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.