Scalar gradients in stirred mixtures and the deconstruction of random fields
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. © 2017 Cambridge University Press.
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Cambridge University Press
2017-02-10
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Subjects: | Mixing, Porous media, Turbulent mixing, |
Online Access: | http://hdl.handle.net/10261/146990 http://dx.doi.org/10.13039/501100000781 |
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dig-idaea-es-10261-1469902018-05-18T10:16:19Z Scalar gradients in stirred mixtures and the deconstruction of random fields Le Borgne, Tanguy Huck, Peter D. Dentz, Marco Villermaux, Emmanuel European Research Council Mixing Porous media Turbulent mixing 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. © 2017 Cambridge University Press. TLB acknowledges the support of the European Research Council (ERC) through the project ReactiveFronts (648377) and of the Agence Nationale de la Recherche (ANR) through the project Subsurface mixing and reaction (ANR-14-CE04-0003). MD acknowledges the support of the European Research Council (ERC) through the project MHetScale (617511). EV acknowledges the Agence Nationale de la Recherche (ANR) for funding of the ANR-DFG grant TurbMix (ANR-14-CE35-0031-01). Peer reviewed 2017-03-20T09:36:27Z 2017-03-20T09:36:27Z 2017-02-10 artículo http://purl.org/coar/resource_type/c_6501 Journal of Fluid Mechanics 812: 578-610 (2017) http://hdl.handle.net/10261/146990 10.1017/jfm.2016.799 http://dx.doi.org/10.13039/501100000781 en #PLACEHOLDER_PARENT_METADATA_VALUE# info:eu-repo/grantAgreement/EC/FP7/617511 Postprint 10.1017/jfm.2016.799 Sí open Cambridge University Press |
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Mixing Porous media Turbulent mixing Mixing Porous media Turbulent mixing Le Borgne, Tanguy Huck, Peter D. Dentz, Marco Villermaux, Emmanuel Scalar gradients in stirred mixtures and the deconstruction of random fields |
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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. © 2017 Cambridge University Press. |
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European Research Council |
author_facet |
European Research Council Le Borgne, Tanguy Huck, Peter D. Dentz, Marco Villermaux, Emmanuel |
format |
artículo |
topic_facet |
Mixing Porous media Turbulent mixing |
author |
Le Borgne, Tanguy Huck, Peter D. Dentz, Marco Villermaux, Emmanuel |
author_sort |
Le Borgne, Tanguy |
title |
Scalar gradients in stirred mixtures and the deconstruction of random fields |
title_short |
Scalar gradients in stirred mixtures and the deconstruction of random fields |
title_full |
Scalar gradients in stirred mixtures and the deconstruction of random fields |
title_fullStr |
Scalar gradients in stirred mixtures and the deconstruction of random fields |
title_full_unstemmed |
Scalar gradients in stirred mixtures and the deconstruction of random fields |
title_sort |
scalar gradients in stirred mixtures and the deconstruction of random fields |
publisher |
Cambridge University Press |
publishDate |
2017-02-10 |
url |
http://hdl.handle.net/10261/146990 http://dx.doi.org/10.13039/501100000781 |
work_keys_str_mv |
AT leborgnetanguy scalargradientsinstirredmixturesandthedeconstructionofrandomfields AT huckpeterd scalargradientsinstirredmixturesandthedeconstructionofrandomfields AT dentzmarco scalargradientsinstirredmixturesandthedeconstructionofrandomfields AT villermauxemmanuel scalargradientsinstirredmixturesandthedeconstructionofrandomfields |
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1777669286652805120 |