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Wang Q, Ding Z, Wong G, Zhou J, Riaud A. Skipping the Boundary Layer: High-Speed Droplet-Based Immunoassay Using Rayleigh Acoustic Streaming. Anal Chem 2023; 95:6253-6260. [PMID: 37018490 DOI: 10.1021/acs.analchem.2c03877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/07/2023]
Abstract
Acoustic mixing of droplets is a promising way to implement biosensors that combine high speed and minimal reagent consumption. To date, this type of droplet mixing is driven by a volume force resulting from the absorption of high-frequency acoustic waves in the bulk of the fluid. Here, we show that the speed of these sensors is limited by the slow advection of analyte to the sensor surface due to the formation of a hydrodynamic boundary layer. We eliminate this hydrodynamic boundary layer by using much lower ultrasonic frequencies to excite the droplet, which drives a Rayleigh streaming that behaves essentially like a slip velocity. At equal average flow velocity in the droplet, both experiment and three-dimensional simulations show that this provides a three-fold speedup compared to Eckart streaming. Experimentally, we further shorten a SARS-CoV-2 antibody immunoassay from 20 min to 40 s taking advantage of Rayleigh acoustic streaming.
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Affiliation(s)
- Qi Wang
- ASIC and System State Key Laboratory, School of Microelectronics, Fudan University, Shanghai 200433, P. R. China
| | - Zhe Ding
- Viral Hemorrhagic Fevers Research Unit, CAS Key Laboratory of Molecular Virology and Immunology, Institut Pasteur of Shanghai, Chinese Academy of Sciences, Shanghai 200031, P. R. China
- University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Gary Wong
- Viral Hemorrhagic Fevers Research Unit, CAS Key Laboratory of Molecular Virology and Immunology, Institut Pasteur of Shanghai, Chinese Academy of Sciences, Shanghai 200031, P. R. China
| | - Jia Zhou
- ASIC and System State Key Laboratory, School of Microelectronics, Fudan University, Shanghai 200433, P. R. China
| | - Antoine Riaud
- ASIC and System State Key Laboratory, School of Microelectronics, Fudan University, Shanghai 200433, P. R. China
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2
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Kadoch B, Bos WJT, Schneider K. Efficiency of laminar and turbulent mixing in wall-bounded flows. Phys Rev E 2020; 101:043104. [PMID: 32422802 DOI: 10.1103/physreve.101.043104] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2019] [Accepted: 03/18/2020] [Indexed: 11/07/2022]
Abstract
A turbulent flow mixes in general more rapidly a passive scalar than a laminar flow does. From an energetic point of view, for statistically homogeneous or periodic flows, the laminar regime is more efficient. However, the presence of walls may change this picture. We consider in this investigation mixing in two-dimensional laminar and turbulent wall-bounded flows using direct numerical simulation. We show that for sufficiently large Schmidt number, turbulent flows more efficiently mix a wall-bounded scalar field than a chaotic or laminar flow does. The mixing efficiency is shown to be a function of the Péclet number, and a phenomenological explanation yields a scaling law, consistent with the observations.
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Affiliation(s)
| | | | - Kai Schneider
- Aix-Marseille Université, I2M-CNRS, Marseille, France
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3
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Ober TJ, Foresti D, Lewis JA. Active mixing of complex fluids at the microscale. Proc Natl Acad Sci U S A 2015; 112:12293-8. [PMID: 26396254 PMCID: PMC4603479 DOI: 10.1073/pnas.1509224112] [Citation(s) in RCA: 108] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
Mixing of complex fluids at low Reynolds number is fundamental for a broad range of applications, including materials assembly, microfluidics, and biomedical devices. Of these materials, yield stress fluids (and gels) pose the most significant challenges, especially when they must be mixed in low volumes over short timescales. New scaling relationships between mixer dimensions and operating conditions are derived and experimentally verified to create a framework for designing active microfluidic mixers that can efficiently homogenize a wide range of complex fluids. Active mixing printheads are then designed and implemented for multimaterial 3D printing of viscoelastic inks with programmable control of local composition.
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Affiliation(s)
- Thomas J Ober
- School of Engineering and Applied Sciences, Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138
| | - Daniele Foresti
- School of Engineering and Applied Sciences, Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138
| | - Jennifer A Lewis
- School of Engineering and Applied Sciences, Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138
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4
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Sturman R, Springham J. Rate of chaotic mixing and boundary behavior. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012906. [PMID: 23410403 DOI: 10.1103/physreve.87.012906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2011] [Revised: 06/27/2012] [Indexed: 06/01/2023]
Abstract
We discuss rigorous results on the rate of mixing for an idealized model of a class of fluid mixing device. These show that the decay of correlations of a scalar field is governed by the presence of boundaries in the domain, and in particular by the behavior of the modeled fluid at such boundaries.
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Affiliation(s)
- Rob Sturman
- Department of Applied Mathematics, University of Leeds, Leeds, United Kingdom.
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5
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Abstract
In many important chemical processes, the laminar flow regime is inescapable and defines the performance of reactors, separators, and analytical instruments. In the emerging field of microchemical process or lab-on-a-chip, this constraint is particularly rigid. Here, we review developments in the use of chaotic laminar flows to improve common transport processes in this regime. We focus on four: mixing, interfacial transfer, axial dispersion, and spatial sampling. Our coverage demonstrates the potential for chaos to improve these processes if implemented appropriately. Throughout, we emphasize the usefulness of familiar theoretical models of transport for processes occurring in chaotic flows. Finally, we point out open challenges and opportunities in the field.
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Affiliation(s)
- Pavithra Sundararajan
- Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA.
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6
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Thiffeault JL, Gouillart E, Dauchot O. Moving walls accelerate mixing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:036313. [PMID: 22060498 DOI: 10.1103/physreve.84.036313] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2011] [Indexed: 05/31/2023]
Abstract
Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario, the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice, several authors have found that the no-slip boundary condition at the walls of a vessel can slow down mixing considerably, turning an exponential decay into a power law. This slowdown affects the whole mixing region, and not just the vicinity of the wall. The reason is that when the chaotic mixing region extends to the wall, a separatrix connects to it. The approach to the wall along that separatrix is polynomial in time and dominates the long-time decay. However, if the walls are moved or rotated, closed orbits appear, separated from the central mixing region by a hyperbolic fixed point with a homoclinic orbit. The long-time approach to the fixed point is exponential, so an overall exponential decay is recovered, albeit with a thin unmixed region near the wall.
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Affiliation(s)
- Jean-Luc Thiffeault
- Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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7
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Yee E, Skvortsov A. Scalar fluctuations from a point source in a turbulent boundary layer. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:036306. [PMID: 22060491 DOI: 10.1103/physreve.84.036306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2011] [Revised: 07/14/2011] [Indexed: 05/31/2023]
Abstract
The downstream development of the concentration probability distribution along the mean-plume centerline of a dispersing plume in the wake of a ground-level continuous point source in a neutrally stratified wall-shear layer is studied. It is shown that the concentration distribution is well described by a family of one-parameter gamma distributions, as first suggested by Villermaux and Duplat [Phys. Rev. Lett. 91, 184501 (2003)] in the context of confined mixing. A prediction of the downstream evolution of the parameter k (which specifies the gamma distribution) is obtained. This prediction includes explicitly the effects of mean shear on the mean-square concentration.
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Affiliation(s)
- Eugene Yee
- Defence R&D Canada Suffield, P.O. Box 4000 Station Main, Medicine Hat, Alberta, Canada T1A 8K6
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8
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Ngan K, Vanneste J. Scalar decay in a three-dimensional chaotic flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056306. [PMID: 21728646 DOI: 10.1103/physreve.83.056306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2011] [Indexed: 05/31/2023]
Abstract
The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomized alternating sine flow employed extensively in studies of mixing in two dimensions. It is used to show that theoretical predictions for two-dimensional flows with small diffusivity carry over to three dimensions even though the stretching properties differ significantly. The variance decay rate, scalar field structure, and time evolution of statistical moments confirm that there are two distinct regimes of scalar decay: a locally controlled regime, which applies when the domain size is comparable to the characteristic length scale of the velocity field, and a globally controlled regime, which applies when the domain is larger. Asymptotic predictions for the variance decay rate in both regimes show excellent agreement with the numerical results. Consideration of both the forward flow and its time reverse makes it possible to compare the scalar evolution in flows with one or two expanding directions; simulations confirm the theoretical prediction that the decay rate of the scalar is the same in both flows, despite the very different scalar field structures.
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Affiliation(s)
- K Ngan
- Met Office, Exeter EX1 3PB, United Kingdom.
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9
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Skvortsov A, Yee E. Scaling laws of peripheral mixing of passive scalar in a wall-shear layer. Phys Rev E 2011; 83:036303. [PMID: 21517583 DOI: 10.1103/physreve.83.036303] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2010] [Indexed: 11/07/2022]
Abstract
The scaling laws governing the concentration moments of a passive scalar released from a ground-level localized source in a neutrally stratified wall-shear layer are investigated using a theoretical framework recently formulated by Lebedev and Turitsyn [Phys. Rev. E 69, 036301 (2004)]. For the current application, this theoretical framework is generalized from the smooth random velocity field applicable in the viscous sublayer to the nonsmooth random velocity field that applies to the bulk of the wall-shear layer. Theoretical relationships for the passive scalar concentration moments are compared to a water-channel simulation of turbulent diffusion from a ground-level source in a wall-shear layer. The diffusion measurements in the wall-shear layer are shown to be consistent with the theoretical description and also imply the robustness of the identified scaling laws for the scalar concentration moments.
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Affiliation(s)
- Alex Skvortsov
- Defence Science and Technology Organisation, 506 Lorimer Street, Fishermans Bend, Victoria 3207, Australia.
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10
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Abstract
Acoustic streaming, the generation of mean flow by dissipating acoustic waves, provides a promising method for flow pumping in microfluidic devices. In recent years, several groups have been experimenting with acoustic streaming induced by leaky surface waves: (Rayleigh) surface waves excited in a piezoelectric solid interact with a small volume of fluid where they generate acoustic waves and, as result of the viscous dissipation of these waves, a mean flow. We discuss the computation of the corresponding Lagrangian mean flow, which controls the trajectories of fluid particles and hence the mixing properties of the flows generated by this method. The problem is formulated using the averaged vorticity equation which extracts the dominant balance between wave dissipation and mean-flow dissipation. Particular attention is paid to the thin boundary layer that forms at the solid/liquid interface, where the flow is best computed using matched asymptotics. This leads to an explicit expression for a slip velocity, which includes the effect of the oscillations of the boundary. The Lagrangian mean flow is naturally separated into three contributions: an interior-driven Eulerian mean flow, a boundary-driven Eulerian mean flow and the Stokes drift. A scale analysis indicates that the latter two contributions can be neglected in devices much larger than the acoustic wavelength but need to be taken into account in smaller devices. A simple two-dimensional model of mean flow generation by surface acoustic waves is discussed as an illustration.
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Affiliation(s)
- J. Vanneste
- School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3JZ, UK
| | - O. Bühler
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
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11
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Skvortsov A, Jamriska M, Dubois TC. Scaling laws of passive tracer dispersion in the turbulent surface layer. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:056304. [PMID: 21230573 DOI: 10.1103/physreve.82.056304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2010] [Revised: 10/15/2010] [Indexed: 05/30/2023]
Abstract
Experimental results for passive tracer dispersion in the turbulent surface layer under stable conditions are presented. In this case, the dispersion of tracer particles is determined by the interplay of three mechanisms: relative dispersion (celebrated Richardson's mechanism), shear dispersion (particle separation due to variation of the mean velocity field) and specific surface-layer dispersion (induced by the gradient of the energy dissipation rate in the turbulent surface layer). The latter mechanism results in the rather slow (ballistic) law for the mean squared particle separation. Based on a simplified Langevin equation for particle separation we found that the ballistic regime always dominates at large times. This conclusion is supported by our extensive atmospheric observations. Exit-time statistics are derived from the experimental data set and show a reasonable match with the simple dimensional asymptotes for different mechanisms of tracer dispersion, as well as predictions of the multifractal model and experimental data from other sources.
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Affiliation(s)
- Alex Skvortsov
- Defence Science and Technology Organisation, 506 Lorimer Street, Fishermans Bend, Victoria 3207, Australia
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12
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Gouillart E, Thiffeault JL, Dauchot O. Rotation shields chaotic mixing regions from no-slip walls. PHYSICAL REVIEW LETTERS 2010; 104:204502. [PMID: 20867031 DOI: 10.1103/physrevlett.104.204502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2009] [Revised: 12/03/2009] [Indexed: 05/29/2023]
Abstract
We report on the decay of a passive scalar in chaotic mixing protocols where the wall of the vessel is rotated, or a net drift of fluid elements near the wall is induced at each period. As a result the fluid domain is divided into a central isolated chaotic region and a peripheral regular region. Scalar patterns obtained in experiments and simulations converge to a strange eigenmode and follow an exponential decay. This contrasts with previous experiments [Gouillart, Phys. Rev. Lett. 99, 114501 (2007)] with a chaotic region spanning the whole domain, where fixed walls constrained mixing to follow a slower algebraic decay. Using a linear analysis of the flow close to the wall, as well as numerical simulations of Lagrangian trajectories, we study the influence of the rotation velocity of the wall on the size of the chaotic region, the approach to its bounding separatrix, and the decay rate of the scalar.
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Affiliation(s)
- E Gouillart
- Surface du Verre et Interfaces, UMR 125 CNRS/Saint-Gobain, 93303 Aubervilliers, France
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13
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Garcia-Ybarra PL. Near-wall turbulent transport of large-Schmidt-number passive scalars. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:067302. [PMID: 19658632 DOI: 10.1103/physreve.79.067302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2009] [Revised: 05/13/2009] [Indexed: 05/28/2023]
Abstract
Turbulent diffusion of a passive scalar with a large-Schmidt number (Sc >> 1) is considered in the viscous sublayer of a turbulent channel flow. Close to the wall, the corresponding eddy diffusivity coefficient is expanded as a power series in terms of the viscous distance to the wall y . The coefficients of the series depend on the Schmidt number and the analysis of recent numerical results allows to conclude that in the close vicinity of the wall (y << Sc(-1/3)) , the y(3) term is the dominant term; whereas, at distances relatively large from the wall (Sc(-1/3)<< y <<1) , the y(4) term becomes dominant. Accordingly, in this region the turbulent Schmidt number is not constant but follows a hyperbolic law in terms of the distance to the wall that matches the values taken in the vicinity of the wall, on the order of Sc(-1/3) , with the values of order unity in the rest of the viscous layer. The implications of this behavior on the surface-transfer coefficient are analyzed.
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Affiliation(s)
- P L Garcia-Ybarra
- Depto. Fisica Matematica y de Fluidos, UNED, Senda del Rey 9, 28040 Madrid, Spain.
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14
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Gouillart E, Dauchot O, Dubrulle B, Roux S, Thiffeault JL. Slow decay of concentration variance due to no-slip walls in chaotic mixing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:026211. [PMID: 18850925 DOI: 10.1103/physreve.78.026211] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2008] [Revised: 05/08/2008] [Indexed: 05/26/2023]
Abstract
Chaotic mixing in a closed vessel is studied experimentally and numerically in different two-dimensional (2D) flow configurations. For a purely hyperbolic phase space, it is well known that concentration fluctuations converge to an eigenmode of the advection-diffusion operator and decay exponentially with time. We illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern. We show for different physical viscous flows that, in the case of a fully chaotic Poincaré section, parabolic periodic points at the walls lead to slower (algebraic) decay. A persistent pattern, the backbone of which is the unstable manifold of parabolic points, can be observed. However, slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain, and hence delays the formation of an eigenmode until it is no longer experimentally observable. Inspired by the baker's map, we introduce a 1D model with a parabolic point that gives a good account of the slow decay observed in experiments. We derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no-slip wall.
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Affiliation(s)
- E Gouillart
- Surface du Verre et Interfaces, UMR 125 CNRS/Saint-Gobain, 93303 Aubervilliers, France
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15
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Burghelea T, Segre E, Steinberg V. Role of elastic stress in statistical and scaling properties of elastic turbulence. PHYSICAL REVIEW LETTERS 2006; 96:214502. [PMID: 16803239 DOI: 10.1103/physrevlett.96.214502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2005] [Indexed: 05/10/2023]
Abstract
The role of elastic stress in statistical and scaling properties of elastic turbulence in a polymer solution flow between two disks is discussed. The analogy with a small-scale magnetodynamics and a passive scalar turbulent advection in the Batchelor regime is used to explain the experimentally observed statistical properties, the flow structure, and the scaling of elastic turbulence. The emergence of a new length scale, namely, the boundary layer thickness, is observed and studied.
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Affiliation(s)
- Teodor Burghelea
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100 Israel
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Simonnet C, Groisman A. Chaotic mixing in a steady flow in a microchannel. PHYSICAL REVIEW LETTERS 2005; 94:134501. [PMID: 15903994 DOI: 10.1103/physrevlett.94.134501] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2004] [Revised: 02/08/2005] [Indexed: 05/02/2023]
Abstract
We report experiments on mixing of a passively advected fluorescent dye in a low Reynolds number flow in a microscopic channel. The channel is a chain of repeating segments with a custom designed profile that generates a steady three-dimensional flow with stretching and folding, and chaotic mixing. A few statistical characteristics of mixing in the flow are studied and are all found to agree with theoretical and experimental results for the flows in the Batchelor regime of mixing that are chaotic in time. The proposed microchannel provides fast and efficient mixing and is simple to fabricate.
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Affiliation(s)
- Claire Simonnet
- Department of Physics, University of California-San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
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17
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Schekochihin AA, Haynes PH, Cowley SC. Diffusion of passive scalar in a finite-scale random flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:046304. [PMID: 15600516 DOI: 10.1103/physreve.70.046304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2004] [Indexed: 05/24/2023]
Abstract
We consider a solvable model of the decay of scalar variance in a single-scale random velocity field. We show that if there is a separation between the flow scale k(-1 )(flow ) and the box size k(-1 )(box ) , the decay rate lambda proportional, variant ( k(box) / k(flow) )(2) is determined by the turbulent diffusion of the box-scale mode. Exponential decay at the rate lambda is preceded by a transient powerlike decay (the total scalar variance approximately t(-5/2) if the Corrsin invariant is zero, t(-3/2) otherwise) that lasts a time t approximately 1/lambda . Spectra are sharply peaked at k= k(box) . The box-scale peak acts as a slowly decaying source to a secondary peak at the flow scale. The variance spectrum at scales intermediate between the two peaks ( k(box) <<k<< k(flow) ) is approximately k+a k(2) +... (a>0) . The mixing of the flow-scale modes by the random flow produces, for the case of large Péclet number, a k(-1+delta) spectrum at k>> k(flow) , where delta proportional lambda is a small correction. Our solution thus elucidates the spectral make up of the "strange mode," combining small-scale structure and a decay law set by the largest scales.
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