Effect of drop volume and surface statistics on the superhydrophobicity of randomly rough substrates

In this paper, a simple theoretical approach is developed with the aim of evaluating shape, interfacial pressure, apparent contact angle and contact area of liquid drops gently deposed on randomly rough surfaces. This method can be useful to characterize the superhydrophobic properties of rough substrates, and to investigate the contact behavior of impacting drops. We assume that (i) the size of the apparent liquid-solid contact area is much larger than the micromorphology of the substrate, and (ii) a composite interface is always formed at the microscale. Results show apparent contact angle and liquid-solid area fraction are slightly influenced by the drop volume only at relatively high values of the root mean square roughness h rms, whereas the effect of volume is practically negligible at small h rms. The main statistical quantity affecting the superhydrophobic properties is found to be the Wenzel roughness parameter r W, which depends on the average slope of the surface heights. Moreover, transition from the Cassie-Baxter state to the Wenzel one is observed when r W reduces below a certain critical value, and theoretical predictions are found to be in good agreement with experimental data. Finally, the present method can be conveniently exploited to evaluate the occurrence of pinning phenomena in the case of impacting drops, as the Wenzel critical pressure for liquid penetration gives an estimation of the maximum impact pressure tolerated by the surface without pinning occurring.