  Hypothesis
  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 hypothesis 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.
  Theory and Simulations
  The theoretical framework is presented followed by application to limiting
cases of various wetting states. The wetting states include those considered in
the Wenzel, Cassie-Baxter and wicking state models. The wetting behaviour of
multiscale surfaces is then explored by conducting direct simulations of a
fluid droplet on a structurally rough surface and a chemically heterogeneous
surface.
  Findings
  The underlying origin of the classical wetting models is shown to be rooted
within the proposed theoretical framework. In addition, integral geometry
provides a topological-based wetting metric that is not contingent on any type
of wetting state. Being of geometrical origin the wetting metric is applicable
to describe any type of wetting phenomena on complex surfaces. The proposed
framework is applicable to any complex fluid topology and multiscale surface.
