The effect of geometry is observable on the onset of instability, where we obtain significant differences from existing results in the rectilinear geometry.

We investigate the stability of radial viscous fingering (VF) in miscible fluids. We show that the instability is decided by an interplay between advection and diffusion during initial stages of flow. Using linear stability analysis and nonlinear simulations, we demonstrate that this competition is a function of the radius r0 of the circular region initially occupied by the less viscous fluid in the porous medium. For each r0, we further determine the stability in terms of Péclet number (P e) and log-mobility ratio (M ). The P e − M parameter space is divided into stable and unstable zones-the boundary between the two zones is well approximated by M = α(r0)P e −0.55 . In the unstable zone, the instability is reduced (enhanced) with an increase (decrease) in r0. Thus, a natural control measure for miscible radial VF in terms of r0 is established. Finally, the results are validated by performing experiments which provide a good qualitative agreement with our numerical study. Implications for observations in oil recovery and other fingering instabilities are discussed.

Abstract

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Abstract