Comptes Rendus
Mixing by porous media
Comptes Rendus. Mécanique, Volume 340 (2012) no. 11-12, pp. 933-943.

This article reports on a set of simple remarks to understand the fine structure of a scalar mixture advected in a random, interconnected, frozen network of paths, i.e. a porous medium. We describe in particular the relevant scales of the mixture, the kinetics of their evolution, the nature of their interaction, and the scaling laws describing the coarsening process of the concentration field as it progresses through the medium, including its concentration distribution.

Published online:
DOI: 10.1016/j.crme.2012.10.042
Keywords: Porous media, Mixing, Statistical distributions

Emmanuel Villermaux 1

1 Aix Marseille Université, IRPHE, 13384 Marseille cedex 13, France
@article{CRMECA_2012__340_11-12_933_0,
     author = {Emmanuel Villermaux},
     title = {Mixing by porous media},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {933--943},
     publisher = {Elsevier},
     volume = {340},
     number = {11-12},
     year = {2012},
     doi = {10.1016/j.crme.2012.10.042},
     language = {en},
}
TY  - JOUR
AU  - Emmanuel Villermaux
TI  - Mixing by porous media
JO  - Comptes Rendus. Mécanique
PY  - 2012
SP  - 933
EP  - 943
VL  - 340
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crme.2012.10.042
LA  - en
ID  - CRMECA_2012__340_11-12_933_0
ER  - 
%0 Journal Article
%A Emmanuel Villermaux
%T Mixing by porous media
%J Comptes Rendus. Mécanique
%D 2012
%P 933-943
%V 340
%N 11-12
%I Elsevier
%R 10.1016/j.crme.2012.10.042
%G en
%F CRMECA_2012__340_11-12_933_0
Emmanuel Villermaux. Mixing by porous media. Comptes Rendus. Mécanique, Volume 340 (2012) no. 11-12, pp. 933-943. doi : 10.1016/j.crme.2012.10.042. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.10.042/

[1] T. Le Borgne; M. Dentz; J. Carrera Lagrangian statistical model for transport in highly heterogeneous velocity fields, Phys. Rev. Lett., Volume 101 (2008), p. 090601

[2] T. Le Borgne; M. Dentz; D. Bolster; J. Carrera; J.R. de Dreuzy; P. Davy Non-Fickian mixing: Temporal evolution of the scalar dissipation rate in heterogeneous porous media, Adv. Water Resour., Volume 33 (2010), pp. 1468-1475

[3] J. Bear Dynamics of Fluids in Porous Media, Elsevier Publishing Company, Inc., New York, 1972

[4] G.F. Carrier; F.E. Fendell; F.E. Marble The effect of strain rate on diffusion flames, SIAM J. Appl. Math., Volume 28 (1975) no. 2, pp. 463-500

[5] W.E. Ranz Application of a stretch model to mixing, diffusion and reaction in laminar and turbulent flows, AIChE J., Volume 25 (1979) no. 1, pp. 41-47

[6] P.B. Rhines; W.R. Young How rapidly is a passive scalar mixed within closed streamlines, J. Fluid Mech., Volume 133 (1983), pp. 133-145

[7] E. Villermaux; H. Rehab Mixing in coaxial jets, J. Fluid Mech., Volume 425 (2000), pp. 161-185

[8] P. Meunier; E. Villermaux How vortices mix, J. Fluid Mech., Volume 476 (2003), pp. 213-222

[9] J. Duplat; E. Villermaux Mixing by random stirring in confined mixtures, J. Fluid Mech., Volume 617 (2008), pp. 51-86

[10] P. Meunier; E. Villermaux The diffusive strip method for scalar mixing in two dimensions, J. Fluid Mech., Volume 662 (2010), pp. 134-172

[11] J.M. Ottino The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press, 1989

[12] K.A. Buch; W.J.A. Dahm Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 1. Sc ≫ 1, J. Fluid Mech., Volume 317 (1996), pp. 21-71

[13] G.K. Batchelor 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., Volume 5 (1959), pp. 113-133

[14] F.E. Marble Mixing, diffusion and chemical reaction of liquids in a vortex field (M. Moreau; P. Turq, eds.), Chemical Reactivity in Liquids: Fundamental Aspects, Plenum Press, 1988

[15] G.I. Taylor Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. London A, Volume 219 (1953), pp. 186-203

[16] G.I. Taylor Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion, Proc. R. Soc. London A, Volume 225 (1954), pp. 473-477

[17] R. Aris On the dispersion of a solute in a fluid flow through a tube, Proc. R. Soc. London A, Volume 235 (1956) no. 1200, pp. 67-77

[18] P.V. Danckwerts Continuous flow systems, Chem. Eng. Sci., Volume 2 (1953) no. 1, pp. 1-13

[19] P.G. de Gennes Hydrodynamic dispersion in unsaturated porous media, J. Fluid Mech., Volume 136 (1983), pp. 189-200

[20] J.P. Bouchaud; A. Georges A simple model for hydrodynamic dispersion, C. R. Acad. Sci., Paris (Serie II), Volume 307 (1988), pp. 1431-1436

[21] J.J. Fried; M. Combarnous Dispersion in porous media, Adv. Hydrosci., Volume 7 (1971), pp. 169-283

[22] P. Renard; G. de Marsily Calculating equivalent permeability: a review, Adv. Water Resour., Volume 20 (1997) no. 5–6, pp. 253-278

[23] D. Stauffer Introduction to Percolation Theory, Taylor & Francis, London and Philadelphia, 1985

[24] E. Villermaux; J. Duplat Coarse grained scale of turbulent mixtures, Phys. Rev. Lett., Volume 97 (2006), p. 144506

[25] E. Villermaux; J. Duplat Mixing as an aggregation process, Phys. Rev. Lett., Volume 91 (2003) no. 18, p. 184501

[26] M. Abramowitz; I.A. Stegun Handbook of Mathematical Functions, Dover Publications, Inc., New York, 1964

[27] A. Erdélyi; W. Magnus; F. Oberhettinger; F.G. Tricomi Tables of Integral Transforms, vol. 1, McGraw–Hill, Inc., New York, 1954

[28] M. Planck On the law of distribution of energy in the normal spectrum, Ann. Phys., Volume 4 (1901) no. 3, pp. 553-563

[29] Y.B. Zeldovich The asymptotic law of heat transfer at small velocities in the finite domain problem, Zh. Eksp. Teor. Fiz., Volume 7 (1937) no. 12, pp. 1466-1468

[30] J.M.P.Q. Delgado Longitudinal and transverse dispersion in porous media, Chem. Eng. Res. Des., Volume 85 (2007) no. A9, pp. 1245-1252

Cited by Sources:

Comments - Policy