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arXiv · 1410.8659

Scaling properties of viscous fingering

Bertrand Lagrée·Stéphane Zaleski·Igor Bondino·Christophe Josserand·Stéphane Popinet
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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 $A \sim L^α$ 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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Bertrand Lagrée, Stéphane Zaleski, Igor Bondino, Christophe Josserand, Stéphane Popinet. 2014-10-31. Scaling properties of viscous fingering. https://arxiv.org/abs/1410.8659

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