On the tip splitting instability - I
Centre de Recherche Paul Pascal, CNRS - Av.
Schweitzer, 33600 Pessac, France
Accepted: 6 September 2002
The local destabilisation of a Saffman-Taylor viscous finger occurs by a splitting of its tip and results in the formation of two branches separated by a fjord. It has been shown recently that the central line of a fjord follows approximately a curve normal to successive stable fingers. In this letter, we present an extensive numerical study of a minimal model of this instability for fingers growing in a wedge of angle . It is shown that the form of the fjords is mainly a surface-tension–driven effect. We also infer the existence of a critical angle such that if , the symmetric tip-splitting becomes unstable.
PACS: 47.20.-k – Hydrodynamic stability
© EDP Sciences, 2002