Suspension Dynamics of Droplets in Acoustic and Gravitational Fields

TL;DR

This paper develops a fluid-based model to analyze droplet suspension in acoustic fields, revealing size-dependent dynamics and critical energy thresholds beyond the Rayleigh limit, aligning with recent experimental observations.

Contribution

It introduces a novel Eulerian acoustic body force model for droplets, capturing interfacial effects and size-dependent suspension behavior beyond the Rayleigh limit.

Findings

Suspension dynamics depend on droplet size beyond the Rayleigh limit.

Critical acoustic energy density varies non-monotonically with droplet size.

Suspension position shifts between nodes and antinodes for larger droplets.

Abstract

In the field of acoustic suspension or levitation of droplets against gravity, the application of Gorkov's acoustic radiation force for small particles (within the Rayleigh limit) or its extensions to larger ones (beyond the Rayleigh limit) is limited to predicting the suspension position of the droplet. Since this approach treats the droplet as a rigid particle, it fails to capture the fluid dynamics of the droplet and is also unsuitable for studying interfacial phenomena such as droplet deformation, splitting, or coalescence. In this work, we employ our recently developed acoustic body force in Eulerian form, which models the droplet as a fluid, to theoretically investigate the suspension dynamics of droplet subjected to standing waves through the interaction between acoustic, interfacial, and gravitational forces. Our theory predicts that when interfacial forces are dominant, the presence of positive and negative acoustic force regions within droplets exceeding the Rayleigh limit reduces the net acoustic force counteracting gravity. As a result, the suspension dynamics become highly dependent on droplet size, in contrast to droplets within the Rayleigh limit, where the dynamics remain size-independent. Thus, beyond the Rayleigh limit, as the droplet size to wavelength ratio increases, the critical acoustic energy density ($E_{cr}$) required to suspend the droplet initially rises sharply, which agrees with recent experimental results. After $E_{cr}$ reaches a local maximum at $d/\lambda \approx 0.65$, it exhibits a pattern of alternating decreases and increases, with each successive peak surpassing the previous one. Remarkably, our study reveals a size-dependent shifting of the suspension position between nodes and antinodes for droplets beyond the Rayleigh limit, whereas droplets within this limit maintain a consistent suspension position regardless of size.