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

We consider the motion of a thin filament of viscous fluid in a HeleShaw 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.

• Type: Journal
• Year: 2006
• Where: APPML
• Authors: C. L. Farmer, Sam D. Howison
• Keywords: APPML 2006, HeleShaw Cell, Lagrangian Variables, Viscous Fluid