To leak or not to leak: deformation of perforated elastic strips driven through a viscous fluid

From dandelions and insect wings to wire fences and parachutes, there are numerous natural and technological instances of porous flexible structures that deform due to fluid loading. Whereas fluid flow through bulk porous media has been studied extensively, the interaction between a perforated, deformable object and a surrounding viscous fluid has received much less attention. Here, we microfabricate flexible, porous, and slender strips containing a precisely designed array of voids that target set permeabilities. We then drive these perforated strips through a fluid, at low Reynolds number conditions, and quantify the extent of deformation due to viscous loading. We use a reduced theoretical model based on Kirchhoff-Euler beam theory coupled with a description of the fluid loading to deduce the drag force from the deflected shape of the strip. In parallel, we perform ad-hoc numerical simulations to capture the details of the fluid-structure interaction, thereby uncovering a nontrivial effect of permeability on the drag experienced by the porous structure. We hope that the gained insight may guide the design of flexible structures that optimize their porosity and permeability to enhance drag, towards light-weight high-drag slender objects.