Finite-Inertia Corrections and Breakdown of Gor'kov Theory in Acoustic Levitation of Droplets

Abstract

Acoustic levitation is widely used for contactless droplet manipulation, yet the standard Gor'kov description obtained by time averaging the acoustic field lacks a quantitative validity criterion. In this work, we derive Gor'kov theory as the leading-order slow time limit of the instantaneous radiation force, compute the first finite-inertia correction, and obtain a simple breakdown parameter. The correction reduces the effective trapping drift and predicts fast time oscillations of amplitude $x_1^{\mathrm{max}}\sim\lambda/8$, corresponding to hundreds of micron for typical ultrasonic levitation experiments. This sets a measurable criterion for experiments using phased transducer arrays. Our results provide a universal rule of thumb for acoustic trap design and clarify where time-averaged radiation force models fail.