Fingering regimes in unstable miscible displacements

Viscous fingering of miscible slices

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Dynamic Scaling in Miscible Viscous Fingering

We consider dynamic scaling in gravity driven miscible viscous fingering. We prove rigorous one-sided bounds on bulk transport and coarsening in regimes of physical interest. The analysis relies on comparison with solutions to one-dimensional conservation laws, and new scale-invariant estimates. Our bounds on the size of the mixing layer are of two kinds: a naive bound that is sharp in the abse...

Surface tension and fingering of miscible interfaces

Experiments on miscible, buoyantly unstable reaction-diffusion fronts and non-reacting displacement fronts in Hele-Shaw cells show a fingering-type instability whose wavelengths (λ) are consistent with an interfacial tension (Σ) caused by the change in chemical composition, even though the solutions are miscible in all proportions. The relation Σ ≈ K/τ , where τ is the interface thickness and K...

Interface evolution during radial miscible viscous fingering.

We study experimentally the miscible radial displacement of a more viscous fluid by a less viscous one in a horizontal Hele-Shaw cell. For the range of tested injection rates and viscosity ratios we observe two regimes for the evolution of the fluid-fluid interface. At early times the interface length increases linearly with time, which is typical of the Saffman-Taylor instability for this radi...

Instability Analysis of Miscible Displacements in Homogeneous Porous Media