Asymptotic solution of ultrasonic near-field levitation problem

Abstract

Ultrasonic near-field levitation allows suspension of a moderately large object at a height of tens of microns above sound actuator. We developed an asymptotic approach to describe the air dynamics in the gap between an acoustic source and the levitating object. The suggested method allows computation of the lifting force. Due to resolving of both viscous and inertial effects, it remains applicable across a wide range of levitation distances. The paper explains theoretical background of the model and presents a numerical solution of the obtained equations. The results are compared to published numerical and experimental data showing very good agreement.

The loaded parabolic-hyperbolic equation and its relation to non-local problems

“…Thus, by virtue of the representation (5), equation (1) Problem 2.1 and Problem 2.2, in view of (9), are all reduced to the following Problem N P 1 and Problem N P 2 for equation (6). We investigate the following problems: Problem N P 1 .…”

“…Particularly, parabolic-hyperbolic equations are considered in some models of spinodal decomposition (so-called hyperbolic diffusion, see, e.g. [7,8]), and also described flow in thin viscous layers subjected to ultrasonic acoustic field [9].…”