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arXiv · 1010.3780

Fluid Mixing from Viscous Fingering

Birendra Jha·Luis Cueto-Felgueroso·Ruben Juanes
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Abstract

Viscous fingering is a well-known hydrodynamic instability that sets in when a less viscous fluid displaces a more viscous fluid. When the two fluids are miscible, viscous fingering introduces disorder in the velocity field and exerts a fundamental control on the rate at which the fluids mix. We present a fluid dynamics video of the mixing process in a viscously unstable flow, generated from a high-resolution numerical simulation using a computational strategy that is stable for arbitrary viscosity ratios. We develop a two-equation dynamic model of concentration variance and mean dissipation rate to quantify the degree of mixing in such a displacement process. The model reproduces accurately the evolution of these two quantities as observed in high-resolution numerical simulations and captures the nontrivial interplay between channeling and creation of interfacial area as a result of viscous fingering.

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Birendra Jha, Luis Cueto-Felgueroso, Ruben Juanes. 2011-10-13. Fluid Mixing from Viscous Fingering. https://doi.org/10.1103/physrevlett.106.194502

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