[Le mélange est un processus d'agrégation]
With the aid of several demonstration experiments, it is shown how a stirred scalar mixture relaxes towards uniformity through an aggregation process. The elementary bricks are stretched sheets whose rates of diffusive smoothing and coalescence build up the overall mixture concentration distribution. The cases studied, in particular, include mixtures in two and three dimensions, with different stirring protocols, which all lead to a family of concentration distributions stable by self-convolution.
Des expériences démonstratives suggèrent qu'un mélange scalaire agité relaxe vers l'uniformité à travers un processus d'agrégation. Les briques élémentaires sont des feuillets étirés qui se diluent dans le milieu en même temps qu'ils s'agrègent, construisant par là l'ensemble de la distribution de concentration de la mixture. Les cas considérés en particulier sont des mélanges en deux et trois dimensions, agités par des protocles très différents et qui pourtant donnent naissance aux mêmes distributions de concentration, stables par auto-convolution.
Accepté le :
Publié le :
Mots-clés : Turbulence, Mélange, Agitation, Diffusion, Agrégation
Emmanuel Villermaux 1 ; Jérôme Duplat 2
@article{CRMECA_2003__331_7_515_0,
author = {Emmanuel Villermaux and J\'er\^ome Duplat},
title = {Mixing is an aggregation process},
journal = {Comptes Rendus. M\'ecanique},
pages = {515--523},
publisher = {Elsevier},
volume = {331},
number = {7},
year = {2003},
doi = {10.1016/S1631-0721(03)00110-4},
language = {en},
}
Emmanuel Villermaux; Jérôme Duplat. Mixing is an aggregation process. Comptes Rendus. Mécanique, Volume 331 (2003) no. 7, pp. 515-523. doi : 10.1016/S1631-0721(03)00110-4. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00110-4/
[1] Théorie analytique de la chaleur, F. Didot, Père & Fils, Paris, 1822
[2] Boundary Layer Theory, McGraw-Hill, New York, 1987
[3] Material-element deformation in isotropic turbulence, J. Fluid Mech., Volume 220 (1990), pp. 427-458
[4] Persistency of material element deformation in isotropic flows and growth rate of lines and surfaces, Eur. Phys. J. B, Volume 18 (2000), pp. 353-361
[5] Turbulence, fractals and mixing (H. Chaté; E. Villermaux; J.M. Chomaz, eds.), Mixing: Chaos and Turbulence, Kluwer Academic/Plenum, New York, 1999
[6] 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
[7] 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
[8] The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press, 1989
[9] Mixing in coaxial jets, J. Fluid Mech., Volume 425 (2000), pp. 161-185
[10] The effect of homogeneous turbulence on material lines and surfaces, Proc. Roy. Soc. A, Volume 213 (1952), pp. 349-366
[11] An Introduction to Probability Theory and its Applications, Wiley, 1970
[12] Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen, Z. Phys. Chem., Volume 92 (1917), pp. 129-168
[13] Dispersed phase mixing: I. Theory and effect in simple reactors, AIChE J., Volume 9 (1963) no. 2, pp. 175-181
[14] Exponential tails and random advection, Phys. Rev. Lett., Volume 66 (1991) no. 23, pp. 2984-2987
[15] Pdf methods for turbulent reacting flows, Prog. Energy Combust. Sci., Volume 11 (1985), pp. 119-192
[16] Scaling of hard thermal turbulence in Rayleigh–Bénard convection, J. Fluid Mech., Volume 204 (1989), pp. 1-30
[17] Probability distributions, conditional dissipation, and transport of passive temperature fluctuations in grid-generated turbulence, Phys. Fluids A, Volume 4 (1992) no. 10, pp. 2292-2307
[18] Exponential tails and skewness of density-gradient probability density functions in stably stratified turbulence, J. Fluid Mech., Volume 244 (1992), pp. 547-566
[19] Mixing of a passive scalar in magnetically forced two-dimensional turbulence, Phys. Fluids, Volume 9 (1997) no. 7, pp. 2061-2080
[20] Experimental observation of Batchelor dispersion of passive tracers, Phys. Rev. Lett., Volume 85 (2000) no. 17, pp. 3636-3639
[21] Turbulent mixing of a passive scalar, Phys. Fluids, Volume 6 (1994) no. 5, pp. 1820-1837
[22] Short circuits in the Corrsin–Oboukhov cascade, Phys. Fluids, Volume 13 (2001) no. 1, pp. 284-289
[23] Efficient mixing at low Reynolds numbers using polymer additives, Nature, Volume 410 (2001), pp. 905-908
[24] Lagrangian path integrals and fluctuations in random flows, Phys. Rev. E, Volume 49 (1994), pp. 2912-2927
[25] Scalar turbulence, Nature, Volume 405 (2000), pp. 639-646
[26] Particles and fields in fluid turbulence, Rev. Mod. Phys., Volume 73 (2001) no. 4, pp. 913-975
[27] Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalr problem, Phys. Rev. E, Volume 60 (1999) no. 4, pp. 4164-4174
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