Mixing is an aggregation process

Emmanuel Villermaux; Jérôme Duplat

doi:10.1016/S1631-0721(03)00110-4

Mixing is an aggregation process
[Le mélange est un processus d'agrégation]

Présenté par : Paul Clavin

Emmanuel Villermaux ¹ ; Jérôme Duplat ²

¹ Université de Provence & institut universitaire de France, IRPHE, 13384 Marseille cedex 13, France
² Université de Provence, IUSTI, 13453 Marseille cedex 13, France

Comptes Rendus. Mécanique, Volume 331 (2003) no. 7, pp. 515-523.

Résumé
Abstract

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.

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.

Reçu le : 2003-02-24
Accepté le : 2003-04-08
Publié le : 2003-07-01

DOI : 10.1016/S1631-0721(03)00110-4

Keywords: Turbulence, Mixing, Stirring, Diffusion, Aggregation
Mot clés : Turbulence, Mélange, Agitation, Diffusion, Agrégation

Affiliations des auteurs :

Emmanuel Villermaux ¹ ; Jérôme Duplat ²

¹ Université de Provence & institut universitaire de France, IRPHE, 13384 Marseille cedex 13, France
² Université de Provence, IUSTI, 13453 Marseille cedex 13, France

@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},
}

TY  - JOUR
AU  - Emmanuel Villermaux
AU  - Jérôme Duplat
TI  - Mixing is an aggregation process
JO  - Comptes Rendus. Mécanique
PY  - 2003
SP  - 515
EP  - 523
VL  - 331
IS  - 7
PB  - Elsevier
DO  - 10.1016/S1631-0721(03)00110-4
LA  - en
ID  - CRMECA_2003__331_7_515_0
ER  -

%0 Journal Article
%A Emmanuel Villermaux
%A Jérôme Duplat
%T Mixing is an aggregation process
%J Comptes Rendus. Mécanique
%D 2003
%P 515-523
%V 331
%N 7
%I Elsevier
%R 10.1016/S1631-0721(03)00110-4
%G en
%F CRMECA_2003__331_7_515_0

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/

Bibliographie
Cité par

[1] J. Fourier Théorie analytique de la chaleur, F. Didot, Père & Fils, Paris, 1822

[2] H. Schlichting Boundary Layer Theory, McGraw-Hill, New York, 1987

[3] S.S. Girimaji; S.B. Pope Material-element deformation in isotropic turbulence, J. Fluid Mech., Volume 220 (1990), pp. 427-458

[4] J. Duplat; E. Villermaux 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] P.E. Dimotakis; H.J. Catrakis Turbulence, fractals and mixing (H. Chaté; E. Villermaux; J.M. Chomaz, eds.), Mixing: Chaos and Turbulence, Kluwer Academic/Plenum, New York, 1999

[6] 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

[7] 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

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

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

[10] G.K. Batchelor The effect of homogeneous turbulence on material lines and surfaces, Proc. Roy. Soc. A, Volume 213 (1952), pp. 349-366

[11] W. Feller An Introduction to Probability Theory and its Applications, Wiley, 1970

[12] M. von Smoluchowski Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen, Z. Phys. Chem., Volume 92 (1917), pp. 129-168

[13] R.L. Curl Dispersed phase mixing: I. Theory and effect in simple reactors, AIChE J., Volume 9 (1963) no. 2, pp. 175-181

[14] A. Pumir; B.I. Shraiman; E.D. Siggia Exponential tails and random advection, Phys. Rev. Lett., Volume 66 (1991) no. 23, pp. 2984-2987

[15] S.B. Pope Pdf methods for turbulent reacting flows, Prog. Energy Combust. Sci., Volume 11 (1985), pp. 119-192

[16] B. Castaing; G. Gunaratne; F. Heslot; L. Kadanoff; A. Libchaber; S. Thomae; X.Z. Wu; S. Zaleski; G. Zanetti Scaling of hard thermal turbulence in Rayleigh–Bénard convection, J. Fluid Mech., Volume 204 (1989), pp. 1-30

[17] X. Jayesh; Z. Warhaft 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] S.T. Thoroddsen; C.W. Van Atta Exponential tails and skewness of density-gradient probability density functions in stably stratified turbulence, J. Fluid Mech., Volume 244 (1992), pp. 547-566

[19] B.S. Williams; D. Marteau; J.P. Gollub Mixing of a passive scalar in magnetically forced two-dimensional turbulence, Phys. Fluids, Volume 9 (1997) no. 7, pp. 2061-2080

[20] M.C. Jullien; P. Castiglione; P. Tabeling Experimental observation of Batchelor dispersion of passive tracers, Phys. Rev. Lett., Volume 85 (2000) no. 17, pp. 3636-3639

[21] M. Holzer; E.D. Siggia Turbulent mixing of a passive scalar, Phys. Fluids, Volume 6 (1994) no. 5, pp. 1820-1837

[22] E. Villermaux; C. Innocenti; J. Duplat Short circuits in the Corrsin–Oboukhov cascade, Phys. Fluids, Volume 13 (2001) no. 1, pp. 284-289

[23] A. Groisman; V. Steinberg Efficient mixing at low Reynolds numbers using polymer additives, Nature, Volume 410 (2001), pp. 905-908

[24] B.I. Shraiman; E.D. Siggia Lagrangian path integrals and fluctuations in random flows, Phys. Rev. E, Volume 49 (1994), pp. 2912-2927

[25] B.I. Shraiman; E.D. Siggia Scalar turbulence, Nature, Volume 405 (2000), pp. 639-646

[26] G. Falkovich; K. Gawedzki; M. Vergassola Particles and fields in fluid turbulence, Rev. Mod. Phys., Volume 73 (2001) no. 4, pp. 913-975

[27] E. Balkovsky; A. Fouxon 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

Cité par Sources :

Commentaires - Politique