Droplet spreading dynamics on hydrophobic textured surfaces: A lattice Boltzmann study

Abstract

A three-dimensional (3D) lattice Boltzmann method based on the Allen-Cahn equation (A-C LBM) is employed to study the spreading dynamics of impacting droplets on the hydrophobic flat and textured surfaces. At first, the simulation of the equilibrium state of a droplet and also the impacting droplet spreading on a flat surface are considered at various wetting conditions to examine the accuracy and efficiency of the present numerical technique. The obtained results for these cases show excellent agreement with available theoretical, numerical, and experimental data in the literature that confirms the validity of the A-C LBM employed for simulation of such complex interfacial dynamics. Upon validation, the implemented A-C LBM is applied for investigation of the droplet impingement on the hydrophobic textured surface and the results are compared with those obtained by considering the flat surface. The present study shows that using microscale textures on a hydrophobic surface dramatically reduces the contact area between the impacting droplet and the solid wall due to the momentum redirection phenomenon. Indeed, the hydrophobic surface used with in-plane circular ridges causes the spreading lamella to eject out-of-plane with a liquid bowl shape. This mechanism converts a part of the horizontal momentum of the spreading to the vertical momentum that prevents droplets to have intense interaction. For an impacting droplet at a high Weber number, it is concluded that the geometrical parameters of the ridge dictate the morphology of the spreading on the hydrophobic surface. However, the droplet dynamics at a low Weber number depend on both the texture size and the surface wettability, so that the physical mechanisms of the droplet spreading and lamella ejection dramatically change by variation of these parameters. The obtained results show that when the adhesion force of the substrate is dominant (lower contact angles), the wetting property of the surface plays an effective role than the texture geometry in the formation of the liquid bowl at low Weber numbers. Also, the present study demonstrates the capability of the A-C LBM for the prediction of the studied multiphase flow structures and characteristics with extremely complex interface phenomena.