Dynamics of Finite-length Rods Near Solid Boundaries

The motion of finite-length cylindrical rods moving near a planar rigid surface is a scenario common across many engineering and natural settings. The rods are allowed to rotate or translate in directions perpendicular or parallel to the plane. We develop a three-dimensional lubrication theory to characterize the pressure and hydrodynamic resistances of the cylinders through a special consideration of the cylinder's end-effects. In addition, three-dimensional numerical simulations were used to solve these Stokes flows for cylinders of varying lengths and with varying gap sizes between the plane, and the numerical results support the developed analytical descriptions. Visualizations of the flow will be presented to provide qualitative insights and rationalize the effect of the ends on the dynamics of the cylinders. We demonstrate our newly developed theory can successfully account for the finite length effects of cylinders moving near planar boundaries.