Evolution of the volumetric interfacial area in two-phase mixtures

Daniel Lhuillier

doi:10.1016/j.crme.2003.12.004

Evolution of the volumetric interfacial area in two-phase mixtures
[Evolution de l'aire interfaciale volumique dans les mélanges diphasiques]

Présenté par : Évariste Sanchez-Palencia

Daniel Lhuillier ¹

¹ Laboratoire de modélisation en mécanique, UPMC et CNRS, case 162, 4, place Jussieu, 75252 Paris cedex 05, France

Comptes Rendus. Mécanique, Volume 332 (2004) no. 2, pp. 103-108.

Résumé
Abstract

Nous cherchons à décrire l'évolution temporelle de la densité d'interfaces dans un mélange diphasique. L'accent est mis sur les effets de la compressibilité, de la dilatabilité et des changements de phase. Deux chemins complémentaires sont suivis : le premier, assez intuitif, est basé sur des résultats concernant les mélanges dilués, résultats qui sont ensuite interpolés à toute concentration ; le second, plus systématique, est basé sur la moyenne statistique de l'équation qui régit l'évolution temporelle d'un élément d'interface.

We investigate the time evolution of the density of interfaces in a two-phase mixture, with particular emphasis on the role of compressibility, dilatability and phase transitions. Two different and complementary routes are considered: a rather intuitive one based on exact results for dilute mixtures which are then interpolated to all concentrations, and a more systematic approach based on the statistical average of the exact transport equation for elementary pieces of interfaces.

Reçu le : 2003-07-10
Accepté le : 2003-12-02
Publié le : 2004-01-29

DOI : 10.1016/j.crme.2003.12.004

Keywords: Rheology, Interfacial area, Transport equation, Two-phase mixtures
Mot clés : Rhéologie, Aire interfaciale, Équation de transport, Mélanges diphasiques

Affiliations des auteurs :

Daniel Lhuillier ¹

¹ Laboratoire de modélisation en mécanique, UPMC et CNRS, case 162, 4, place Jussieu, 75252 Paris cedex 05, France

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     title = {Evolution of the volumetric interfacial area in two-phase mixtures},
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     pages = {103--108},
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Daniel Lhuillier. Evolution of the volumetric interfacial area in two-phase mixtures. Comptes Rendus. Mécanique, Volume 332 (2004) no. 2, pp. 103-108. doi : 10.1016/j.crme.2003.12.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.12.004/

Bibliographie
Cité par

[1] M. Ishii Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris, 1975 (p. 179)

[2] J.M. Delhaye Some issues related to the modelling of interfacial areas in gas-liquid flows II. Modelling the source terms for dispersed flows, C. R. Acad. Sci. Paris, Ser. IIb, Volume 329 (2001), pp. 473-486

[3] F.E. Marble, J.E. Broadwell, The coherent flame model for turbulent chemical reactions, Project Squid Tech. Rep. TRW-9-PU, 1977

[4] S.M. Candel; T. Poinsot Flame stretch and the balance equation for the flame surface area, Combust. Sci. Tech., Volume 70 (1990), pp. 1-15

[5] D. Lhuillier Dynamics of interfaces and rheology of immiscible liquid–liquid mixtures, C. R. Mécanique, Volume 331 (2003), pp. 113-118

[6] C.M. Marle On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media, Int. J. Engrg. Sci., Volume 20 (1982), pp. 643-662 (see Appendix)

[7] D.A. Drew Evolution of geometric statistics, SIAM J. Appl. Math., Volume 50 (1990), pp. 649-666

[8] D. Lhuillier A mean-field description of two-phase flows with phase changes, Int. J. Multiphase Flow, Volume 29 (2003), pp. 511-525

[9] N. Wagner; H.C. Öttinger; B. Edwards Generalized Doi–Ohta model for multiphase flows developed by GENERIC, AIChE J., Volume 45 (1999), pp. 1169-1181

[10] M. Doi; T. Ohta Dynamics and rheology of complex interfaces, J. Chem. Phys., Volume 95 (1991), pp. 1242-1248

[11] E.D. Wetzel; C.L. Tucker Area tensors for modelling microstructure during laminar liquid–liquid mixing, Int. J. Multiphase Flow, Volume 25 (1999), pp. 35-61

[12] J.M. Delhaye Jump conditions and entropy sources in two-phase systems. Local instant formulation, Int. J. Multiphase Flow, Volume 1 (1974), pp. 395-409

[13] H.M. Lee; O.O. Park Rheology and dynamics of immiscible polymer blends, J. Rheology, Volume 38 (1994), pp. 1405-1425

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