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IMA Journal of Applied Mathematics Advance Access published online on March 25, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp012
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Asymptotic solution of slender viscous jet break-up

S. P. Decent{dagger}

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

{dagger} Email: s.p.decent{at}bham.ac.uk

Received on October 19, 2008; Revision received October 19, 2008. Accepted on January 29, 2009

The break-up of a slender viscous jet is examined using the Needham–Leach asymptotic method. This method enables the calculation of the large time asymptotic structure of the model evolution equations using matched asymptotic expansions. An equation which describes the dynamics of non-linear travelling waves at large times is derived using this method. In particular, the wave speed, wavelength, growth rate and frequency of these travelling waves are determined. This provides information on how the jet breaks up, the region of break-up and the possibility for multiple break-up points. Also, this method gives information on how non-linear jets may be controlled.

Keywords: Needham-Leach method; jet; rupture.


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