Abstract
The chaotic advection of the interface between two miscible liquids inside a closed cavity, generated by a damped oscillatory buoyancy-driven (BD) regular flow field, is investigated experimentally for BD mixing. The Lagrangian history of interface motion, determined using the planar laser-induced fluorescence and the photographic full-field view method, is contrasted against the Eulerian flow field measured from particle image velocimetry. Chaotic advection stretches and folds the interface at an early stage to produce an asymmetric pairwise Rayleigh–Taylor (RT) morphology (RTM) structure from long wavelength RT instability and short-time Richtmyer–Meshkov instability and its fractal interface structure at a high impulsive-Reynolds number. The mechanism of folding, from global bifurcation of the flow field, caused by a hyperbolic point, served as an organizing center for multiple vortex interactions. The intermediate-stage kinematics of the RTM structure exhibits RT mixing and shows unfolding of the lamellar structure from the net effect of stretching, folding, and molecular diffusion prior to its breakdown; and it has a probabilistic outcome of exhibiting topological transitions through a breakup of the RTM structure in phase space from necking singularity and pinch-off, indicating sensitivity to the initial conditions. The effectiveness of mixing determined from mixing efficiency is contrasted against mechanical and lamellar models of mixing. The determination of topological entropy, from an approximate Gaussian distribution of the interface length stretch, yields time scale for information decay comparable to time scale for which a low-order horseshoe map emerges from flow, indicating local chaos of the interface. The late-stage breakdown of the RTM structure from internal and wall collision drives the interaction between advection and diffusion, which indicates that critical mixing time scales as the logarithmic of Peclet number, comparable to time-periodic sine flow and blinking vortex flow chaotic mapping models.
Highlights
Buoyancy-driven (BD) mixing is of fundamental importance for applications to transport processes conducted in a microgravity environment, such as the International Space Station (ISS), and represents a model problem in chaotic advection
We show that the group theory properties11,12 that characterize RT mixing–invariance, inhomogeneity, anisotropy, fluctuations, non-locality, and sensitivity to initial conditions–are exhibited by the BD mixing experiments; in addition, the stabilization and destabilization of the interface for the microgravity and groundbased BD mixing experiments are in accord to the theoretical prediction of the conservative dynamics (CD) model,16 whereas the flow field structure in ground-based BD mixing experiments is comparable to the classic Landau–Darrieus (LD) model
The measurement of the flow field in relation to interface motion, which showed a self-similar interface length stretch with nearly Gaussian distribution, which contains the continuum mechanics of mixing, indicated that the transition from stretching to folding of the interface originated from a hyperbolic point in the flow field, from which the Rayleigh–Taylor morphology (RTM) structure unfolds owing to long wavelength RT instability that leads to RT interfacial mixing
Summary
Buoyancy-driven (BD) mixing is of fundamental importance for applications to transport processes conducted in a microgravity environment, such as the International Space Station (ISS), and represents a model problem in chaotic advection. The interaction between advection and diffusion in the late stage, caused by the breakdown of the interface from internal and wall collision, for the damped oscillatory flow field of our BD mixing experiment, is contrasted with the time-periodic flow of prototype chaotic mapping models, such as the TPSF mapping models and the blinking vortex flow model.. Sensitivity to the initial conditions, from perturbation of the density ratio or Atwood number parameter, shows the evolution of non-repeatable quasi-sinusoidal interfaces, driven by the Kelvin–Helmholtz instability mechanism for the short time scale in ground-based BD mixing experiments.
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