Numerical study of the droplet impact onto liquid film on the rough solid surface via lattice Boltzmann method

The process of the droplet impact onto the liquid film on the rough solid surface, as one of the basic multiphase problems, is very important in many fields of science and engineering. On the other hand, the problem is also very complicated since there are many parameters that may influence the process of the droplet impact on the rough solid surface with a liquid film. Up to now, there are still little research on this problem, and to gain a better understanding on the physical mechanics of the droplet impact onto the film on the rough solid surface, it is desirable to conduct a detailed study. To clearly understand the physical phenomena appearing in the process of droplet impact on the liquid film, a parametric study on this problem is also carried out based on a recently developed lattice Boltzmann method in which a MRT lattice Boltzmann model is used to solve the Navier-Stokes equations, and the other is adopted to solve the Cahn-Hilliard equation that is used to depict the interface between different phases. In this paper, the effects of the relative thickness of film ( h ), the relative width of cavity ( d * ) and the relative depth of cavity ( L * ) on the dynamic behavior of interface are investigated in detail, and the velocity and pressure fields are also presented. In order to reduce the influence of lattice, we fix the lattice to be 600×120 for gas, which is fine enough to give accurate results. In addition, in our simulations, We =500, Re =480, viscosity ratio and density ratio are set to be 2:1. The numerical results first show that, the phenomena of crown and entrainment can be observed obviously during the process of droplet impact onto the liquid film on the rough interface when We and Re are large. The radius of spray ( r ), which is formed by the droplet impact onto liquid film, is related to time through the relation r / 2 R ≈ α U t / 2 R when h is small, which is coincident with the result of droplet impact onto the liquid film on smooth surface, and additionally the coefficient α would decrease with the increase of h . However, this relation seems not accurate for the case with a large h , and simultaneously, the splashing phenomenon has not been observed. Secondly, the relative width of cavity d * plays an important role on the phenomena of splashing. When d * =1, there will be two small droplets through the splashing phenomenon (left half part), then with this parameter increase, the number of small droplet and the point where the splashing occur will also change, and there also are much difference in relation of spray radius and time. Actually, if d * is small, the coefficient α would first decrease and then increase with the increase of d * , while if d * >8, the cavity width would only have a little influence on the behavior of spray. Finally, it is also found that the pressure change near the cavity bottom is small at different L * , that is to say, the relative depth of cavity L * seems to has no apparent effect on the formation of spray, but it brings a great influence on the splashing of spray and the movement of the droplet which is produced in the process of splashing.