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arXiv · 2601.00043

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

Hollis Williams
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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.

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Hollis Williams. 2025-12-31. Finite-Inertia Corrections and Breakdown of Gor'kov Theory in Acoustic Levitation of Droplets. https://arxiv.org/abs/2601.00043

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