Hydraulic resistance of channels obstructed by a dense array of elastic fibers

Dense arrays of soft hair-like structures protruding from surfaces are ubiquitous in living systems. Fluid flows can easily deform these soft hairs, which in turn impact the flow properties. At the microscale, flows are often confined which exacerbates this feedback loop: the hair deformation strongly affects the flow geometry. Here, I investigate experimentally and theoretically pressure driven flows in laminar channels obstructed by a dense array of elastic fibers or `hairs'. I show that the system displays a non-linear hydraulic resistance that I model by treating the hair bed as a deformable porous medium whose height results from the deflection of individual fibers. This fluid-structure interaction model encompassing flow in porous media, confinement, and elasticity is then leveraged to identify the key dimensionless parameter governing the problem: $\hat{f}_0$ a dimensionless drag that combines fluid, solid, and geometrical properties. Finally, I demonstrate how these results can be harnessed to design passive flow control elements for microfluidic networks.