It is estimated that 10% of energy costs worldwide are due to efforts made to overcome fluid drag, where the major contributors are the transport industry (ships, planes, trains) and transport of water/gas in pipes. Here, the challenge is to design multi-scale surfaces with appropriate features (e.g. anti-fouling) that interact with the overlying flowing fluid to reduce drag/noise or increase mixing.
Essentially all natural surfaces are to some extent made of porous deformable multi-scale structures and exposed to dynamic flows. However, we lack a fundamental understanding of how the macroscopic overlying flow is altered by the underlying mesoscopic texture (e.g. filaments, roughness, patterns) and the microscopic molecular details of the texture. The figure above shows the multiscale surface of the Salvinia molesta leaf (first described by Wilhelm Barthlott), which has a dense coating of elastic hairs shaped as egg-beaters with nanoscopic wax crystals. The crystals are however absent in the terminal cells of each hair, which makes a superhydrophobic surface locally hydrophilic. These evenly distributed hydrophilic patches are capable of pinning and stabilizing the air-water interface, and preventing losses of air for weeks even in turbulent flow conditions.
These hierarchical surfaces effectively modify boundary conditions and provide new ways to manipulate flows. Their full numerical description has not yet been undertaken since it requires resolving the physical/chemical processes to determine properties such as the contact angle, the mesoscale fluid-structure interaction of the anisotropic and elastic bed and, finally, macroscale modifications of the flow such as unsteady vortices above the surface.