Effects of manifolds and corner singularities on stretching in chaotic cavity flows

Liu, M.; Muzzio, Fernando J.; Peskin, Richard L.

doi:10.1016/0960-0779(94)90036-1

Cited by 17 publications

(7 citation statements)

References 25 publications

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“…This structure is very similar to the structure revealed by mixing dyed tracers for the same flow condition. 17,18 Low stretching values occur not only inside the islands but also in several small pockets throughout the chaotic region. High stretching values occur in segregated regions, whose location, size, and intensity are determined by an interplay of unstable manifolds of hyperbolic periodic points and of singularities at the cavity corners.…”

Section: Spatial Structure Of the Curvature Fieldmentioning

confidence: 99%

“…High stretching values occur in segregated regions, whose location, size, and intensity are determined by an interplay of unstable manifolds of hyperbolic periodic points and of singularities at the cavity corners. 17,18 The question examined in this section is whether the curvature field exhibits a similar degree of complexity. The curvature field is examined by placing infinitesimal vectors uniformly in the entire flow domain and computing curvature as a function of time.…”

Section: Spatial Structure Of the Curvature Fieldmentioning

confidence: 99%

“…In contrast, high stretching regions in time-periodic chaotic flows can preserve their coherence for 20 or more periods. 17,18 The reason for this difference in behavior between stretching and curvature is that stretching accumulates exponentially with time. The rate of increase of stretching is proportional to the total amount of stretching accumulated by a particle up to that point.…”

Section: Spatial Structure Of the Curvature Fieldmentioning

confidence: 99%

“…[2][3][4][5][6] Exponential stretching of material elements also occurs in deterministic chaotic flows, and is a direct consequence of sensitivity to initial conditions, which is one of the signatures of chaos. [7][8][9][10][11][12][13][14][15][16][17][18] Folding processes, on the other hand, have been the subject of just a handful of studies, which have focused mainly on homogeneous isotropic turbulent flows. The mathematics required to describe folding processes are more complicated, involving second derivatives ͑and therefore requiring more accurate representations͒ of the velocity field.…”

Section: Introductionmentioning

confidence: 99%

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The curvature of material lines in chaotic cavity flows

Liu

Muzzio

1996

Physics of Fluids

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Material line folding is studied in two-dimensional chaotic cavity flows. Line folding is measured by the local curvature kϭl؋lЈ/͉l͉ 3 , where l(q) is an infinitesimal vector in the tangential direction of the line, q is a coordinate along the line, and lЈ is the derivative of l with respect to q. It is shown both analytically and numerically that folding is always accompanied by compression. The vector lЈ plays a crucial role as a driving force for the stretching and folding processes. A material line is stretched when lЈ is tangential to the line and it is folded when lЈ is normal to the line. The spatial structure of the curvature field is computed numerically. The short-time structure of the curvature field is similar to the structure of unstable manifolds of periodic hyperbolic points, and closely resembles patterns observed in tracer mixing experiments and in stretching field computations. The long time structure of the field asymptotically approaches an entirely different time-independent structure. Probability density functions of curvature are independent of both time and initial conditions.

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Section: Spatial Structure Of the Curvature Fieldmentioning

confidence: 99%

Section: Spatial Structure Of the Curvature Fieldmentioning

confidence: 99%

Section: Spatial Structure Of the Curvature Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The curvature of material lines in chaotic cavity flows

Liu

Muzzio

1996

Physics of Fluids

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“…The numerical simulations were quite helpful in understanding the chaotic nature of the flow in the screw channel. [3][4][5][6] It would be of great value to screw designers to be capable of systematically determining design variables of the chaos screw for purposes of mixing as uniformly and efficiently as possible. In this regard, it would be desirable to have a reliable measure of mixing for reasons of quality.…”

Section: Kim Andmentioning

confidence: 99%

A new representative measure of chaotic mixing in a chaos single-screw extruder

Lee

Kwon

1999

Adv. Polym. Technol.

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Chaotic mixing characteristics in static mixers with different axial twisted‐tape inserts

Meng

Song

et al. 2015

Can J Chem Eng

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The distinction of chaotic advection and mixing of high‐viscosity fluids in tubes equipped with four different twisted tapes, including KSM, MSM, RSM, and SSM, were evaluated by Lagrangian simulation. ∼23 550 massless particle tracers marked by red and black colours were respectively released in the semicircle and concentric circles of the inlet cross‐section. Mixing performance was evaluated qualitatively by tracking Poincaré sections, and quantitatively by the variation coefficient as a function of axial position. Poincaré sections of tracers showed that KSM had the best mixing performance and RSM had two oval‐shaped segregated areas which periodically moved clockwise 90° in the cross‐sections of adjacent twisted tapes. Extensional efficiencies were computed radially and axially for all configurations. Both results showed that large dispersive mixing areas existed in the transition section. At the beginning of the first and end of the last element, the largest extensional efficiencies emerged, which were 1.07−1.21 times that at the transitions. The profiles of stretching rate showed that RSM tape had the weakest micro‐mixing ability, and the other three mixers had nearly identical stretching rates, much higher than RSM for Re < 10. With increasing Re, the mixing performance of MSM decreased first and then increased to be slightly higher than that of RSM. The secondary flows at transition regions were largely weakened for the different twist direction in the MSM. The respective roles of flow reversal and twist direction on mixing were evaluated with the stretching rates between static mixers and conventional stirred vessels.

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Effects of manifolds and corner singularities on stretching in chaotic cavity flows

Cited by 17 publications

References 25 publications

The curvature of material lines in chaotic cavity flows

The curvature of material lines in chaotic cavity flows

A new representative measure of chaotic mixing in a chaos single-screw extruder

Chaotic mixing characteristics in static mixers with different axial twisted‐tape inserts

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