Length Scale Effects in Wetting of Chemically Heterogeneous Surfaces

Wetting of chemically heterogeneous surfaces is modeled using phase field theory. Phase field theory involves constructing a coarse-grained free energy functional. A kinetic evolution equation is developed based on this free energy functional, which allows the phase field to evolve following a variational derivative of the free energy functional with respect to the phase field variable. Contact angle hysteresis is incorporated by a modified kinetic parameter. Using this model, we demonstrate the effect of variation in the length scale of a chemically heterogeneous surface as deviation from the Cassie theory for a surface with a finite length scale. We demonstrate the realm of applicability of Cassie theory as being for surfaces where the component materials are intricately alloyed such that they are not discernible on the length scale associated with the thickness of the diffuse molecular interface. In this context, the interface between the wetted and non-wetted regions is a diffuse interface suffering steep but continuous changes from wetted to non-wetted regions. When the length scale associated with either of the component materials is greater than the interface thickness, the specific arrangement of the materials affects the evolution and shape of the three-phase contact line, and thereby affecting the macroscopic contact angle. These results are of importance to surface designers for a range of applications, where targeted wetting characteristics can be achieved by suitably alloying component materials.