Modeling of the Boundary Regions between a Spreading Droplet and a Rough Surface of Solid

Drop impact onto a solid surface is a complex phenomenon, which is depending on a variety of factors. To describe the fluid motion, the incompressible Navier-Stokes equations will be used. It is known that the inertial effects and the viscous and surface tension forces affect the evolution of the drop spreading and accordingly of the receding. The arising singularity in the solution for the stresses at the contact line requires special treatment. The interface is divided into three regions with different length scales. At the inner region, the local viscous drag near the moving contact line determines the value of the microscopic dynamic contact angle. Due to numerical difficulties to resolve a mesh of the order of the slip length, which is comparable with the molecular size, the inner region is removed from the computational domain. We substitute the interplay between the microscopic angle and the macroscopic hydrodynamics by an additional force applied to the contact line. The Navier slip boundary conditions appear on the intermediate region. At the outer region the inertial effects become significant. This region is characterized by the no-slip boundary condition. Both fluids are assumed to be incompressible and Newtonian with constant properties (density, viscosity and surface tension). Some preliminary numerical results for an axisymmetric problem are presented