User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

Stability analysis of Couette flows of spatially inhomogeneous complex fluids

Primary tabs

Varsakelis, Christos [UCL] Papalexandris, Miltiadis [UCL]

In this paper, the stability of unidirectional Couette flows of a spatially inhomogeneous complex fluid is investigated via the means of a linear stability analysis. The employment of a classical normal-mode analysis results in a fourth-order polynomial eigenvalue problem that is solved numerically via a Chebyshev polynomial method. The results of this study suggest that the flow of interest is unconditionally unstable but nevertheless the growth rates remain small so that the observability of the instability requires a very large time window. The observed instability manifests itself through the formation of downstream-propagating concentration waves that, due to their location at the bottom of the channel, closely resemble a series of superposed, high-concentration piles.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès interdit
Publication date 2015
Language Anglais
Journal information "Proceedings of the Royal society of London. Mathematics, physical sciences and engineering" - Vol. 471, p. 20150529 (21 octobre 2015)
Peer reviewed yes
Publisher Royal Society Publishing
issn 1364-5021
e-issn 1471-2946
Publication status Publié
Affiliation UCL - SST/IMMC/TFL - Thermodynamics and fluid mechanics
Links
  1. VARSAKELIS C., PAPALEXANDRIS M. V., Low-Mach-number asymptotics for two-phase flows of granular materials, 10.1017/s0022112010005173
  2. Grmela Miroslav, Weakly nonlocal hydrodynamics, 10.1103/physreve.47.351
  3. Bdzil J. B., Menikoff R., Son S. F., Kapila A. K., Stewart D. S., Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues, 10.1063/1.869887
  4. Korteweg, Arch. Néerl. Sci. Exactes Nat. Ser. II, 6, 1 (1901)
  5. Savage Stuart B., Gravity flow of cohesionless granular materials in chutes and channels, 10.1017/s0022112079000525
  6. Stickel Jonathan J., Powell Robert L., FLUID MECHANICS AND RHEOLOGY OF DENSE SUSPENSIONS, 10.1146/annurev.fluid.36.050802.122132
  7. Liu Andrea J., Nagel Sidney R., 10.1038/23819
  8. Varsakelis Christos, Papalexandris Miltiadis V., Existence of solutions to a continuum model for hydrostatics of fluid-saturated granular materials, 10.1016/j.aml.2013.11.009
  9. Nakano Naoto, Tani Atusi, Navier’s Slip Problem for Motion of Inhomogeneous Incompressible Fluid-like Bodies, 10.1007/s00021-009-0003-4
  10. , On dense granular flows, 10.1140/epje/i2003-10153-0
  11. Varsakelis C., Papalexandris M.V., The equilibrium limit of a constitutive model for two-phase granular mixtures and its numerical approximation, 10.1016/j.jcp.2010.02.005
  12. Málek J., Rajagopal K.R., On the modeling of inhomogeneous incompressible fluid-like bodies, 10.1016/j.mechmat.2005.05.020
  13. Ladyzhenskaya, Mathematical theory of viscous, incompressible flow (1987)
  14. Drazin, Hydrodynamic stability (2011)
  15. Maxima.sourceforge.net. 2011 Maxima, a computer algebra system, version 5.25.1. See http://www.maxima.sourceforge.net .
  16. Lin C. C., Some mathematical problems in the theory of the stability of parallel flows, 10.1017/s0022112061001025
  17. Weideman J. A. C., Reddy S. C., A MATLAB differentiation matrix suite, 10.1145/365723.365727
  18. Driscoll, Chebfun guide (2014)
  19. Yih Chia-Shun, Instability due to viscosity stratification, 10.1017/s0022112067000357
  20. Hickox Charles E., Instability due to Viscosity and Density Stratification in Axisymmetric Pipe Flow, 10.1063/1.1693422
  21. ERN PATRICIA, CHARRU FRANÇOIS, LUCHINI PAOLO, Stability analysis of a shear flow with strongly stratified viscosity, 10.1017/s0022112003006372
  22. Pramanik Satyajit, Mishra Manoranjan, Linear stability analysis of Korteweg stresses effect on miscible viscous fingering in porous media, 10.1063/1.4813403
  23. Abarbanel Henry D. I., Holm Darryl D., Marsden Jerrold E., Ratiu Tudor, Richardson Number Criterion for the Nonlinear Stability of Three-Dimensional Stratified Flow, 10.1103/physrevlett.52.2352
  24. Goodman M.A., Cowin S.C., A continuum theory for granular materials, 10.1007/bf00284326
  25. Kirchner N. P., Thermodynamically consistent modelling of abrasive granular materials. I Non-equilibrium theory, 10.1098/rspa.2002.0963
  26. PAPALEXANDRIS MILTIADIS V., A two-phase model for compressible granular flows based on the theory of irreversible processes, 10.1017/s0022112004000874
  27. Ván Peter, Berezovski Arkadi, Engelbrecht Jüri, Internal Variables and Dynamic Degrees of Freedom, 10.1515/jnetdy.2008.010
  28. Passman Stephen L., Nunziato Jace W., Bailey Paul B., Reed Kenneth W., Shearing motion of a fluid‐saturated granular material, 10.1122/1.549894
  29. Wang Yongqi, Hutter Kolumban, A constitutive model of multiphase mixtures and its application in shearing flows of saturated solid-fluid mixtures, 10.1007/s100350050023
  30. Massoudi Mehrdad, Boyle Edward J., A continuum–kinetic theory approach to the rapid flow of granular materials: the effects of volume fraction gradient, 10.1016/s0020-7462(00)00027-5
Bibliographic reference Varsakelis, Christos ; Papalexandris, Miltiadis. Stability analysis of Couette flows of spatially inhomogeneous complex fluids. In: Proceedings of the Royal society of London. Mathematics, physical sciences and engineering, Vol. 471, p. 20150529 (21 octobre 2015)
Permanent URL http://hdl.handle.net/2078.1/165257