Cummings, L. J. and Howell, P. D. (1999) On the evolution of nonaxisymmetric viscous fibres with surface tension, inertia and gravity. Journal of Fluid Mechanics, 389 . pp. 361389.

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Abstract
We consider the free boundary problem for the evolution of a nearly straight slender fibre of viscous fluid. The motion is driven by prescribing the velocity of the ends of the fibre, and the free surface evolves under the action of surface tension, inertia and gravity. The threedimensional NavierStokes equations and freesurface boundary conditions are analysed asymptotically, using the fact that the inverse aspect ratio, defined to be the ratio between a typical fibre radius and the initial fibre length, is small. This first part of the paper follows earlier work on the stretching of a slender viscous fibre with negligible surface tension effects. The inclusion of surface tension seriously complicates the problem for the evolution of the shape of the crosssection. We adapt ideas applied previously to twodimensional Stokes flow to show that the shape of the crosssection can be described by means of a conformal map which depends on time and distance along the fibre axis. We give some examples of suitable relevant maps and present numerical solutions of the resulting equations. We also use analytic methods to examine the coupling between stretching and the evolution of the crosssection shape.
Item Type:  Article 

Subjects:  D  G > Fluid mechanics 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  125 
Deposited By:  Peter Howell 
Deposited On:  09 Sep 2004 
Last Modified:  29 May 2015 18:16 
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