Complete chaotic mixing in an electro-osmotic flow by destabilization of key periodic pathlines

Chabreyrie, Rodolphe; Chandre, Cristel; Aubry, Nadine

doi:10.1063/1.3596127

Cited by 14 publications

(13 citation statements)

References 40 publications

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“…If the presence of the non-mixing islands gradually reduces with increasing Ra, the effect of the walls is weakly dependent on the value of Ra and should manifest itself in all regimes from laminar to fully turbulent. The extraction of a large number of UPOs of the Lagrangian system (3.1) allows one for visualising the tangles resulting from intersecting bundles of manifolds (Feudel et al 2005), i.e. the mixing regions.…”

Section: Discussionmentioning

confidence: 99%

“…In other words the mixing area associated with a given periodic point X P in Π coincides with the closure of its stable and unstable manifolds, themselves being interpreted as the skeleton of the hyperbolic mixing zone. This point of view is prominent in the study by Feudel et al (2005) who suggest that the total area occupied by mixing in the system corresponds to the closure of a bundle of manifolds.…”

Section: Periodic Points In the Stroboscopic Sectionmentioning

confidence: 95%

“…The box resolution is therefore a function of n, the longest period among all of the UPOs considered here. In this coarse-grained approach, the number of cells filled at least with one tracer is B 1/(2 X 2 ) as in Stremler (2008) and Chabreyrie et al (2011). The total fraction C of chaos is defined as the area covered by the B cells normalised by the surface of the cavity: C = 2B X 2 .…”

Section: Mixing Versus Ramentioning

confidence: 99%

“…The mixing property implies that the system is ergodic and that particle trajectories are chaotic (Falkovich 2004). More intuitively, the chaotic nature of mixing can be seen as a succession of stretching and folding events (see Ottino 1990;Sturman, Ottino & Wiggins 2006).…”

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confidence: 97%

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Lagrangian chaos in confined two-dimensional oscillatory convection

2014

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The chaotic advection of passive tracers in a two-dimensional confined convection flow is addressed numerically near the onset of the oscillatory regime. We investigate here a differentially heated cavity with aspect ratio 2 and Prandtl number 0.71 for Rayleigh numbers around the first Hopf bifurcation. A scattering approach reveals different zones depending on whether the statistics of return times exhibit exponential or algebraic decay. Melnikov functions are computed and predict the appearance of the main mixing regions via the break-up of the homoclinic and heteroclinic orbits. The non-hyperbolic regions are characterised by a larger number of Kolmogorov-ArnoldMoser (KAM) tori. Based on the numerical extraction of many unstable periodic orbits (UPOs) and their stable/unstable manifolds, we suggest a coarse-graining procedure to estimate numerically the spatial fraction of chaos inside the cavity as a function of the Rayleigh number. Mixing is almost complete before the first transition to quasiperiodicity takes place. The algebraic mixing rate is estimated for tracers released from a localised source near the hot wall.

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Section: Discussionmentioning

confidence: 99%

Section: Periodic Points In the Stroboscopic Sectionmentioning

confidence: 95%

Section: Mixing Versus Ramentioning

confidence: 99%

mentioning

confidence: 97%

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Lagrangian chaos in confined two-dimensional oscillatory convection

2014

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“…Such an indirect Lagrangian or dynamical systems strategy during the past two decades has provided new insights into a variety of fluid mechanics problems [23]. A characteristic example is that of small-scale fluid systems for which chaos theory has provided ways to create efficient and controllable microfluidic mixers [24][25][26]. Finally, in the results section we present both qualitative and quantitative results illuminating the origin of the kinematics switch.…”

Section: Introductionmentioning

confidence: 99%

Lagrangian approach to understanding the origin of the gill-kinematics switch in mayfly nymphs

et al. 2014

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The mayfly nymph breathes under water through an oscillating array of plate-shaped tracheal gills. As the nymph grows, the kinematics of these gills change abruptly from rowing to flapping. The classical fluid dynamics approach to consider the mayfly nymph as a pumping device fails in giving clear reasons for this switch. In order to shed some light on this switch between the two distinct kinematics, we analyze the problem under a Lagrangian viewpoint. We consider that a good Lagrangian transport that effectively distributes and stirs water and dissolved oxygen between and around the gills is the main goal of the gill motion. Using this Lagrangian approach, we are able to provide possible reasons behind the observed switch from rowing to flapping. More precisely, we conduct a series of in silico mayfly nymph experiments, where body shape, as well as gill shapes, structures, and kinematics are matched to those from in vivo. In this paper, we show both qualitatively and quantitatively how the change of kinematics enables better attraction, confinement, and stirring of water charged of dissolved oxygen inside the gills area. We reveal the attracting barriers to transport, i.e., attracting Lagrangian coherent structures, that form the transport skeleton between and around the gills. In addition, we quantify how well the fluid particles are stirred inside the gills area, which by extension leads us to conclude that it will increase the proneness of molecules of dissolved oxygen to be close enough to the gills for extraction.

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Numerical study of the vortex‐induced electroosmotic mixing of non‐Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size

2021

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We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.

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Complete chaotic mixing in an electro-osmotic flow by destabilization of key periodic pathlines

Cited by 14 publications

References 40 publications

Lagrangian chaos in confined two-dimensional oscillatory convection

Lagrangian chaos in confined two-dimensional oscillatory convection

Lagrangian approach to understanding the origin of the gill-kinematics switch in mayfly nymphs

Numerical study of the vortex‐induced electroosmotic mixing of non‐Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size

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