Micro Structures in Thin Coating Layers: Micro Structure Evolution and Macroscopic Contact Angle

Micro structures of coating surfaces lead to new industrial applications. They allow to steer the wetting and dewetting behaviour of surfaces and in particular to enhance hydrophobicity. Here, we discuss the formation of micro structures in the drying process of a coating. Furthermore, for a given micro structured surface we show how to predict the effective contact angle of drops on the surface. At first, we derive a new approach for the simulation of micro structure evolution based on a gradient flow perspective for thin liquid films. This formulation includes a solvent dependent surface tension, viscosity and evaporation rate. In each time step of the resulting algorithm a semi implicit Rayleigh functional is minimized. The functional itself depends on the solution of a transport problem. We apply a finite difference discretization both for the functional and the transport process. As in PDE optimization a duality argument allows the efficient computation of descent directions. Next, given a certain micro structured coating we mathematically describe effective contact angles in different configurations and their impact on the macroscopic hydrophilic or hydrophobic surface properties. On periodic surfaces we aim at the computation of effective contact angles. This involves a geometric free boundary problem on the fundamental cell. Its solution describes vapor inclusions on the wetted surface. The free boundary problem is solved by a suitable composite finite element approach.