Turbulent mixing with physical mass diffusion

Abstract

Simulated mixing rates of the Rayleigh-Taylor instability for miscible fluids with physical mass diffusion are shown to agree with experiment; for immiscible fluids with physical values of surface tension the numerical data lie in the center of the range of experimental values. The simulations are based on an improved front tracking algorithm to control numerical surface tension and on improved physical modeling to allow physical values of mass diffusion or surface tension. Compressibility, after correction for variable density effects, has also been shown to have a strong influence on mixing rates. In summary, we find significant dependence of the mixing rates on scale breaking phenomena. We introduce tools to analyze the bubble merger process and confirm that bubble interactions, as in a bubble merger model, drive the mixing growth rate.

Terascale Simulation Tools and Technologies

“…Using TSTT developed front tracking software, we cured the first problem [15,15,14,8], excess numerical mass diffusion, and by enhancements to this software, we also address the second problem, insufficient physics models for physical mass diffusion and/or physical surface tension, see [34]. The result is complete agreement or nearly so in the match of simulation to experiment for Rayleigh-Taylor mixing.…”

Nonequilibrium Interfacial Tension in Simple and Complex Fluids

“…Simulations [33] and experiments [34,35] probing the Saffman-Taylor instability led to the conclusions that no interfacial tension exists between miscible fluids; in particular, the observation of a fractal-like interface between two miscible fluids was attributed to a vanishing interfacial energy cost, i.e., to Γ e ¼ 0 [34,35]. This has to be contrasted with experiments and simulations on miscible fluids probing capillary waves [14,15,36], the shape of drops and menisci [13,16,17,37,38], and that of patterns in hydrodynamic instabilities [18,[27][28][29][39][40][41], which all claimed the existence of an effective interfacial tension. The sign of Γ e is also debated.…”

“…(1) can only exist transiently, before diffusion or other mixing mechanisms smear out the interface leading to a single, homogeneous phase. Notwithstanding this transient, nonequilibrium character, the effective interfacial tension between miscible fluids plays a key role in a wide range of research fields of both academic and practical interest [19], from geosciences (e.g., in mantle convection, magma fragmentation, and the dynamics of Earth's core [20,21]) to hydrology [22], oil recovery [10], filtration and flow in porous media (e.g., in a chromatography column [23]), fluid removal [24], aquifer and soil remediation [25,26], and the modeling of hydrodynamic instabilities, e.g., in Rayleigh-Taylor [27] and Hele-Shaw [28,29] flows. Very recently, convection induced by Korteweg stresses has been proposed as a new mechanism for self-propulsion of droplets [30] and vesicles [31], demonstrating artificial chemotaxis and opening new scenarios in active matter and drug delivery systems.…”

New directions for Rayleigh–Taylor mixing

“…We consider the Rayleigh-Taylor (RT) mixing problem [1,2], in which a light fluid accelerates a heavy fluid. Numerical efforts to solve this problem date back more than 60 years, and only recently have systematic numerical solutions based on compressible fluid dynamics been found that address an experimental range of fluid parameters for both immiscible and miscible fluids, the latter over a range of Schmidt numbers [3][4][5][6]. The problem is to predict the growth rate α, defined in terms of the penetration distance h of the light fluid into the heavy fluid, via the equation…”