Pressure corrections for viscous potential flow analysis of radial fingering in Hele-Shaw cell

Abstract

Pressure corrections for the viscous potential flow analysis of radial fingering in two-phase gas/liquid flow in a Hele-Shaw cell were determined. In viscous potential flow theory, viscosity enters through the normal stress balance and the effect of shearing stresses is completely neglected. We have included viscous pressure in the normal stress balance, along with irrotational pressure, and it is assumed that this viscous pressure will resolve the discontinuity of the shearing stresses at the interface of two fluids. Both fluids are taken as viscous and incompressible with different mobilities. A dispersion relation was obtained, and stability is discussed both theoretically as well as numerically. It was observed that the effect of irrotational shearing stresses stabilizes the system.