A thermodynamic approach to predict apparent contact angles on microstructures using surface polygonal maps

The thermodynamic model of wetting developed and tested in this work allows the understanding and prediction of apparent contact angles on topographic maps of real and digitally-generated microstructures. The model considers the solid component as a set of finite areal elements in the form of a polygonal map. Liquid and gas components are instead evaluated as continuous and incompressible volumes. In this study, the concept of the wetting topographic spectrum (WTS) is proposed to simulate the changes in the liquid-solid contact areas and of the interfacial energies while wetting the microstructure from the top to the bottom of the topographic map, passing through various states of metastable equilibrium, to find a stable configuration. The model was successfully applied to predict the wetting apparent contact angles on randomly micro-structured polypropylene (PP) surfaces and on a superhydrophobic and superoleophobic transparent polydimethylsiloxane (PDMS) microstructure previously presented as a communication in this journal by other authors. The method presented in this study can be used to design and predict the geometry of microstructures with special wetting characteristics.