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.
Emmanuel Villermaux 1
@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}, }
Emmanuel Villermaux. Mixing by porous media. Comptes Rendus. Mécanique, Out of Equilibrium Dynamics, 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] Lagrangian statistical model for transport in highly heterogeneous velocity fields, Phys. Rev. Lett., Volume 101 (2008), p. 090601
[2] Non-Fickian mixing: Temporal evolution of the scalar dissipation rate in heterogeneous porous media, Adv. Water Resour., Volume 33 (2010), pp. 1468-1475
[3] Dynamics of Fluids in Porous Media, Elsevier Publishing Company, Inc., New York, 1972
[4] The effect of strain rate on diffusion flames, SIAM J. Appl. Math., Volume 28 (1975) no. 2, pp. 463-500
[5] 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] How rapidly is a passive scalar mixed within closed streamlines, J. Fluid Mech., Volume 133 (1983), pp. 133-145
[7] Mixing in coaxial jets, J. Fluid Mech., Volume 425 (2000), pp. 161-185
[8] How vortices mix, J. Fluid Mech., Volume 476 (2003), pp. 213-222
[9] Mixing by random stirring in confined mixtures, J. Fluid Mech., Volume 617 (2008), pp. 51-86
[10] The diffusive strip method for scalar mixing in two dimensions, J. Fluid Mech., Volume 662 (2010), pp. 134-172
[11] The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press, 1989
[12] 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] 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] 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] Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. London A, Volume 219 (1953), pp. 186-203
[16] 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] 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] Continuous flow systems, Chem. Eng. Sci., Volume 2 (1953) no. 1, pp. 1-13
[19] Hydrodynamic dispersion in unsaturated porous media, J. Fluid Mech., Volume 136 (1983), pp. 189-200
[20] A simple model for hydrodynamic dispersion, C. R. Acad. Sci., Paris (Serie II), Volume 307 (1988), pp. 1431-1436
[21] Dispersion in porous media, Adv. Hydrosci., Volume 7 (1971), pp. 169-283
[22] Calculating equivalent permeability: a review, Adv. Water Resour., Volume 20 (1997) no. 5–6, pp. 253-278
[23] Introduction to Percolation Theory, Taylor & Francis, London and Philadelphia, 1985
[24] Coarse grained scale of turbulent mixtures, Phys. Rev. Lett., Volume 97 (2006), p. 144506
[25] Mixing as an aggregation process, Phys. Rev. Lett., Volume 91 (2003) no. 18, p. 184501
[26] Handbook of Mathematical Functions, Dover Publications, Inc., New York, 1964
[27] Tables of Integral Transforms, vol. 1, McGraw–Hill, Inc., New York, 1954
[28] On the law of distribution of energy in the normal spectrum, Ann. Phys., Volume 4 (1901) no. 3, pp. 553-563
[29] 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] Longitudinal and transverse dispersion in porous media, Chem. Eng. Res. Des., Volume 85 (2007) no. A9, pp. 1245-1252
Cited by Sources:
Comments - Policy