Gap Size Effects for the Kelvin-Helmholtz Instability in a Hele-Shaw Cell

Laurent Meignin, Patricia Ern, Philippe Gondret & Marc Rabaud

Laboratoire Fluides, Automatique & Systèmes Thermiques (UMR CNRS n°7608)
Bât. 502, Campus Universitaire 91405 Orsay Cedex, France
(Received 11 January 2001; revised manuscript received 16 April 2001; published 24 July 2001)

Abstract

We report experimental results for the Kelvin-Helmholtz instability between two immiscible fluids in parallel flow in a Hele-Shaw cell. We focus our interest on the influence of the gap size between the walls on the instability characteristics. Experimental results show that the instability threshold, the critical wavelength, the phase velocity, and the spatial growth rate depend on this gap size. These results are compared to both the previous two-dimensional analysis of Gondret and Rabaud [Phys. Fluids 9, 3267 (1997)] and the three-dimensional analysis recently derived by Plouraboué and Hinch [Phys. Fluids (to be published)], showing that the agreement is still not complete especially when gap size increases.

Physical Review E 64, 026308-1 (2001). [pdf(128ko)|gzipped ps(128ko)]