (eq) represents the equilibria of the distribution functions, f i ( x , t ) indicates a distribution function of lattice node x and time t , and it is moving along the discrete velocity direction e i with i = 0, ..., N . S is a non-negative diagonal relaxation times matrix, boldS = diag (…”

“…Surface tension will lead to spherical droplets on plain substrates without considering the effect of gravity. Spherical cap models obtain contact angles as a theoretical method by measuring the width of the droplet at the base as well as the height. − The method can be applied to calculate dynamic contact angles during the evaporation of sessile droplets on curved surfaces, for which it is a typical situation that the droplet is axisymmetric and the Bond number, namely, the gravity effect here, is very small. When the droplet is reduced to the nanometer scale, we need to fit the descending contours by the least-square method due to instabilities at the liquid–gas transition region. , The spherical cap method is simple and achievable, but it cannot be used in gravity or nonequilibrium environments.…”

Contact angle measurement on curved wetting surface in multiphase lattice Boltzmann method

“…Lattice Boltzmann (LB) method has developed into a very effective numerical method for simulating complex fluid flow [33][34][35][36][37][38][39]. LBM is derived from the concept of cellular automata and kinetic theory, and its inherent mesoscopic properties make it excellent in modeling fluid systems involving interface dynamics [40][41][42] and phase transitions [21,43].…”

Multiphase curved boundary condition in lattice Boltzmann method

“…The application of multiphase flows has been the subject of much interest [38][39][40] and several popular multiphase models have been developed. Wen et al [28] proposed a chemical-potential-based multiphase model well applied in measure various types of contact angles [29] and for analyze the lateral rebound of droplets [32].…”