Universal description of wetting on multiscale surfaces using integral geometry

Emerging energy-related technologies deal with multiscale hierarchical structures, intricate surface morphology, non-axisymmetric interfaces, and complex contact lines where wetting is difficult to quantify with classical methods. We hypothesise that a universal description of wetting on multiscale surfaces can be developed by using integral geometry coupled to thermodynamic laws. The proposed approach separates the different hierarchy levels of physical description from the thermodynamic description, allowing for a universal description of wetting on multiscale surfaces.

The theoretical framework is presented followed by application to limiting cases of wetting on multiscale surfaces. Limiting cases include those considered in the Wenzel, Cassie-Baxter, and wicking state models. Wetting characterisation of multiscale surfaces is explored by conducting simulations of a fluid droplet on a structurally rough surface and a chemically heterogeneous surface.

The underlying origin of the classical wetting models is shown to be rooted within the proposed theoretical framework. Integral geometry provides a topological-based wetting metric that is not contingent on any type of wetting state. The wetting metric is demonstrated to account for multiscale features along the common line in a scale consistent way; providing a universal description of wetting for multiscale surfaces.