Fluid Mixing from Viscous Fingering

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.

Fluid dynamics video is included

References in corpus (2)

• Rheology of Active-Particle Suspensions
• Genetic Demixing and Evolutionary Forces in the One-Dimensional Stepping Stone Model

Cited by in corpus (16)

• Effects of Pore-Scale Disorder on Fluid Displacement in Partially-Wettable Porous Media
• Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux
• Control of radial miscible viscous fingering
• Immiscible fluid displacement in porous media with spatially correlated particle sizes
• Viscous fingering at ultralow interfacial tension
• Hydrodynamic instabilities in miscible fluids
• Influence of Langmuir adsorption and viscous fingering on transport of finite size samples in porous media
• Scaling behavior of density gradient accelerated mixing rate in shock bubble interaction
• Emergence of transient reverse fingers during radial displacement of a shear-thickening fluid
• Viscosity scaling of fingering instability in finite slices with Korteweg stress
• Hamiltonian formulation towards minimization of viscous fluid fingering
• Interfacial instabilities in confined displacements involving non-Newtonian fluids
• Measurement of Pressure Gradients near the Interface in the Viscous Fingering Instability
• Global Well-Posedness and Numerical Approximation of a Coupled Darcy-Convection-Diffusion System with Exponential Nonlinearity
• Linear stability analysis on the onset of viscous fingering due to a non monotonic viscosity profile for immiscible fluids
• Electrically-controlled self-similar evolution of viscous fingering patterns in radial Hele-Shaw flows