Viscoacoustic squeeze-film force on a rigid disk undergoing small axial oscillations

This paper investigates the air flow induced by a rigid circular disk or piston vibrating harmonically along its axis of symmetry in immediate vicinity parallel surface. Previous attempts to characterize these so-called ‘squeeze-film’ systems largely relied on simplifications afforded neglecting either fluid acceleration viscous forces inside thin enclosed gas layer. The present viscoacoustic analysis employs asymptotic limit small vibration amplitudes investigate systematic reduction Navier–Stokes equations two distinct regions, namely, inner gaseous film where streamlines are nearly confining walls and near-edge region non-slender that features exchange with surrounding stagnant atmosphere. depends relevant Stokes number, defined as ratio characteristic time across oscillation time, compressibility parameter, square acoustic for radial pressure equilibration time. A Strouhal number based local residence emerges an additional governing parameter region, which is incompressible at leading order. method matched expansions used describe solution both time-averaged exhibits comparable variations give opposing contributions resulting force experienced piston. diagram structured coordinates reveals this steady squeeze-film force, typically repulsive values alternates attraction critical separation contour parametric domain exists all numbers. provides, first unifying theory axisymmetric squeeze films, yields reduced description repulsion/attraction potentially useful applications including non-contact bearings robot locomotion.