Shear flow past slender elastic rods attached to a plane

Shear flow past an elastic rod or a doubly periodic array of elastic rods attached to a plane is investigated with reference to flow over a ciliated surface or a carbon nanomat. In the absence of flow, the rods are straight cylinders with circular cross-sectional shape. The mathematical framework combines slender-body theory for computing the hydrodynamic load with classical beam theory for computing the rod deflection. Small deflections are computed using a finite-element method and large deflections are computed using an iterative procedure where a rod shape is assumed, the hydrodynamic load is found, and a new shape is obtained by solving a boundary-value problem involving ordinary differential equations at equilibrium. Deflected rod profiles are presented and the macroscopic slip velocity is computed in the case of flow past a doubly periodic square or triangular array of rods over a broad range of surface coverage.