Journal of Fluid Mechanics



Density-driven unstable flows of miscible fluids in a Hele-Shaw cell


J. FERNANDEZ a1, P. KUROWSKI a1, P. PETITJEANS a1 and E. MEIBURG a1a2
a1 Laboratoire de Physique et Mécanique des Milieux Hétérogènes (LPMMH), Ecole Supérieure de Physique et de Chimie Industrielles (ESPCI), 10, rue Vauquelin, 75231 Paris Cedex 05, France
a2 Department of Mechanical and Environmental Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA

Abstract

Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are investigated by means of experimental measurements, as well as two- and three-dimensional numerical simulations. The experiments focus on the early stages of the instability growth, and they provide detailed information regarding the growth rates and most amplified wavenumbers as a function of the governing Rayleigh number Ra. They identify two clearly distinct parameter regimes: a low-Ra, ‘Hele-Shaw’ regime in which the dominant wavelength scales as Ra−1, and a high-Ra ‘gap’ regime in which the length scale of the instability is 5±1 times the gap width. The experiments are compared to a recent linear stability analysis based on the Brinkman equation. The analytical dispersion relationship for a step-like density profile reproduces the experimentally observed trend across the entire Ra range. Nonlinear simulations based on the two- and three-dimensional Stokes equations indicate that the high-Ra regime is characterized by an instability across the gap, wheras in the low-Ra regime a spanwise Hele-Shaw mode dominates.

(Received February 2 2001)
(Revised July 17 2001)



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