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Mixing lamellae in a shear flow

Published online by Cambridge University Press:  24 January 2018

Mathieu Souzy ,
Imen Zaier ,
Henri Lhuissier Open the ORCID record for Henri Lhuissier [Opens in a new window] ,
Tanguy Le Borgne  and
Bloen Metzger Open the ORCID record for Bloen Metzger [Opens in a new window]
Mathieu Souzy
Affiliation:
Geosciences Rennes, UMR CNRS 6118, Université Rennes 1, 35042 Rennes, France
Imen Zaier
Affiliation:
Aix-Marseille Université, IUSTI-CNRS UMR 7343, 13453 Marseille CEDEX 13, France
Henri Lhuissier
Affiliation:
Aix-Marseille Université, IUSTI-CNRS UMR 7343, 13453 Marseille CEDEX 13, France
Tanguy Le Borgne
Affiliation:
Geosciences Rennes, UMR CNRS 6118, Université Rennes 1, 35042 Rennes, France
Bloen Metzger*
Affiliation:
Aix-Marseille Université, IUSTI-CNRS UMR 7343, 13453 Marseille CEDEX 13, France
*
†Email address for correspondence: bloen.metzger@univ-amu.fr
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Abstract

Mixing dynamics in flows are governed by the coupled action of diffusion and stretching by velocity gradients. This leads to the development of elongated lamellar structures in scalar fields where concentration fluctuations exist at scales set by the Batchelor scale. Because the latter is generally too small to be resolved experimentally, observation of these mechanisms remains an outstanding challenge. Here we present high-resolution experiments allowing for the precise quantification of the evolution of concentration distributions at the scale of a single lamella experiencing diffusion, stretching and aggregation with other lamellae. Quantitative agreement is found with analytical predictions for the lamella’s concentration profile, Batchelor time, Batchelor length scale, and concentration distribution for a large range of Péclet numbers and without adjustable parameter. This benchmark configuration is used to set the experimental spatial resolution required to quantify the concentration probability density functions (PDFs) of scalar mixtures in fluids. The diffusive coalescence of two nearby lamellae, the mechanism by which scalar mixtures ultimately reach uniformity, is shown to induce a complex transient evolution of the concentration PDFs.

JFM classification

Flow Control: Flow Control Mixing: Mixing Flow Control: Mixing enhancement
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 838 , 10 March 2018 , R3
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Copyright
© 2018 Cambridge University Press 

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References

Allègre, C. J. & Turcotte, D. L. 1986 Implications of a two-component marble-cake mantle. Nature 323, 123–127.Google Scholar
Axelrod, D., Koppel, D. E., Schlessinger, J., Elson, E. & Webb, W. W. 1976 Mobility measurement by analysis of fluorescence photobleaching recovery kinetics. Biophys. J. 16, 1055–1069.Google Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in a turbulent fluid. part 1. general discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.Google Scholar
Dentz, M., Leborgne, T., Englert, A. & Bijeljic, B. 2011 Mixing, spreading and reaction in heterogeneous media: A brief review. J. Contam. Hydrol. 120‐121, 1–17.CrossRefGoogle ScholarPubMed
Duplat, J. & Villermaux, E. 2003 Mixing by random stirring in confined mixtures. J. Fluid Mech. 617, 51–86.Google Scholar
Falkovich, G., Gawedzki, K. & Vergassola, M. 2001 Particles and fields in fluid turbulence. Rev. Mod. Phys. 73 (4), 913–975.Google Scholar
Fourier, J. 1822 Théorie Analytique de la Chaleur. Firmin Didot.Google Scholar
Kalda, J. 2000 Simple model of intermittent passive scalar turbulence. Phys. Rev. Lett. 84 (3), 471–474.CrossRefGoogle ScholarPubMed
Le Borgne, T., Dentz, M. & Villermaux, E. 2015 The lamellar description of mixing in porous media. J. Fluid Mech. 770, 458–498.CrossRefGoogle Scholar
Meunier, P., Huck, P., Nobili, C. & Villermaux, E. 2015 Transport and diffusion around a homoclinic point. In Chaos, Complexity and Transport: Proceedings of the CCT 15, pp. 152–162. World Scientific.Google Scholar
Meunier, P. & Villermaux, E. 2003 How vortices mix. J. Fluid Mech. 476, 213–222.CrossRefGoogle Scholar
Meunier, P. & Villermaux, E. 2010 The diffusive strip method for scalar mixing in two dimensions. J. Fluid Mech. 662, 134–172.Google Scholar
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.Google Scholar
Ranz, W. E. 1979 Applications of a stretch model diffusion, and reaction in laminar and turbulent flows. AIChE J. 25 (1), 41–47.CrossRefGoogle Scholar
Rhines, P. B. & Young, W. R. 1983 How rapidly is a passive scalar mixed within closed streamlines? J. Fluid Mech. 133, 133–145.Google Scholar
Shraiman, B. I. & Siggia, E. D. 2000 Scalar turbulence. Nature 405, 639–646.Google Scholar
Souzy, M., Lhuissier, H., Villermaux, E. & Metzger, B. 2017 Stretching and mixing in sheared particulate suspensions. J. Fluid Mech. 812, 611–635.Google Scholar
Villermaux, E. 2012 Mixing by porous media. C. R. Méc. 340, 933–943.Google Scholar
Villermaux, E. & Duplat, J. 2003 Mixing as an aggregation process. Phys. Rev. Lett. 91 (18), 184501.CrossRefGoogle ScholarPubMed
Villermaux, E. & Duplat, J. 2006 Coarse grained scale of turbulent mixtures. Phys. Rev. Lett. 97, 144506.Google Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.Google Scholar

Souzy et al. supplementary movie 1

Movie of a lamella, obtained by photo-bleaching, advected by the laminar shear flow at Pe=20

Download Souzy et al. supplementary movie 1(Video)
Video 221.4 KB

Souzy et al. supplementary movie 2

Coalescence between two adjacent lamellae: evolution of the concentration profiles and concentration distributions.

Download Souzy et al. supplementary movie 2(Video)
Video 250.1 KB