Academic literature on the topic 'Chaotic stirring'
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Journal articles on the topic "Chaotic stirring"
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Rypina, Irina I., Lawrence J. Pratt, Julie Pullen, Julia Levin, and Arnold L. Gordon. "Chaotic Advection in an Archipelago*." Journal of Physical Oceanography 40, no. 9 (September 1, 2010): 1988–2006. http://dx.doi.org/10.1175/2010jpo4336.1.
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Abstract Techniques from dynamical systems theory have been applied to study horizontal stirring of fluid in the Philippine Archipelago. The authors’ analysis is based on velocity fields produced by two high-resolution (3 and 6 km) numerical models. Particular attention is paid to identifying robust surface flow patterns and associating them with dominant Lagrangian coherent structures (LCSs). A recurrent wind-driven dipole in the lee of the coastline is considered in detail. The associated LCSs form a template for stirring, exchange, and biological transport in and around the dipole. Chaotic advection is argued to provide a relevant framework for interpreting mesoscale horizontal stirring processes in an archipelago as a whole. Implications for the formation of filaments, the production of tracer variance, and the scale at which stirring leads to mixing are discussed in connection with an observed temperature record.
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Lekien, Francois, and Chad Coulliette. "Chaotic stirring in quasi-turbulent flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365, no. 1861 (September 14, 2007): 3061–84. http://dx.doi.org/10.1098/rsta.2007.0020.
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Transport in laminar flows is governed by chaotic stirring and striation in long thin filaments. In turbulent flows, isotropic mixing dominates and tracers behave like stochastic variables. In this paper, we investigate the quasi-turbulent, intermediate regime where both chaotic stirring and turbulent mixing coexist. In these flows, the most common in nature, aperiodic Lagrangian coherent structures (LCSs) delineate particle transport and chaotic stirring. We review the recent developments in LCS theory and apply these techniques to measured surface currents in Monterey Bay, California. In the bay, LCSs can be used to optimize the release of drifting buoys or to minimize the impact of a coastal pollution source.
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Ridderinkhof, H., and J. T. F. Zimmerman. "Chaotic Stirring in a Tidal System." Science 258, no. 5085 (November 13, 1992): 1107–11. http://dx.doi.org/10.1126/science.258.5085.1107.
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Brown, Michael G., and Kevin B. Smith. "Ocean stirring and chaotic low‐order dynamics." Physics of Fluids A: Fluid Dynamics 3, no. 5 (May 1991): 1186–92. http://dx.doi.org/10.1063/1.858047.
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Pratt, L. J., I. I. Rypina, T. M. Özgökmen, P. Wang, H. Childs, and Y. Bebieva. "Chaotic advection in a steady, three-dimensional, Ekman-driven eddy." Journal of Fluid Mechanics 738 (December 5, 2013): 143–83. http://dx.doi.org/10.1017/jfm.2013.583.
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AbstractWe investigate and quantify stirring due to chaotic advection within a steady, three-dimensional, Ekman-driven, rotating cylinder flow. The flow field has vertical overturning and horizontal swirling motion, and is an idealization of motion observed in some ocean eddies. The flow is characterized by strong background rotation, and we explore variations in Ekman and Rossby numbers, $E$ and ${R}_{o} $, over ranges appropriate for the ocean mesoscale and submesoscale. A high-resolution spectral element model is used in conjunction with linear analytical theory, weakly nonlinear resonance analysis and a kinematic model in order to map out the barriers, manifolds, resonance layers and other objects that provide a template for chaotic stirring. As expected, chaos arises when a radially symmetric background state is perturbed by a symmetry-breaking disturbance. In the background state, each trajectory lives on a torus and some of the latter survive the perturbation and act as barriers to chaotic transport, a result consistent with an extension of the KAM theorem for three-dimensional, volume-preserving flow. For shallow eddies, where $E$ is $O(1)$, the flow is dominated by thin resonant layers sandwiched between KAM-type barriers, and the stirring rate is weak. On the other hand, eddies with moderately small $E$ experience thicker resonant layers, wider-spread chaos and much more rapid stirring. This trend reverses for sufficiently small $E$, corresponding to deep eddies, where the vertical rigidity imposed by strong rotation limits the stirring. The bulk stirring rate, estimated from a passive tracer release, confirms the non-monotonic variation in stirring rate with $E$. This result is shown to be consistent with linear Ekman layer theory in conjunction with a resonant width calculation and the Taylor–Proudman theorem. The theory is able to roughly predict the value of $E$ at which stirring is maximum. For large disturbances, the stirring rate becomes monotonic over the range of Ekman numbers explored. We also explore variation in the eddy aspect ratio.
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BOYLAND, PHILIP L., HASSAN AREF, and MARK A. STREMLER. "Topological fluid mechanics of stirring." Journal of Fluid Mechanics 403 (January 25, 2000): 277–304. http://dx.doi.org/10.1017/s0022112099007107.
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A new approach to regular and chaotic fluid advection is presented that utilizes the Thurston–Nielsen classification theorem. The prototypical two-dimensional problem of stirring by a finite number of stirrers confined to a disk of fluid is considered. The theory shows that for particular ‘stirring protocols’ a significant increase in complexity of the stirred motion – known as topological chaos – occurs when three or more stirrers are present and are moved about in certain ways. In this sense prior studies of chaotic advection with at most two stirrers, that were, furthermore, usually fixed in place and simply rotated about their axes, have been ‘too simple’. We set out the basic theory without proofs and demonstrate the applicability of several topological concepts to fluid stirring. A key role is played by the representation of a given stirring protocol as a braid in a (2+1)-dimensional space–time made up of the flow plane and a time axis perpendicular to it. A simple experiment in which a viscous liquid is stirred by three stirrers has been conducted and is used to illustrate the theory.
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Gilpin, William. "Cryptographic hashing using chaotic hydrodynamics." Proceedings of the National Academy of Sciences 115, no. 19 (April 23, 2018): 4869–74. http://dx.doi.org/10.1073/pnas.1721852115.
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Fluids may store and manipulate information, enabling complex applications ranging from digital logic gates to algorithmic self-assembly. While controllable hydrodynamic chaos has previously been observed in viscous fluids and harnessed for efficient mixing, its application to the manipulation of digital information has been sparsely investigated. We show that chaotic stirring of a viscous fluid naturally produces a characteristic signature of the stirring process in the arrangement of particles in the fluid, and that this signature directly satisfies the requirements for a cryptographic hash function. This includes strong divergence between similar stirring protocols’ hashes and avoidance of collisions (identical hashes from distinct stirs), which are facilitated by noninvertibility and a broad chaotic attractor that samples many points in the fluid domain. The hashing ability of the chaotic fluidic map implicates several unexpected mechanisms, including incomplete mixing at short time scales that produces a hyperuniform hash distribution. We investigate the dynamics of hashing using interparticle winding statistics, and find that hashing starts with large-scale winding of kinetically disjoint regions of the chaotic attractor, which gradually gives way to smaller scale braiding of single-particle trajectories. In addition to providing a physically motivated approach to implementing and analyzing deterministic chaotic maps for cryptographic applications, we anticipate that our approach has applications in microfluidic proof-of-work systems and characterizing large-scale turbulent flows from sparse tracer data.
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Abraham, Edward R., and Melissa M. Bowen. "Chaotic stirring by a mesoscale surface-ocean flow." Chaos: An Interdisciplinary Journal of Nonlinear Science 12, no. 2 (June 2002): 373–81. http://dx.doi.org/10.1063/1.1481615.
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Gleeson, James P. "Transient micromixing: Examples of laminar and chaotic stirring." Physics of Fluids 17, no. 10 (2005): 100614. http://dx.doi.org/10.1063/1.1928627.
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Kweon Suh, Yong. "A Chaotic Stirring by an Oscillating Point Vortex." Journal of the Physical Society of Japan 60, no. 3 (March 15, 1991): 896–906. http://dx.doi.org/10.1143/jpsj.60.896.
Full textDissertations / Theses on the topic "Chaotic stirring"
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Menon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." Thesis, The University of Sydney, 2008. http://hdl.handle.net/2123/3685.
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A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.
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Menon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." University of Sydney, 2008. http://hdl.handle.net/2123/3685.
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Doctor of PhilosophyA detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.
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Kemoun, Abdenour. "Caractérisation expérimentale de la structure de l'écoulement dans une cuve agitée : mélange." Vandoeuvre-les-Nancy, INPL, 1995. http://www.theses.fr/1995INPL081N.
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On étudie le mélange en cuve agitée par une approche mécanique des fluides. L’écoulement engendré est complexe, tridimensionnel, instationnaire, instable et la turbulence est inhomogène et anisotrope. Ce type d'écoulement nécessite un maillage de mesure fin et l'accès aux trois composantes de la vitesse. Un banc automatisé de vélocimétrie à laser bidimensionnelle rend praticable l'acquisition et le traitement de cette information dont on déduit une cartographie détaillée des champs moyens 3D et des quantités turbulentes. Un premier type d'analyse de ces données, conduit à la connaissance des grandeurs telles que : le tenseur de Reynolds, le taux de dissipation d'énergie, etc. , qui notamment au voisinage de la turbine, constituent des conditions aux limites pour les codes de calcul, des paramètres globaux utiles au contrôle du mélange (temps caractéristiques, coefficients de débit et de puissance, etc. ). L’autre approche concerne l'analyse de la dynamique de l'écoulement, avec pour projet de réduire cette dynamique très complexe à des modèles plus simples. Dans cette perspective le jet de la turbine est décrit comme une structure autonome ; des phénomènes de déstabilisation sont mis en évidence. Enfin la partie fluctuante de la vitesse dans le jet est décomposée en une partie aléatoire et une partie déterministe à un petit nombre de degrés de liberté
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Selemani, Kamardine. "Analyse et optimisation des chambres réverbérantes à l'aide du concept de cavité chaotique ouverte." Thesis, Paris Est, 2014. http://www.theses.fr/2014PEST1043/document.
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Ce travail porte sur l'optimisation de la géométrie de chambre réverbérante en s'inspirant du concept de cavité chaotique. Les chambres réverbérantes (RC) sont de plus en plus utilisées comme moyen de test de compatibilité électromagnétique. Elles sont utilisées au-delà d'une fréquence minimale à parti de laquelle les champs sont, dans le volume central de la cavité, statistiquement homogènes et isotropes ; l'obtention de ces propriétés statistiques nécessite l'utilisation d'un mécanisme de brassage, pouvant être mécanique ou électronique. Or, dans les cavités chaotiques, la plupart des modes sont associés à des champs statistiquement homogènes et isotropes, et ceci sans avoir recours à aucun brassage. C'est pourquoi un rapprochement entre chambres réverbérantes et cavités chaotiques a été fait dans ce travail.En premier lieu, nous nous intéressons à des cavités chaotiques 2D obtenues par des modifications successives d'une cavité rectangulaire. Les mesures effectuées dans ces cavités à l'aide d'une théorie perturbative, validées par des résultats de simulation, montrent qu'un champ électrique homogène est obtenu. Les principes retenus pour modifier la géométrie de la cavité rectangulaire seront repris dans les cavités 3D.Les propriétés de trois cavités 3D obtenues en modifiant une cavité parallélépipédique sont étudiées et comparées à celles d'une chambre réverbérante classique munie d'un brasseur de modes. Les modes propres et fréquences de résonance sont déterminés pour ces quatre cavités à l'aide du logiciel HFSS d'Ansoft, tout d'abord en considérant des cavités de géométrie figée, puis en y incluant un brassage mécanique.L'étude de l'homogénéité et de l'isotropie des modes propres montre clairement que les meilleures performances sont obtenues pour une des cavités chaotiques proposées, et ceci quels que soient les critères utilisés.Par ailleurs, il est montré que, dans la chambre réverbérante classique, un grand nombre de modes présente une forte localisation spatiale de l'énergie électrique, alors que ce phénomène ne se produit pas dans la cavité chaotique retenue. Ce phénomène, non détectable par les mesures classiquement effectuées en chambre réverbérante, est dommageable à l'obtention des propriétés d'homogénéité et d'isotropie requises dans le volume de travail.Enfin, l'étude de la distribution des écarts entre fréquences de résonance montre, comme prédit par la Théorie des Matrices Aléatoire, une concordance entre le suivi de la loi asymptotique prévue dans une cavité chaotique et les propriétés d'homogénéité et d'isotropie des champs. Ceci ouvre la voie vers l'utilisation de critères de caractérisation basés sur les fréquences de résonance et non plus uniquement sur les distributions des champsThis work deals with the optimization of the geometry of a reverberation chamber, drawing inspiration from the concept of chaotic cavity. Reverberation chambers, widely used for electromagnetic compatibility tests, are used above a minimal frequency from which the fields are statistically isotropic and uniform; however to respect these properties, a mode stirring process is necessary, that can be mechanical or electronic. As, in chaotic cavities, most modes are isotropic and uniform without the help of any stirring process, we take advantage of the knowledge gained from the studies of chaotic cavities to optimize reverberation chamber behavior.We firstly consider 2D chaotic cavities obtained by modifying a rectangular cavity. Measurements besed on a perturbative approch, and validated by simulations, show uniformly distributed electric fields. Similar geometrical modifications are then proposed in 3D.Three 3D different geometries of cavities obtained from a 3D rectangular cavity are then studied, and their properties are compared with those of a classical reverberation chamber equipped witdh a mode stirrer. Eigenmodes and resonant frequencies are determined numerically using Ansoft HFSS software, first by considering fixed cavity geometries, then by moving the stirrer.Electric field uniformity and isotropy are studied using several criteria; all of them clearly show that the best performances are attained within one of the proposed chaotic cavities.Moreover, a strong energy localization effect appears for numerous modes in the classical reverberation chamber, whereas it is not observed in the proposed 3D chaotic cavity. This effect, never reported in reverberation chamber studies, affects the field uniformity and isotropy within the working volume.The cavities properties are also compared width respect to their eigenfrequency spacing distributions. As predicted by the Random matrix Theory, the best agrement width the asymptotic law associated to chaotic cavities corresponds to the best field properties in terms of uniformity and isotropy. It leads to the proposal of reverberation chamber characterization criteria based on resonant frequencies instead of field distributions
Book chapters on the topic "Chaotic stirring"
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Aref, Hassan. "Stirring by chaotic advection." In Hamiltonian Dynamical Systems, 725–45. CRC Press, 2020. http://dx.doi.org/10.1201/9781003069515-52.
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"Characterization of Chaotic Stirring and Mixing Using Numerical Tools." In Microfluidics and Nanofluidics Handbook, 209–28. CRC Press, 2016. http://dx.doi.org/10.1201/b11188-10.
Full textConference papers on the topic "Chaotic stirring"
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Areejit, Suwilai, Poomyos Payakkawan, Anurak Jansri, Kitdakorn Klomkarn, Hisayuki Aoyama, and Pitikhate Sooraksa. "Chaotic application for Industrial Microwave Heating System without mode-stirring mechanism." In 2012 International Conference on Microwave and Millimeter Wave Technology (ICMMT). IEEE, 2012. http://dx.doi.org/10.1109/icmmt.2012.6230424.
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Sotiropoulos, Fotis, Tahirih C. Lackey, and S. Casey Jones. "Experimental and Computational Studies of Chaotic Stirring in Complex 3D Flows." In ASME 2002 Joint U.S.-European Fluids Engineering Division Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/fedsm2002-31357.
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Recent progress in experimental and computational studies of complex chaotically advected 3D flows is reviewed for the confined swirling flow in a cylindrical container with a rotating bottom and the open flow in a helical static mixer. The concept of Lagrangian averaging along particle paths, whose theoretical foundation stems from ergodic theory, is proposed as a powerful tool for constructing Poincare´ maps in numerical studies of confined flows. The same concept has also been employed to develop the first non-intrusive experimental technique for constructing Poincare´ maps in complex 3D flows. The potential of these ergodic concepts is demonstrated in computational and experimental studies for the confined swirling flow. Numerical computations for the helical mixer flow show that increasing the Reynolds number from Re = 100 to 500 leads to the appearance of unmixed islands in the flow. The mechanism that leads to the formation of such islands is shown to be linked to the growth of coherent helical vortices in the flow.
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Le Guer, Yves, and Kamal El Omari. "Thermal Chaotic Mixing in a Two Rod Mixer With Imposed Heat Flux." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78044.
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We investigate the mixing and heat transfer enhancement in a two rod mixer for a highly viscous fluid. The mixer is composed of two circular rods maintained vertically in a cylindrical tank. The rods and tank can rotate around their revolution axis. Chaotic flows are obtained by imposing temporal modulations of the rotational wall velocities. The fluid is incompressible, Newtonian and the thermophysical properties, at first approximation, are kept constant with temperature. We study the effect of different stirring protocols and flow configurations leading to chaotic flows on the efficiency of mixing and heat transfer for the particular wall boundary condition of constant heat flux (i.e. Neumann condition). For this purpose we use different statistical indicators as tools to characterize the mean value of fluid temperature and its homogenization. The results show a significant enhancement of heat transfer for the case of an alternated stirring protocol (a result we have already obtained for the constant wall temperature boundary condition [1]).
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Yi, Mingqiang, and Haim H. Bau. "The Kinematics of Bend-Induced Stirring in Micro-Conduits." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1136.
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Abstract The absence of turbulence and the difficulty associated with introducing moving stirrers into microfluidic systems make the mixing problem in microdevices challenging. We studied theoretically steady, laminar, incompressible flow through a sequence of conduits with rectangular cross-sections aligned to form 90° with each other. The feasibility of taking advantage of bend-induced vortices to stir the fluid and enhance the mixing process was evaluated. Since at very low Reynolds numbers the bend-induced vortices decay rapidly, it was necessary to utilize a large number of bends to achieve the desired effects. Since it is not practical to directly simulate the flow through a large number of bends, we borrowed Jones et. al.’s (1989) idea of constructing a two-dimensional map to project fluid particles from a cross-section upstream of the bend to a cross-section downstream of the bend. This map was then applied repetitively to trace particle trajectories in various bend arrangements. Under certain conditions, chaotic advection was observed.
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El Omari, Kamal, and Yves Le Guer. "Thermal Chaotic Mixing of Non-Newtonian Fluids in a Two Rod Mixer." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78043.
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We investigate the mixing and heat transfer enhancement in a two rod mixer for highly viscous non-Newtonian fluids. The mixer is composed of two circular rods maintained vertically in a cylindrical tank. Chaotic flows are obtained by imposing temporal modulations of the rotational velocities of the walls. We study the effect of different stirring protocols leading to non-chaotic and chaotic flows on the efficiency of mixing and heat transfer for three different rheological fluid behaviors: shear-thinning, Newtonian and shear thickening. For this purpose we use statistical indicators characterizing the mean value of fluid temperature and its homogenization. We find that chaotic mixing is suitable for shear-thickening fluids for which we observe a manifest enhancement of the thermal mixing (heat extraction and homogenization). This is due to the increase of apparent fluid viscosity in the vicinity of the rotating walls. This aspect confirms the relevance of chaotic mixing for highly viscous fluids.
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Rodrigo, A. J. S., J. P. B. Mota, and E. Saatdjian. "Chaotic Mixing in Time-Periodic 3-D Flows." In ASME 2002 Joint U.S.-European Fluids Engineering Division Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/fedsm2002-31365.
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Mixing in a special class of three-dimensional, non-inertial time-periodic flows is studied quantitatively. In the type of flow considered here, the cross-sectional velocity components are independent of the axial flow which is assumed to be fully developed. Using the eccentric helical annular mixer as a prototype, the time-periodic flow field is induced by adding a sinusoidal component to the rotation speed of the inner cylinder. For a given 3-D mixer geometry, the degree of mixing achieved is a function of two parameters that measure the strength of the cross-sectional stirring protocol relative to the mean residence time of the fluid in the mixer: the average number of turns of the outer cylinder, and the average number of modulation periods. We find that for a given mixer geometry and mean residence time, there is an optimum modulation frequency for which the standard deviation of the temperature field at the exit is a minimum.
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Beskok, Ali. "An Electroosmotically Stirred Continuous Micro Mixer." In ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62022.
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A continuous microfluidic mixer concept is developed by superposition of time-periodic electroosmotic flow on zeta potential patterned surfaces and pressure driven flow. Finite time Lyapunov exponents and filament stretching are utilized to quantify the chaotic strength, and to identify the chaotic and regular zones in the mixer at various operation conditions. Numerical solutions of the species transport equation are performed as a function of the Peclet number (Pe) at fixed kinematic conditions. Mixing efficiency is quantified using mixing index that is based on standard deviation of the scalar species distribution. The mixing length (lm) is characterized as a function of the Peclet number, and lm ∝ ln (Pe) scaling is observed under locally-optimum stirring conditions.
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Kim, Ho Jun, and Ali Beskok. "Numerical Studies of Mixing in an Electroosmotically Stirred Continuous Micro Mixer." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42730.
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A continuous microfluidic mixer concept is developed by superposition of time-periodic electroosmotic flow on zeta potential patterned surfaces and pressure driven flow. Finite time Lyapunov exponents and filament stretching are utilized to quantify the chaotic strength, and to identify the chaotic and regular zones in the mixer at various operation conditions. Numerical solutions of the species transport equation are performed as a function of the Peclet number (Pe) at fixed kinematic conditions. Mixing efficiency is quantified using mixing index that is based on standard deviation of the scalar species distribution. The mixing length (lm) is characterized as a function of the Peclet number, and lm ∝ ln (Pe) scaling is observed under locally-optimum stirring conditions.
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Ascanio, Gabriel, Ste´phane Foucault, and Philippe A. Tanguy. "New Chaotic Approach for Mixing Shear-Thinning Fluids in Stirred Tanks." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45296.
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The mixing of inelastic shear-thinning fluids has been investigated by using a chaotic approach. Two different scenarios based on single and dual off-centered impellers have been proposed and compared to the standard configuration (steady stirring) showing the potentialities and drawbacks of the proposed arrangements. Mixing times were evaluated by means of color-discoloration technique based on a fast acid-base indicator reaction. An aqueous solution of low concentrated purple bromocresol was used as tracer and added to the tank in the beginning of the experiments and then NaOH or HCl were added to the fluid to be tested in order to change its pH and as a consequence its color. It is demonstrated that, if the operating conditions of the proposed scenarios are properly set, the mixing times can be drastically reduced compared to those obtained under the standard configuration.
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Goullet, Arnaud, and Nadine Aubry. "Using Chaos for Fluid Mixing in Pulsed Micro Flows." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98449.
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Even though mixing is crucial in many microfluidic applications where biological and chemical reactions are needed, efficient mixing remains a challenge since the Reynolds number of these flows is typically low, thus excluding turbulence as a potential mechanism for stirring. While various approaches relying on clever geometries, cross-flows, miniature stirrers or external fields have been used in the past, our work has focused on generating stirring in microchannels of simple geometry by merely pulsing flow rates at the inlets through which the two fluids are brought into the device. Flow visualizations from experiments, as well as numerical simulations, have indicated that the majority of the mixing takes place in the confluence region. Even though it has been shown in previous work that good mixing can be achieved at relatively large scales using this technique, one of the challenges is to make sure that mixing occurs at small scales (i.e., particle scales) as well. To address this issue, we carefully study the dynamics of tracer particles using both computational fluid dynamics and dynamical systems theory, and explore the parameter space in terms of the Reynolds number, Strouhal number and phase difference between the two inlet flows. Specifically, we generate a bifurcation diagram in which both regular and chaotic dynamics occur. As expected, the chaotic regime exhibits stretching and folding of material lines at all (large and small) scales, and is thus promising as an effective mixing tool.