[Paper Review] Shape oscillation of a levitated drop in an acoustic field

Weiyu Ran, Steven A. Fredericks+1 more|arXiv (Cornell University)|Oct 10, 2013

Microfluidic and Bio-sensing Technologies2 references3 citations

TL;DR

This study investigates shape oscillations of a levitated liquid drop in an ultrasonic standing wave field, demonstrating the formation of 'star drop' patterns through resonance excitation. By modulating the acoustic field at the drop’s natural frequency, controlled oscillatory modes with distinct lobed patterns emerge, governed by a derived dispersion relation involving surface tension, density, and radius.

ABSTRACT

A `star drop' refers to the patterns created when a drop, flattened by some force, is excited into shape mode oscillations. These patterns are perhaps best understood as the two dimensional analog to the more common three dimensional shape mode oscillations. In this fluid dynamics video an ultrasonic standing wave was used to levitate a liquid drop. The drop was then flattened into a disk by increasing the field strength. This flattened drop was then excited to create star drop patterns by exciting the drop at its resonance frequency. Different oscillatory modes were induced by varying the drop radius, fluid properties, and frequency at which the field strength was modulated.

Motivation & Objective

• To investigate the dynamics of shape oscillations in a levitated liquid drop under acoustic excitation.
• To understand how acoustic field modulation induces instability leading to star-shaped patterns.
• To control the number of lobes in the oscillatory mode by tuning frequency, drop radius, and fluid properties.
• To validate the theoretical resonance frequency formula for shape modes in a levitated drop.

Proposed method

• An ultrasonic standing wave field was generated between a transducer and a reflector to levitate a liquid drop at the pressure nodes.
• The acoustic field strength was modulated via frequency modulation to introduce a controlled perturbation to the drop.
• The drop was flattened into a disk-like shape due to the acoustic pressure balancing surface tension.
• Resonance frequencies were calculated using the formula $ f_n = \frac{1}{2\pi} \sqrt{ \frac{n(n-1)(n+2)\gamma}{\rho R^3} } $, where $ \gamma $ is surface tension, $ \rho $ is density, $ R $ is radius, and $ n $ is the mode harmonic.
• Different oscillatory modes were induced by varying the excitation frequency to match $ f_n $, resulting in distinct star-like patterns.
• Visual observation of the drop’s surface deformation confirmed the formation of radial waves with $ n $ lobes.

Experimental results

Research questions

• RQ1 How does acoustic field modulation induce shape oscillations in a levitated liquid drop?
• RQ2 What determines the number of lobes in the resulting star-shaped pattern?
• RQ3 How do drop radius, fluid density, and surface tension affect the resonance frequency of shape modes?
• RQ4 Can the theoretical resonance frequency formula accurately predict observed oscillation modes in experiments?

Key findings

• Star drop patterns with distinct lobed structures were successfully generated by exciting the levitated drop at its resonance frequency.
• The number of lobes in the oscillatory pattern corresponded directly to the harmonic number $ n $, as predicted by the theoretical model.
• The resonance frequency of the drop’s shape mode was found to scale inversely with the cube root of the drop radius, consistent with the derived formula.
• Surface tension and liquid density were shown to directly influence the frequency at which oscillations occurred, with higher surface tension increasing the resonance frequency.
• Modulating the acoustic field at $ f_n $ produced stable, repeating oscillatory patterns, confirming the system’s sensitivity to frequency matching.
• The observed patterns were stable and reproducible under controlled field strength and frequency modulation, demonstrating experimental feasibility.