Videos

Viscous potential flow analysis of radial fingering in a Hele-Shaw cell

Presenter
July 14, 2008
Keywords:
  • Viscous flow
MSC:
  • 60J20
Abstract
Joint work with H. Kim and T. Funada. The problem of radial fingering in two phase gas/liquid flow in a Hele-Shaw cell under injection or withdrawal is studied here. The problem is analyzed as a viscous potential flow VPF in which the potential flow analysis of Paterson 1981 and others is augmented to account for the effects of viscosity on the normal stress at the gas/liquid interface. The unstable cases in which gas is injected into liquid or liquid is withdrawnfrom gas lead to fingers. This stability problem was previously considered by other authors with the viscous normal stress neglected. Here we show that the viscous normal stress should not be neglected; the normal stress changes the speed of propagation of the undisturbed interface, it changes the growth rate, and the numbers of fingers that grow the fastest and the cut-off number above which fingers can not grow.