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IMA Journal of Applied Mathematics Advance Access originally published online on October 31, 2007
IMA Journal of Applied Mathematics 2008 73(1):37-68; doi:10.1093/imamat/hxm043
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Surface-tension-driven flow in a slender cone

S. P. Decent{dagger} and A. C. King

School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

{dagger} Email: decentsp{at}for.mat.bham.ac.uk

Received on September 29, 2006; Revision received March 15, 2007. Accepted on May 18, 2007

After a droplet has broken away from a slender thread or jet of liquid, the tip of the thread or jet recoils rapidly. At the moment of break-off, the tip of the thread/jet is observed to have the shape of a cone close to the bifurcation point. In this paper, we study the evolution of an ideal fluid which is initially conical, where the only force acting on the fluid is due to surface tension. We find an asymptotic solution to the problem in terms of the aspect ratio of the cone which is assumed to be small. Using a similarity transformation, which is valid for small times after the bifurcation, we identify a rapidly oscillating non-linear wave which propagates away from the tip, as observed in experiments.

Keywords: bifurcation; cone; surface tension.


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