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Scalar gradients in stirred mixtures and the deconstruction of random fields

Published online by Cambridge University Press:  05 January 2017

T. Le Borgne ,
P. D. Huck ,
M. Dentz  and
E. Villermaux
T. Le Borgne*
Affiliation:
Université de Rennes 1, CNRS, Geosciences Rennes UMR6118, 35042 Rennes, France
P. D. Huck
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France
M. Dentz
Affiliation:
IDAEA-CSIC, Barcelona, Spain
E. Villermaux
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France Institut Universitaire de France, Paris, France
*
†Email address for correspondence: tanguy.le-borgne@univ-rennes1.fr
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Abstract

A general theory for predicting the distribution of scalar gradients (or concentration differences) in heterogeneous flows is proposed. The evolution of scalar fields is quantified from the analysis of the evolution of elementary lamellar structures, which naturally form under the stretching action of the flows. Spatial correlations in scalar fields, and concentration gradients, hence develop through diffusive aggregation of stretched lamellae. Concentration levels at neighbouring spatial locations result from a history of lamella aggregation, which is partly common to the two locations. Concentration differences eliminate this common part, and thus depend only on lamellae that have aggregated independently. Using this principle, we propose a theory which envisions concentration increments as the result of a deconstruction of the basic lamella assemblage. This framework provides analytical expressions for concentration increment probability density functions (PDFs) over any spatial increments for a range of flow systems, including turbulent flows and low-Reynolds-number porous media flows, for confined and dispersing mixtures. Through this deconstruction principle, scalar increment distributions reveal the elementary stretching and aggregation mechanisms building scalar fields.

JFM classification

Mixing: Mixing Low-Reynolds-number flows: Porous media Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 578 - 610
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Copyright
© 2017 Cambridge University Press 

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