A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions

We propose an efficient numerical method for the simulation of multi-phase flows with moving contact lines in three dimensions. The mathematical model consists incompressible Navier-Stokes equations two immiscible fluids standard interface conditions, Navier slip condition along solid wall, and a angle which relates dynamic to normal velocity line (Ren et al. (2010) \cite{Ren10}). In method, governing fluid dynamics are coupled advection equation level-set function. latter models interface. Following practice, conditions taken into account by introducing singular force on momentum equation. This results single set whole domain. Similar treatment is imposed force, acts direction line, condition. new boundary condition, unifies wall. solved using finite difference method. Numerical results, including convergence study, presented spreading droplet both homogeneous inhomogeneous walls, as well inclined plate under gravity.