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Local interfacial stability near a zero vorticity point

Published online by Cambridge University Press:  30 June 2015

Yu-Hau Tseng  and
Andrea Prosperetti
Yu-Hau Tseng
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Andrea Prosperetti*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Faculty of Science and Technology and Burgerscentrum, University of Twente, AE 7500 Enschede, The Netherlands
*
†Email address for correspondence: prosperetti@jhu.edu
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Abstract

It is often observed that small drops or bubbles detach from the interface separating two co-flowing immiscible fluids. The size of these drops or bubbles can be orders of magnitude smaller than the length scales of the parent fluid mass. Examples are tip-streaming from drops or coaxial jets in microfluidics, selective withdrawal, ‘skirt’ formation around bubbles or drops, and others. It is argued that these phenomena are all reducible to a common instability that can occur due to a local convergence of streamlines in the neighbourhood of a zero-vorticity point or line on the interface. When surfactants are present, this converging flow tends to concentrate them in these regions weakening the effect of surface tension, which is the only mechanism opposing the instability. Several analytical and numerical calculations are presented to substantiate this interpretation of the phenomenon. In addition to some idealized cases, the results of two-dimensional simulations of co-flowing jets and a rising drop are presented.

JFM classification

Drops and Bubbles: Drops and Bubbles Instability: Instability Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 776 , 10 August 2015 , pp. 5 - 36
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Copyright
© 2015 Cambridge University Press 

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Footnotes

‡

Present address: Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung City 81148, Taiwan, ROC.

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