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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: [email protected]
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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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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