Rake or Sieve: design principles for flow past an array of rigid hairs

Crustaceans have appendages with an array of rigid hairs covered in chemoreceptors, used to sense and track food. By changing the speed of flow past the hairy surface, and thereby manipulating the Reynolds number (Re) of the flow, crustaceans directly influence the flow behavior. Flow acts either as a rake – diverting flow around the hair array, or as a sieve – penetrating into the hair array. In our experiments, we uncover a third transitional phase: deflection – where the flow partially penetrates the hair array and is deflected laterally. We develop a design principle for constructing hair arrays that exhibit each flow phase. We find that the flow is characterized by the depth of the boundary layer on a single hair. As Re increases, the depth of the boundary layer decreases non-linearly. If the distance δ between hairs is less than the depth of the boundary layer, then we observe rake flow. Conversely, if δ is greater than twice the boundary layer depth, then we observe sieve flow. And we observe deflection flow for intermediate values of δ. This principle can be used to design steady state devices that use beds of rigid hairs to direct flow. Potential applications include chemo-sensing and filtering particles.