3D lattice Boltzmann simulation for a saturated liquid droplet at low Ohnesorge numbers impact and breakup on a solid surface surrounded by a saturated vapor

In this paper, new simulation results of a saturated liquid droplet impact dynamics on hydrophilic (θ = 80°) and hydrophobic (θ = 170°) solid surfaces surrounded by a saturated vapor are obtained based on a 3D lattice Boltzmann method (LBM). A novel piecewise relaxation time is proposed to overcome numerical instability at high liquid/vapor density ratios and low liquid droplet viscosities. Simulations are carried out for low Ohnesorge (Oh) numbers in the range from 0.01 to 0.05, corresponding to a water droplet diameter in the range of 1 µm to 130 µm. The impinging droplet deformation process including breakup phenomena is illustrated on hydrophilic and hydrophobic surfaces at different Weber (We) numbers. Droplet spread factors obtained from simulations match well with existing experimental data and theoretical values, validating the accuracy of the present 3D LBM. It is found that a water droplet, after reaching its maximum spread factor, breaks up into a toroid shape with a vapor cavity or a liquid film left at its center at large We numbers on a hydrophilic and a hydrophobic surface, respectively. A map in terms of We number versus Oh number is obtained for predicting the breakup occurrence. The critical We number is monotonically increasing with the increase of the Oh number, meaning that the smaller diameter water droplet requires a larger We number for breakup. Droplet breakup is more likely to occur on a hydrophobic surface than on a hydrophilic surface at larger Oh numbers, while the behavior is opposite at lower Oh numbers.