Physics – Fluid Dynamics
Scientific paper
2010-10-19
Physical Review Letters, 106(19), 194502 (2011)
Physics
Fluid Dynamics
Fluid dynamics video is included
Scientific paper
10.1103/PhysRevLett.106.194502
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.
Cueto-Felgueroso Luis
Jha Birendra
Juanes Ruben
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