Lattice Boltzmann simulation of the droplet impact onto liquid film

The process of the droplet impact onto the liquid film, 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 liquid film. To clearly understand the physical phenomena appearing in the process droplet impact on the liquid film, a parametric study on this problem is conduced based on a recently developed lattice Boltzmann method in which a 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, we mainly focus on the effects of the Reynolds number (Re), the Weber number (We), the relative thickness of film (h) and the surface tension (sigma) on the dynamic behavior of interface between different phases, and the velocity and pressure fields are also presented. It is found that with the increase of Re and We, the phenomena of crown and entrainment can be observed obviously during the process of droplet impact onto the liquid film, and the radius of the crown seems not dependent on the We and Re where the relative thickness of film and surface tension are fixed to be 0.5 and 0.003. However, when Re becomes much larger, the splashing phenomenon is produced, and the small droplets caused by the splashing can fall and then impact onto the liquid film again. We also find that if the relative thickness of film is small, the surface tension, Re and We are set to be 0.003, 480 and 500, the film can break up during the process of the droplet impact onto the liquid film, while with the increase of relative thickness, although more liquid are induced in the splashing process, the film can't break up. In addition, with the increase of surface tension, the resistance which prevents the change of interface becomes large, and thus the change of interface is not large when the droplet impacts onto liquid film, as expected. And finally, a quantitative study on the relation between the radius of crown (formed by droplet impact onto liquid film) and the time is also performed, and the expression r/(2R) approximate to sigma root Ut/(2R) where the parameter alpha is about 1.0 and is also independent of We and Re, can be used to describe the relation.