Journal of Fluid Mechanics


The instability of thermal and fluid fronts during radial injection in a porous medium

a1 BP Institute for Multiphase Flow, University of Cambridge, Madingley Rise, Madingley Road, Cambridge CB3 0EZ, UK

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We investigate viscous fingering instabilities of the double-front system which results when fluid is injected into a porous medium containing fluid of a different composition and temperature. We describe a linear stability analysis based on an eigenfunction expansion method which enables us to investigate the structure of the discrete eigenvalue spectrum. We investigate the extent to which the properties of each front contribute to the tendency of the system to become unstable: we find that instabilities on the compositional front dominate because of the high ratio of thermal to solute diffusion. It is difficult for a stable compositional front to stabilize an unstable thermal front; however, this situation can result in a new fingering phenomenon in which the perturbations undergo coupled oscillations of growing amplitude.

(Received August 5 2003)
(Revised January 8 2004)