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A model to predict the oscillation frequency for drops pinned on a vertical planar surface

Published online by Cambridge University Press:  08 October 2021

J. Sakakeeny Open the ORCID record for J. Sakakeeny [Opens in a new window] ,
C. Deshpande ,
S. Deb ,
J.L. Alvarado  and
Y. Ling Open the ORCID record for Y. Ling [Opens in a new window]
J. Sakakeeny
Affiliation:
Department of Mechanical Engineering, Baylor University, Waco, TX 76643, USA
C. Deshpande
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
S. Deb
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
J.L. Alvarado
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA Department of Engineering Technology and Industrial Distribution, Texas A&M University, College Station, TX 77843, USA
Y. Ling*
Affiliation:
Department of Mechanical Engineering, Baylor University, Waco, TX 76643, USA
*
†Email address for correspondence: stanley_ling@baylor.edu
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Abstract

Accurate prediction of the natural frequency for the lateral oscillation of a liquid drop pinned on a vertical planar surface is important to many drop applications. The natural oscillation frequency, normalized by the capillary frequency, is mainly a function of the equilibrium contact angle and the Bond number ($Bo$), when the contact lines remain pinned. Parametric numerical and experimental studies have been performed to establish a comprehensive understanding of the oscillation dynamics. An inviscid model has been developed to predict the oscillation frequency for wide ranges of $Bo$ and the contact angle. The model reveals the scaling relation between the normalized frequency and $Bo$, which is validated by the numerical simulation results. For a given equilibrium contact angle, the lateral oscillation frequency decreases with $Bo$, implying that resonance frequencies will be magnified if the drop oscillations occur in a reduced gravity environment.

JFM classification

Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A28
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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