Numerical Study of Droplet Impact on the Inner Surface of a Cylinder

Droplet impact on a solid surface is ubiquitous in daily life and various engineering fields such as ink-jet printing and surface coating. Most of existing studies focused on the droplet impact on flat or convex surface whereas the droplet impact on a concave surface has been less investigated. The purpose of this paper is to investigate the dynamic process of droplet impact on the inner surface of a cylinder numerically by using the phase-field-based lattice Boltzmann method. This method combines the finite-difference solution of the Cahn-Hilliard equation to capture the interface dynamics and the lattice Boltzmann method for the hydrodynamics of the flow. Besides, a recently proposed method is employed to deal with the wetting boundary condition on the curved wall. The method is first verified through the study of the equilibrium contact angle of a droplet on the inner surface of a cylinder and the droplet impact on a thin film, for which good agreement is obtained with theoretical results or other numerical solutions in the literature. Then, different droplet impact velocity, initial height of the droplet, surface wettability and radius of the cylinder are considered for the main problem and their effects on the evolution of the droplet shape are investigated. The physical properties of the droplet including the density and viscosity are also varied to assess their effects on the impact outcome. It is found that the impact Weber number, the liquid/gas density and dynamic viscosity ratios, the wettability of the inner surface of the cylinder, and the radius of the cylinder may have significant effects on the deformation and spreading of the droplet. At low Weber numbers, when the density and dynamic viscosity ratios are sufficiently high, their variations have little effect on the droplet impact process. At high Weber numbers, changes of these two ratios have more noticeable effects. When the Weber number is high enough, droplet splashing appears. When the density and dynamic viscosity ratios are high, the initial height of the droplet only has a minor effect on the impact results. The increment of the cylinder radius not only increases the maximum spreading radius but also enlarges the oscillation period of the droplet after its impact. Rebound of the droplet may be observed when the contact angle of the inner surface of the cylinder is large enough. Besides, the gravity force is found to suppress the oscillation of the droplet on the cylinder's inner surface. This work may broaden our understanding of the droplet impact on curved surfaces.