Instabilities of the upstream meniscus in directional viscous fingering

Abstract

New instabilities affecting the meniscus of a viscous fluid are presented. They occur in an experimental set-up introduced previously by Rabaud et al. (1990) in which a small quantity of a viscous fluid is placed in the narrow gap between two rotating cylinders. In this geometry the downstream meniscus located in the region where the two solid surfaces move away from each other is known to be unstable and to exhibit directional viscous fingering. In the present article it is shown that the upstream meniscus can also be unstable. Two types of instabilities are observed. In the first supercritical transition the front becomes time-dependent with either standing or propagating waves. In a second transition, which is subcritical, parallel fingers of finite amplitude are formed. The various types of spatio-temporal dynamical behaviour are discussed.