Lattice Boltzmann simulations of the motion induced by variable surface tension

Abstract

Methods for implementing variable surface tension in the multiphase Lattice Boltzmann model with the color model and Shan-Chen scheme are tested by analyzing the models' abilities to reproduce a theoretical result by Levich and Kuznetzov. If the surface tension around a droplet is asymmetrical, the droplet moves towards the side where the surface tension is lower. The droplet's velocity is proportional to the surface tension gradient, the droplet's radius, and the inverse of the viscosity. The model is tested to determine whether the simulated droplets move in the manner predicted by theory. Although the discreteness of the underlying lattice causes a spurious oscillation to the velocity, the numerical results concerning the average velocity show a good correspondence between theory and the model in regards to the surface tension gradient and droplet size. The color model also produces good simulations in the scenarios with different viscosities, while the diffusive properties and unknown relationships between the parameters and surface tension in the Shan-Chen model make the numerical results of that model more dubious, even though several of the results are qualitatively in agreement.