Sharp interface Cartesian grid method II: A technique for simulating droplet interactions with surfaces of arbitrary shape

Abstract

A fixed-grid, sharp interface method is developed to simulate droplet impact and spreading on surfaces of arbitrary shape. A finite-difference technique is used to discretize the incompressible Navier–Stokes equations on a Cartesian grid. To compute flow around embedded solid boundaries, a previously developed sharp interface method for solid immersed boundaries is used. The ghost fluid method (GFM) is used for fluid–fluid interfaces. The model accounts for the effects of discontinuities such as density and viscosity jumps and singular sources such as surface tension in both bubble and droplet simulations. With a level-set representation of the propagating interface, large deformations of the boundary can be handled easily. The model successfully captures the essential features of interactions between fluid–fluid and solid–fluid phases during impact and spreading. Moving contact lines are modeled with contact angle hysteresis and contact line motion on non-planar surfaces is computed. Experimental observations and other simulation results are used to validate the calculations.