Biomimetic model systems of rigid hair beds: Part I - Theory

Crustaceans - such as lobsters, crabs, and stomapods - have hairy appendages that they use to recognize and track odorants in the surrounding fluid. An array of rigid hairs impedes flow at different rates depending on the spacing between hairs and the Reynolds number, Re. At larger Reynolds numbers (Re \textgreater 1), fluid travels through the hairs rather than around them, a phenomenon called leakiness. Crustaceans flick their appendages at different speeds in order to manipulate the leakiness between the hairs, allowing the hairs to either detect odors in a sample of fluid or collect a new sample. A single hair can be represented as a slender body attached at one end to a wall. Using both slender body theory and numerical methods, we observe that there is a region of flow around the hair that speeds up relative to the unobstructed flow. As the Reynolds number increases, this fast flow region moves closer to the hair. Using this model, we predict that an array of hairs can be engineered to have a desired leakiness profile.