Stability of viscous fingering.

Abstract

Flows in a two-dimensional Hele-Shaw cell are studied analytically and numerically by conformal-mapping methods. In the presence of surface tension the fingers are linearly stable. However, the structure of the linear stability problem is exponentially sensitive to noise, which implies the existence of a finite-amplitude nonlinear instability appearing at low surface tensions. Numerical simulations demonstrate the existence of this instability. The most unstable modes are predicted and compared with real and numerical experiments.