Oscillation of cylinders of rectangular cross section immersed in fluid

The ability to calculate flows generated by oscillating cylinders immersed in fluid is a cornerstone in micro- and nanodevice development. In this article, we present a detailed theoretical analysis of the hydrodynamic load experienced by an oscillating rigid cylinder, of arbitrary rectangular cross section, that is immersed in an unbounded viscous fluid. We also consider the formal limit of inviscid flow for which exact analytical and asymptotic solutions are derived. Due to its practical importance in application to the atomic force microscope and nanoelectromechanical systems, we conduct a detailed assessment of the dependence of this load on the cylinder thickness-to-width ratio. We also assess the validity and accuracy of the widely used infinitely-thin blade approximation. For thin rectangular cylinders of finite thickness, this approximation is found to be excellent for out-of-plane motion, whereas for in-plane oscillations it can exhibit significant error. A database of accurate numerical results for the hydrodynamic load as a function of the thickness-to-width ratio and normalized frequency is also presented, which is expected to be of value in practical application and numerical benchmarking. (C) 2010 American Institute of Physics. [doi:10.1063/1.3397926]