Global instability of viscous fingering in a Hele–Shaw cell: formation of oscillatory fingers

Abstract

This work deals with the global instability mechanism of viscous fingering in a Hele–Shaw cell with the inclusion of surface tension. We investigate the interaction and propagation of travelling waves in the system, and obtain two discrete sets of global wave modes: symmetrical modes and anti-symmetrical modes. We call the instability mechanism determined by these global modes the global trapped wave (GTW) instability. A unique global, neutrally stable state of the system is found; it explains the formation of the narrow, oscillatory fingers discovered by Couder el al. (1986) and by Kopf-Sill & Homsy (1987).