A homogenization strategy in fluid-structure interaction

In Nature, fluid-structure interactions are often characterized by separation of scales, due to the presence of small-scale roughness on macroscopic surfaces. It is the case, for instance, of the scales which cover the wings of the butterflies or the shark’s skin and the microscopic protrusions present on the surface of lotus’ leaves. A way to bypass the complexity of fine-grained numerical simulations is to consider macroscopic approaches which disregard the microscopic properties of the structure aside from the presence of effective tensorial properties which results from the solution of microscopic problems. This homogenization perspective allows to formally develop a new macroscopic boundary condition to be used when an incompressible fluid flows over a rough surface, together with an univocal definition of the effective properties of the surface, such as the slip length and the permeability of the rough layer.