Chaos, Symmetry, and Self-Similarity: Exploiting Order and Disorder in Mixing Processes

Ottino, Julio M.; Muzzio, Fernando J.; Tjahjadi, Mahari; Franjione, J. G.; Jana, Sadhan; Kusch, H. A.

doi:10.1126/science.257.5071.754

Cited by 176 publications

(101 citation statements)

References 59 publications

(22 reference statements)

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“…Closed advection is largely governed by the symmetries of the base flow and boundary conditions (Ottino et al 1992;Speetjens et al 2006). Open advection is largely governed by filamentary unstable manifolds (Tél et al 2005).…”

Section: Theorymentioning

confidence: 99%

“…Points approach stable manifolds as they move forward in time and approach unstable manifolds as they move backward in time. Periodic elliptic points are important because they have disconnected (possibly large) island regions around them that sequester or hinder (through cantori) material transport and reaction activity (Ottino et al 1992;Speetjens et al 2006). Islands are regions of rotation without much deformation that have KAM surfaces separating them from the rest of the flow.…”

Section: Theorymentioning

confidence: 99%

See 1 more Smart Citation

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

Metcalfe

Lester

Ord

et al. 2010

Phil. Trans. R. Soc. A.

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The minimum-energy method to generate chaotic advection should be to use an irrotational flow. However, irrotational flows have no saddle connections to perturb in order to generate chaotic orbits. To the early work of Jones & Aref (Jones & Aref 1988 Phys. Fluids 31, 469-485 (doi:10.1063/1.866828)) on potential flow chaos, we add periodic reorientation to generate chaotic advection with irrotational experimental flows. Our experimental irrotational flow is a dipole potential flow in a disc-shaped Hele-Shaw cell called the rotated potential mixing flow; it leads to chaotic advection and transport in the disc. We derive an analytical map for the flow. This is a partially open flow, in which parts of the flow remain in the cell forever, and parts of it pass through with residencetime and exit-time distributions that have self-similar features in the control parameter space of the stirring. The theory compares well with the experiment.

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Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

Metcalfe

Lester

Ord

et al. 2010

Phil. Trans. R. Soc. A.

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show abstract

“…Several techniques, including Poincaré section, Lyapunov exponent, and local bifurcation analyses, were used to explore the existence of chaos. In addition, a Finite-Time Lyapunov exponent (FTLE) (Pierrehumbert, 1991;Muzzio, 1991;Ottino et al, 1992;Tang & Boozer, 1996;Thiffeault, 2004) was introduced as a mixing index for the evaluation of mixing performance of our micro mixer.…”

Section: Introductionmentioning

confidence: 99%

Experimental study and nonlinear dynamic analysis of time-periodic micro chaotic mixers

et al. 2007

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The efficiency of MEMS-based time-periodic micro chaotic mixers was experimentally and theoretically investigated in this study. A time-periodic flow perturbation was realized using digitallycontrolled solenoid valves to alternately activate a source and sink, acting together as a pair, with different driving frequencies. Working fluids with and without fluorescent dye were used in the micro mixing experiments. The spatiotemporal variation of the mixing concentration during the mixing process was characterized at different Strouhal numbers, ranging from 0.03 to 0.74, under fluorescence microscopy. A simple kinematical model for the micro mixer was used to demonstrate the presence of chaotic mixing using different methods. The specific stretching rate, Lyapunov exponent, as well as local bifurcation and Poincaré section analyses were used to identify the emergence of chaos. Two different numerical methods were employed to verify that the maximum Lyapunov exponent was positive in the proposed micro mixer model. A simplified analytical analysis of the effect of Strouhal number was presented. Kolmogorov-Arnold-Mose (KAM) curves, which are mixing barriers, were also found in Poincaré sections. From a comparative study of the experimental results and theoretical analysis, a Finite-Time Lyapunov exponent (FTLE) was shown to be a more practical mixing index compared to the classical Lyapunov exponent because the time spent in mixing is the main concern in practical applications, such as bio-medical diagnosis. In addition, the FTLE takes into account both fluid stretching in terms of the stretching rate and fluid folding in terms of curvature.

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“…Strategies to mix fluids 1,9,10 and control particles 11,12 using engineered systems exist, often relying on chaotic fluid transformations as an effective tool 13,14 to disrupt sustained regions of order in the flow 10,15 . Rather than apply flow transformations to prevent order, here we develop a hierarchical approach to engineer fluid streams into a broad class of complex configurations.…”

mentioning

confidence: 99%

Engineering fluid flow using sequenced microstructures

et al. 2013

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Controlling the shape of fluid streams is important across scales: from industrial processing to control of biomolecular interactions. Previous approaches to control fluid streams have focused mainly on creating chaotic flows to enhance mixing. Here we develop an approach to apply order using sequences of fluid transformations rather than enhancing chaos. We investigate the inertial flow deformations around a library of single cylindrical pillars within a microfluidic channel and assemble these net fluid transformations to engineer fluid streams. As these transformations provide a deterministic mapping of fluid elements from upstream to downstream of a pillar, we can sequentially arrange pillars to apply the associated nested maps and, therefore, create complex fluid structures without additional numerical simulation. To show the range of capabilities, we present sequences that sculpt the cross-sectional shape of a stream into complex geometries, move and split a fluid stream, perform solution exchange and achieve particle separation. A general strategy to engineer fluid streams into a broad class of defined configurations in which the complexity of the nonlinear equations of fluid motion are abstracted from the user is a first step to programming streams of any desired shape, which would be useful for biological, chemical and materials automation.

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Chaos, Symmetry, and Self-Similarity: Exploiting Order and Disorder in Mixing Processes

Cited by 176 publications

References 59 publications

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

Experimental study and nonlinear dynamic analysis of time-periodic micro chaotic mixers

Engineering fluid flow using sequenced microstructures

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