Topographies that mantain a constant Wenzel roughness factor over the nanometer to macroscopic vertical range

Abstract

The wetting of solid surfaces is directly involved in a large number of processes as important as the lubrication or corrosion of materials, and indirectly in the biocompatibility of implants or bacterial adhesion, and as such is currently a very active field of research. The surface roughness of the material plays an important role in its interaction with the wetting liquid. One of the parameters used in one of the most used models to analyze the wetting of materials, the Wenzel model, captures the roughness of the material through the so-called Wenzel roughness parameter, which by definition is the ratio between the surface area that develops a rough surface and the one it would have if it were perfectly flat. This model was intuitively developed in 1936 to account for experimental results showing that the wettability of a material increased by imposing roughness. In this brief note we present a characteristic of this parameter, and it is that for a series of topographies structured in the form of periodic patterns of protrusions whose height can vary from the order of nm to macroscopic values, of hemispherical, conical, cylindrical, and pyramidal shapes, this parameter does not show any variation with the height of the same (thereby predicting a null influence of the roughness in the wetting). We present this broad set of topographic designs (to which more can be added) to account for this limitation of the Wenzel roughness factor and contribute to the debate about its applicability and usefulness in the analysis of real-world materials and phenomena.