Scaling properties of viscous fingering

2014/10/31 by Lagrée, Bertrand, Zaleski, Stéphane, Bondino, Igor +2
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)

paper · doi:10.48550/arxiv.1410.8659

Abstract

We present a study of viscous fingering using the Volume Of Fluid method and a central injection geometry, assuming a Laplacian field and a simple surface tension law. As in experiments we see branched structures resulting from the Saffman-Taylor instability. We find that the area A of a viscous-fingering cluster varies as a simple power law A ∼ L^α of its interface length L. Our results are compared to previously published simulations in which the viscosity of the invading fluid is vanishing. We find differences in exponent α and in the appearance of detached droplets and bubbles.

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