Oil droplet in alcohol
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Citation
La Foy, Roderick R., Jesse Belden, Tadd T. Truscott, Anna M.
Shih, and Alexandra H. Techet. Oil Droplet in Alcohol. Physics
of Fluids 22, no. 9 (2010): 091107. © 2010 American Institute of
Physics.
As Published
http://dx.doi.org/10.1063/1.3483217
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American Institute of Physics
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http://hdl.handle.net/1721.1/79362
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Oil droplet in alcohol
Roderick R. La Foy, Jesse Belden, Tadd T. Truscott, Anna M. Shih, and Alexandra H. Techet
Citation: Phys. Fluids 22, 091107 (2010); doi: 10.1063/1.3483217
View online: http://dx.doi.org/10.1063/1.3483217
View Table of Contents: http://pof.aip.org/resource/1/PHFLE6/v22/i9
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PHYSICS OF FLUIDS 22, 091107 共2010兲
FIG. 1. Formations made by an oil droplet falling through alcohol from drop heights of 25 mm 共top兲 and 50 mm 共bottom兲.
Oil droplet in alcohol
Roderick R. La Foy, Jesse Belden, Tadd T. Truscott,
Anna M. Shih, and Alexandra H. Techet
Department of Mechanical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, USA
共Received 4 August 2010; published online 30 September 2010兲
关doi:10.1063/1.3483217兴
The elegant patterns formed by fluid droplets falling
through a dissimilar liquid were first studied over a century
ago.1 The emerging patterns are driven by hydrodynamic instabilities set up by velocity and density gradients between
the liquids. We perform experiments using 3 mm droplets of
naphthenic oil released from two heights 共25 mm, 50 mm兲
into isopropyl alcohol. The oil is denser than and miscible in
the alcohol 共␳oil / ␳al = 1.17兲, which results in the drop descending and eventually diffusing. Images are captured with
a digital SLR camera looking at a black background through
the tank of alcohol, which is lit from both sides. The difference in index of refraction between the oil and alcohol
causes the edges of the oil droplet to appear brighter than the
surrounding fluid.
For lower drop heights 共top sequence of Fig. 1兲, the oil
droplet behavior resembles that described for miscible drops
placed on the surface of a lighter fluid.2 Initially, large velocity gradients between the droplet and the alcohol cause the
1070-6631/2010/22共9兲/091107/1/$30.00
droplet to roll up into a vortex ring, which grows into an
oscillatory shape as a result of Rayleigh–Taylor instabilities.
The unstable ring stretches and then fragments into smaller
and smaller rings, which creates cascading tiers of vortex
rings, until diffusion takes over.
When released from 50 mm above the free surface 共bottom sequence of Fig. 1兲, the droplet does not immediately
cascade into tiers of vortex rings. Initially viscous shear on
the outside layer of the oil droplet causes it to form into an
upside-down “wine glass” shape. The thin sheet of oil rolls
up into the first vortex ring, which expands radially as the
droplet continues to descend. The droplet shape elongates as
its denser core descends faster than the vortex ring. A second
central vortex ring forms at the lowest point of the droplet,
and then another ring follows suit thereafter. Each ring remains attached to the others by a thin oil sheet. Rayleigh–
Taylor instabilities begin to set up the vortex ring cascade as
witnessed in the top image sequence, which ultimately occurs for all of the central rings.
1
J. J. Thomson and H. F. Newall, “On the formation of vortex rings by
drops falling into liquids, and some allied phenomena,” Proc. R. Soc.
London 39, 417 共1885兲.
2
S. Residori, P. K. Buah-Bassuah, and F. T. Arecchi, “Fragmentation instabilities of a drop as it falls in a miscible fluid,” Eur. Phys. J. Spec. Top.
146, 357 共2007兲.
22, 091107-1
© 2010 American Institute of Physics
Downloaded 10 Jun 2013 to 18.51.3.76. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions