Modified surface tension model for free surface flow with single-phase lattice Boltzmann method

A single-phase lattice Boltzmann model with modified surface tension is developed in this paper to solve the problem of high-density-ratio free surface flow. The computational efficiency and accuracy are both enhanced. The restriction to the relaxation factor (which needs to be smaller than 1) is circumvented by the new surface tension algebra, due to its rational physical nature compared with the treatment of Xing, Buther and Yang in their paper (Comp. Mater. Sci., 2007, 39(2): 282–290). The proposed stable surface tension scheme is applied to simulate the free deformation of a square droplet with surface tension effect and the process of a droplet impinging on a liquid film. The numerical solution for free deformation of a droplet agrees well with thermodynamic principles, and also achieves high accuracy in comparison with Xing, et al.’s model. Three typical impinging modes are successfully obtained with the new scheme, and another particular mode found by Wang and Chen is also successfully simulated. The evolutions of liquid crown agree well with the power law related to time.