To Leak or not to Leak through Holey Sheets

From spider webs and insect wings, to wire fences and parachutes, Nature and technology present vast examples of porous and perforated flexible structures that deform due to fluid flow. Whereas fluid flow through porous media has been studied extensively, the fluid-structure interactions of a perforated, elastic object with a surrounding viscous fluid has received much less attention. Here, we use precision desktop experiments and finite element simulations to focus on the prototypical problem of a perforated elastic plate moving through a viscous fluid, at low Reynolds numbers. We seek to provide a predictive framework for the large deformation of perforated plates due to hydrodynamic loading so as to rationalize our experimental findings. For this purpose, we use a reduced theoretical model based on Kirchhoff-Euler beam theory coupled with a description of the fluid loading, at low Reynolds numbers. Moreover, we perform ad-hoc numerical simulations to capture the details of the fluid-structure interactions, highlighting the effect of permeability on the drag experienced by the structure. We hope that our findings may lead to a better understanding of the interactions between porous slender structures and viscous flows, across biological and technological applications.