An experimental investigation of initial oscillations in a radial Hele-Shaw cell

Abstract

Hele-Shaw cell is a laboratory device consisting of two parallel plates of glass separated by a thin gap. In this cell, in the flow of two immiscible fluids, when a fluid of higher viscosity is displaced by a fluid of lower viscosity, the less viscous fluid is observed to form “fingers” into the more viscous one due to the unstable interface. The Saffman-Taylor or viscous finger instability has been examined and modeled for over forty years for the rectilinear Hele-Shaw cell and about half as long for the radial Hele-Shaw cell. In this paper, we study, in detail, the early development of viscous instabilities in a radial Hele-Shaw cell. This source flow configuration has been chosen so that the instability can be monitored precisely. The objective of this study is to examine the onset of fingering, i.e. initial number of fingers that form, and the evolution of interface instability. Our experiments suggest that there may be some order in this formation process and one can model this aspect by considering the unsteady velocity components and predicting temporal changes in wavenumber responsible for the initial number of fingers and may be later accounting for the fingertip oscillations and splitting.