The Mathematical Institute, University of Oxford, Eprints Archive

The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations

Farmer, C. L. and Howison, S. D. (2005) The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations. Applied Mathematics Letters . (In Press)

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Abstract

We consider the motion of a thin filament of viscous fluid in a Hele-Shaw cell. The appropriate thin film analysis and use of Lagrangian variables leads to the Cauchy-Riemann system in a surprisingly direct way. We illustrate the inherent ill-posedness of these equations in various contexts.

Item Type:Article
Uncontrolled Keywords:Hele-Shaw flow, Saffman-Taylor finger
Subjects:D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:173
Deposited By:Sam Howison
Deposited On:03 May 2005
Last Modified:20 Jul 2009 14:19

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