Computation of asymmetrical drops at rest on surfaces with regular roughness according to the Wenzel equation

The computation ofthe shape of a sessile or pendant drop at restis a classical problem of Fluid Mechanics. The problem possesses relevant experimental interest to deduce the interfacial tension and the contact angle from the geometrical properties of the drop. The exact knowledge of both quantities is required by many mathematical models of two-phase flow. However the compu tation usually assumes the solid plane to be perfectly smooth an d chemically homo geneous, w hile actual surfaces are always rough and often smeared by contaminants. Recent researches on oil-water flow have shown that sometimes the flow regime depends critically upon th e roughness and wettability of the in ner pipe surface. Even assuming the chemical homogen eity of the solid, roughness may influence heavily the drop shape and size, wettability and contact angle, but it is difficult to classify because it involves various parameters (average roughness, root mean square, texture, etc.). A case of peculiar interest is periodic roughness having a parallel rectilinear texture because such surfaces are already available as industrial products, suitable for experiments. The key idea of the ongoing research, not found in any other paper known to the author, is that diffraction gratings u sed in optics possess this kin d of texture, whic h is accurate to a small fraction of the wavelength of visible light. Moreover they are made of high-quality glass with carefully controlled composition, hence they guarantee good chemical homogeneity. Another promising surface which possesses a regular roughness is the old microgroove record. An original mathematical model, not previously found in the literature, is constructed according to the Wenzel equation (1936) and a numerical algorithm to solve the model is described which adapts general ideas taken from the rapidly growing field of Computational Fluid Dynamics. This mathematical model p romises to improve the con tact angle measuremen t on the above mentio ned artificial surfaces, as a first stage before dealing with actual surfaces. This improvement will benefit in turn the mathematical modelling of oil-water flow inside pipes having a rough surface.