Critical pressure versus mechanical criteria for the analytical modeling of wetting on multiscale surfaces

Abstract

HypothesisIn order to better understand the outstanding wetting behaviors of many vegetal surfaces, it is necessary to properly carry out an analytical modeling of mixed-state wetting on real and multiscale surfaces. The energetical approach is limited with regards to its ability to describe the dynamics of the impregnation of surface asperities and therefore, a mechanical or a critical pressure approach can be more suitable. Nevertheless, as yet they have not been applied on natural surfaces with a sufficiently accurate description of the latter and have only yielded qualitative results. ExperimentsThe theoretical basis underlying both the mechanical and the critical pressure approaches to capillary phenomena is thoroughly derived and discussed. Critical pressure criteria that are applicable to real multiscale surfaces are introduced and applied to the case of the sacred Lotus, accounting for its nanoscale topography. FindingsEffective anchorage depths, solid-liquid contact areas and triple line lengths are calculated. Results quantitatively show that the presence of a nanoscale topography leads to a more superficial mixed-state wetting and increases the maximal overpressure sustainable by the menisci in a composite-wetting state. It is also demonstrated that the surface asperities of Nelumbo nucifera leaves have evolved to withstand severe raindrop impacts without being over-sized. Eventually, we show that the mechanical approach is flawed. Therefore, we strongly advocate using critical pressure criteria when designing multiscale water-repellent surfaces, for which we suggest design guidelines.