A Falling Fluid Droplet in an Oscillating Flow Field

Iolo T. Williams, Serafim Kalliadasis, Sotos Generalis, Philip Trevelyan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We examine the flow in and around a falling fluid droplet in a vertically oscillating flow. We assume axisymmetric Stokes flow, and for small deformations to the droplet, the governing equations can be linearized leading to an infinite system of linear ordinary differential equations. In this study, we have analytically solved the problem in the small-capillary limit. We note that the solution locally breaks down at the poles of the droplet. The drag and center of the mass were also obtained. In the case when only odd modes are present, the droplet shows three-dimensional axisymmetric heart-shaped solutions oscillating vertically in time. When only even modes are present, the droplet exhibits axisymmetric stretching and squeezing.

Original languageEnglish
Article number022113
Number of pages21
JournalPhysics of Fluids
Issue number2
Early online date16 Feb 2024
Publication statusPublished - 29 Feb 2024

Bibliographical note

Copyright © 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Data Access Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.


  • Droplet, Fluid Dynamics, Oscillations


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