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

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

13 Downloads (Pure)

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.

Funding

EC Horizon 2020 Framework Programme (H2020): RISE-ATM2BT-824022

Funders	Funder number
Horizon 2020 Framework Programme	RISE-ATM2BT-824022

Keywords

Droplet, Fluid Dynamics, Oscillations

Access to Document

10.1063/5.0187932Licence: CC BY 4.0

IT Williams et al_falling fluid droplet in an oscillating flow field
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/).
Final published version, 2.93 MBLicence: CC BY 4.0

Cite this

@article{9cecbb0b0b54421396a07436db977127,

title = "A Falling Fluid Droplet in an Oscillating Flow Field",

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.",

keywords = "Droplet, Fluid Dynamics, Oscillations",

author = "Williams, \{Iolo T.\} and Serafim Kalliadasis and Sotos Generalis and Philip Trevelyan",

note = "Copyright {\textcopyright} 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/). ",

year = "2024",

month = feb,

day = "29",

doi = "10.1063/5.0187932",

language = "English",

volume = "36",

journal = "Physics of Fluids",

issn = "1070-6631",

publisher = "American Institute of Physics",

number = "2",

}

TY - JOUR

T1 - A Falling Fluid Droplet in an Oscillating Flow Field

AU - Williams, Iolo T.

AU - Kalliadasis, Serafim

AU - Generalis, Sotos

AU - Trevelyan, Philip

PY - 2024/2/29

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.

KW - Droplet, Fluid Dynamics, Oscillations

UR - https://pubs.aip.org/aip/pof/article/36/2/022113/3265915/A-falling-fluid-droplet-in-an-oscillating-flow

UR - https://www.scopus.com/pages/publications/85185343165

U2 - 10.1063/5.0187932

DO - 10.1063/5.0187932

M3 - Article

SN - 1070-6631

VL - 36

JO - Physics of Fluids

JF - Physics of Fluids

IS - 2

M1 - 022113

ER -

A Falling Fluid Droplet in an Oscillating Flow Field

Abstract

Bibliographical note

Data Access Statement

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Continuum Modeling of Slightly Wet Fluidization with Electrical Capacitance Tomograph Validation

Pattern competition in the sequential bifurcation approach to turbulence in homogeneously heated inclined fluid and solid layers

Cite this