Elastohydrodynamics induced by a rapidly moving microscopic body

The simple model involving a moving rigid particle, separated from a compliant wall by a thin film of viscous fluid, has previously been applied successfully to a number of important problems. For example, transport of blood cells, particle clearance in the lungs and the late stages of particle sedimentation. Considerable fluid forces are generated in the film, causing the compliant surface to deform. Hence, the usual goal is derivation and solution of an appropriate deformation evolution equation. In the applications considered to-date, however, flow inertia is neglected as flow speeds are not especially high. In this study, we are interested in regimes where unsteady flow inertia is significant, such as found in certain microdevices or thermal excitation of light particles. We present a novel model, which for the first time accounts for inertial effects in both the flow, and the deformable surface. The significant role that inertia plays is fully illustrated through surface deformation profiles, computed under a variety of parameter regimes, as well as calculations of associated hydrodynamic loading. Frequency response curves are seen to exhibit distinct shifts in resonant frequency and quality factor under different levels of inertia, a finding which we believe has important practical implications.