A Falling Fluid Droplet in an Oscillating Flow Field

Iolo T.  Williams; Serafim Kalliadasis; Sotos Generalis; Philip Trevelyan

doi:10.1063/5.0187932

A Falling Fluid Droplet in an Oscillating Flow Field

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

^*Corresponding author for this work

Applied Mathematics & Data Science

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Article number	022113
Number of pages	21
Journal	Physics of Fluids
Volume	36
Issue number	2
Early online date	16 Feb 2024
DOIs	https://doi.org/10.1063/5.0187932
Publication status	Published - 29 Feb 2024

Bibliographical note

Data Access Statement

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

Keywords

Droplet, Fluid Dynamics, Oscillations

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10.1063/5.0187932Licence: CC BY 4.0

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Cite this

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AU - Williams, Iolo T.

AU - Kalliadasis, Serafim

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Y1 - 2024/2/29

N2 - 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.

AB - 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.

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A Falling Fluid Droplet in an Oscillating Flow Field

Abstract

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Data Access Statement

Keywords

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