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Mixing lamellae in a shear flow

  • Mathieu Souzy (a1), Imen Zaier (a2), Henri Lhuissier (a2), Tanguy Le Borgne (a1) and Bloen Metzger (a2)...

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.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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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

 Video (221 KB)
221 KB

Souzy et al. supplementary movie 2
Coalescence between two adjacent lamellae: evolution of the concentration profiles and concentration distributions.

 Video (250 KB)
250 KB


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