Levitation force induced by pressure radiation in gas squeeze films

An analytical and numerical study on the levitation force induced by pressure radiation in gas squeeze films is investigated. The levitation phenomenon is known to occur when a planar object is placed at close proximity to a vibrating piston. The existing analytical approaches are based on either conventional acoustic radiation, where the fluid is assumed inviscid or on a variant of the Reynolds equation that incorporates viscous effects. Alas, these solutions are often in poor agreement with accurate numerical results and, at best, describe appropriately cases that include a limited range of object weights and vibration frequencies. In this work, two cases are addressed: the flow induced by vibrations perpendicular to a flat surface and that by flexural wave propagation parallel to the surface. For the first case, numerical and second-order analytical perturbation solutions are obtained and compared, proving them to be in good agreement. In addition, a novel, analytical expression for the levitation force is also suggested that proves to be valid for a wider physical range of squeeze numbers and vibration amplitudes. For the second and more complex case (recently used in noncontacting transportation systems where the driving surface exhibited flexural traveling waves), the skin-friction force exerted on the flat surface is derived analytically based on a first-order perturbation solution, and the levitation force is analyzed numerically. Some insights on the physical behavior are then highlighted and discussed. (C) 2004 Acoustical Society of America.