Self-dilating viscous fingers in wedge-shaped Hele-Shaw cells

Abstract

Viscous fingering in a wedge-shaped Hele-Shaw cell is analyzed. The shape of a self-dilating viscous finger is shown to obey a time-independent nonlinear integrodifferential equation that is solved numerically. The results show that there is a continuum of zero-surface-tension solutions for any wedge angle between O and π/2. When surface tension is taken into account only a discrete set of solutions exist. In contrast to the classical case, different branches merge for finite values of the surface tension parameter. © 1991 American Institute of Physics.