The Mathematical Institute, University of Oxford, Eprints Archive

The evolution of a slender non-axisymmetric drop in an extensional flow

Howell, P. D. and Siegel, M. (2004) The evolution of a slender non-axisymmetric drop in an extensional flow. Journal of Fluid Mechanics, 521 . pp. 155-180.

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An asymptotic method for analysing slender non-axisymmetric drops, bubbles and jets in a general straining flow is developed. The method relies on the slenderness of the geometry to reduce the three-dimensional equations to a sequence of weakly coupled, quasi-two-dimensional Stokes flow problems for the cross-sectional evolution. Exact solution techniques for the flow outside a bubble in two-dimensional Stokes flow are generalised to solve for the transverse flow field, allowing large non-axisymmetric deformations to be described. A generalisation to the case where the interior contains a slightly viscous fluid is also presented.

Our method is used to compute steady non-axisymmetric solution branches for inviscid bubbles and slightly viscous drops. We also present unsteady numerical solutions showing how the eccentricity of the cross-section adjusts to a non-axisymmetric external flow. Finally, we use our theory to investigate how the pinch-off of a jet of relatively inviscid fluid is affected by a two-dimensional straining cross-flow.

Item Type:Article
Subjects:D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:209
Deposited By: Peter Howell
Deposited On:06 Oct 2005
Last Modified:29 May 2015 18:18

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