This dissertation investigates the fluid–structure dynamics involved in squeeze-film levitation, in pursuit of a theoretical explanation for the anomalously large, attractive load-bearing forces observed in recent experiments.

Consider a rigid disk vibrating rapidly along its axis of symmetry near a parallel wall, inducing oscillatory airflow in the thin film of air separating the disk and the wall as well as its periphery. Due to the nonlinear effects of fluid inertia and compressibility, the air pressure within the film varies in time asymmetrically about its ambient value, providing a nonzero time-averaged pressure force on the disk. Prior studies of this “squeeze-film” effect report that the time-averaged force typically repels the disk from the wall, making it a suitable mechanism for bearing lubrication. The strong attractive forces reported recently thus constitute a radical departure from this historical norm, expanding the range of possible applications to include wall-climbing robots and versatile contactless grippers. This dissertation aims to understand the fluid–structure physics underlying the emergence of strong attraction, through the derivation of reduced mathematical formulations that may ultimately aid the development of such novel systems.

Gas-lubricated systems represent an exceptional family of slender fluid flows for which the effects of compressibility and viscous shear enter simultaneously while maintaining small values of the Knudsen number, thereby guaranteeing applicability of the continuum hypothesis in describing the flow. Thus, the classical Navier–Stokes equations are used here to investigate the gas dynamics in the thin film as well as the effectively incompressible discharge and entrainment of air across a small region surrounding its edge. An approximate solution obtained using the method of matched asymptotic expansions indicates that the augmented attractive forces observed in recent experiments can be attributed to the pronounced dynamic bending of the highly flexible disks utilized. The theoretical formulation is then generalized to describe two-way fluid–structure coupling between the undulating disk and the thin-film airflow, thereby yielding predictions of system behavior that exhibit greatly improved agreement with experimental data. The canonical problems outlined herein can be readily extended to describe more complex configurations of practical interest—in particular, those involving transportation of the levitated object.