Studying of droplet impingement on hydrophilic and hydrophobic curved surfaces by lattice Boltzmann method based on Allen-Cahn equation

In this paper, an efficient lattice Boltzmann method is applied for the simulation of two-phase flow problems at high density and viscosity ratios. The present lattice Boltzmann method employs the Allen-Cahn equation to model the interfacial dynamics between two phases and an appropriate collision operator is implemented to ensure the stability of the numerical solutions. The performance of the numerical algorithm is examined by studying droplet dynamics at different flow conditions. Herein, the equilibrium state of a droplet on the flat and curved walls is verified by considering the wetting properties, namely the hydrophilic and hydrophobic characteristics, for solid surfaces. The multiphase flow pattern and interfacial dynamics of an impinging droplet on a cylinder surface and a semicircular cavity are also investigated and the obtained results are compared with the available data. The present study demonstrates that the curved wall considering the wettability effects significantly affects the droplet dynamics, depending on the properties of the liquid phase and the flow conditions. This work also shows that the lattice Boltzmann method with the Allen-Cahn equation is more stable for simulation of liquid-gas systems at density ratio 1000 and viscosity ratio 100 which makes this method more suitable for predicting practical flow characteristics.