Shear flow over cylindrical rods attached to a substrate

Shear flow over a periodic array of cylindrical rods attached to a substrate is studied as a model of flow over a nanomat consisting of aligned carbon nanotubes. The objectives are to evaluate the macroscopic slip velocity, compute the hydrodynamic load exerted at the rod side surface and tip, and estimate the flow-induced deflection. The hydrodynamic traction and macroscopic slip velocity are computed by solving the equations of Stokes flow for a doubly periodic square or hexagonal arrangement using a boundary-element method. The results illustrate the dependence of the slip velocity on the surface coverage expressed by the ratio of the rod radius to separation, and confirm the occurrence of hydrodynamic screening due to surrounding rods confining the traction near the exposed tip of each rod. An estimate for the flexural stiffness of nanotubes is made using available information on the flow-induced deflection. Computations for shear flow past an isolated attached rod are carried out using a highly accurate boundary-element method coupled with a finite-element method for solving the Euler–Bernoulli beam equation, and an iterative procedure involving a boundary-element implementation coupled with a boundary-value formulation involving ordinary differential equations for describing large beam deformation. The results illustrate the precise shape of deflected rods.