| Popis: |
Beds of passive, hair-like fibers can be found in many biological systems, including inside ourselves. Intestines, tongues, and blood vessels contain these types of surfaces, making us ‘hairy’ on the inside. A coupled elastoviscous problem arises when hairy surfaces are sub- jected to shear-driven Stokes flows. The hairs deform in response to fluid flows, and in turn, hair deformation affect fluid stresses. The the- oretical model that accounts for the large-deformation flow response of a biomimetic model system of elastomer hair beds is known. However, the solution to the differo-integral equation governing the behavior of a bed of hairs immersed in fluid is difficult to uncover. Here we show a method to find the analytic solution to this equation of equilibrium. The time-independent equation of motion describing the bending of the hairs can be found by extending the pendulum problem for large angles to the case of bed hairs subject to Stokes flows. We consider the Hamiltonian formalism, analyze phase portraits, and utilize elliptic integrals to reduce the problem to a numerical problem. By these methods we find a solution that characterizes the hairs’ shape by giving the angle with respect to the surface normal at any distance along the hair. Since it was found that biological hairy surfaces reduce fluid drag, angled hairs may be used in the design of integrated microfluidic components, such as diodes and pumps. Thus our solution would be useful to manufacture these devices. |
