nach oben

Journal of Engineering Mathematics

Erschienen in:

21.02.2018

Stability of concentrated suspensions under Couette and Poiseuille flow

verfasst von: Tobias Ahnert, Andreas Münch, Barbara Niethammer, Barbara Wagner

Erschienen in: Journal of Engineering Mathematics | Ausgabe 1/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. A linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated, and the connections to the stability problem for the related classical Bingham flow problem are discussed.

Vorheriger Artikel Streamwise-travelling viscous waves in channel flows

Nächster Artikel Selective withdrawal from an intake channel connected to a reservoir

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

Orszag SA (1971) Accurate solution of the Orr-Sommerfeld stability equation. J Fluid Mech 50(04):689CrossRefMATH

Drazin PG, Reid WH (1981) Hydrodynamic stability. Cambridge University Press, CambridgeMATH

Trefethen NL, Trefethen AE, Teddy SC, Driscoll TA (1993) Hydrodynamic stability without eigenvalues. Science 261(5121):578–584MathSciNetCrossRefMATH

Bolotnov IA, Lahey RT, Drew DA, Jansen KE (2008) Turbulent cascade modeling of single and bubbly two-phase turbulent flows. Int J Multiph Flow 34(12):1142–1151CrossRef

Georgievskii DV (2013) Stability of Bingham flows: from the earliest works of A. A. Il’yushin to the present. J Eng Math 78:9–17MathSciNetCrossRefMATH

Garifullin FA, Galimov KZ (1974) Hydrodynamic stability of non-newtonian media. Sov Appl Mech 10(8):807–824MathSciNetCrossRefMATH

Ahnert T, Münch A, Wagner B (2017) Models for the two-phase flow of concentrated suspensions. arXiv:1709.01068

Leighton D, Acrivos A (1987) Shear-induced migration of particles in concentrated suspensions. J Fluid Mech 181(1):415–439CrossRef

Frigaard IA, Howison SD, Sobey IJ (1994) On the stability of Poiseuille flow of a Bingham fluid. J Fluid Mech 263:133–150MathSciNetCrossRefMATH

10.

Frigaard IA, Nouar C (2003) On the three-dimensional linear stability of Poiseuille flow of Bingham fluids. Phys Fluids 15:2843–2851MathSciNetCrossRefMATH

11.

Métivier C, Nouar C, Brancher J-P (2005) Linear stability involving the Bingham model when the yield stress approaches zero. Phys Fluids 17(10):104106CrossRefMATH

12.

Drew DA, Segel LA (1971) Shock solutions for particle-laden thin films. Stud Appl Math 50:205–205CrossRef

13.

Ishii M (1975) Thermo-fluid dynamic theory of two-phase flow. Eyrolles, Paris

14.

Stewart HB, Wendroff B (1984) Two-phase flow: models and methods. J Comput Phys 356:363–409MathSciNetCrossRefMATH

15.

Lhuillier D, Chang C-H, Theofanous TG (2013) On the quest for a hyperbolic effective-field model of disperse flows. J Fluid Mech 731:184–194MathSciNetCrossRefMATH

16.

Keyfitz BL, Kranzer HC (1995) Spaces of weighted measures for conservation laws with singular shock solutions. J Differ Equ 118:420–451MathSciNetCrossRefMATH

17.

Keyfitz BL (2011) Singular shocks: retrospective and prospective. Conflu Math 03(03):445–470MathSciNetCrossRefMATH

18.

Keyfitz BL, Sanders R, Sever M (2003) Lack of hyperbolicity in the two-fluid model for two-phase incompressible flow. Discret Contin Dyn Syst Ser B 3(4):541–563MathSciNetCrossRefMATH

19.

Drew DA, Passman SL (1999) Theory of multicomponent fluids, volume 135 of Appl. Math. Sci. Springer, New York

20.

Boyer F, Guazzelli É, Pouliquen O (2011) Unifying suspension and granular rheology. Phys Rev Lett 107(18):188301CrossRef

21.

Cassar C, Nicolas M, Pouliquen O (2005) Submarine granular flows down inclined planes. Phys Fluids 17(10):103301CrossRefMATH

22.

Manning ML, Bamieh B, Carlson JM (2007) Descriptor approach for eliminating spurious eigenvalues in hydrodynamic equations. arXiv:0705.1542v2

23.

Maple 16. Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario

24.

Inkson NJ, Plasencia J, Lo S (2014) Predicting emulsion pressure drop in pipes through CFD multiphase rheology models. 10th international conference on CFD in oil & gas, metallurgical and process industries. In: CFD2014, pp 453–458

25.

Tatsuno T, Volponi F, Yoshida Z (2001) Transient phenomena and secularity of linear interchange instabilities with shear flows in homogeneous magnetic field plasmas. Phys Plasmas 8(2):399CrossRef

26.

Schmid PJ, Kytömaa HK (1994) Transient and asymptotic stability of granular shear flow. J Fluid Mech 264:255–275MathSciNetCrossRefMATH

27.

Schmid PJ (2007) Nonmodal stability theory. Annu Rev Fluid Mech 39:129–162MathSciNetCrossRefMATH

28.

Pope SB (2000) Turbulent flows. Cambridge University Press, CambridgeCrossRefMATH

29.

Muraki DJ (2007) A simple illustration of a weak spectral cascade. SIAM J Appl Math 67(5):1504–1521MathSciNetCrossRefMATH

30.

Pavlov KB, Romanov AS, Simkhovich SL (1974) Hydrodynamic stability of Poiseuille flow of a viscoplastic non-Newtonian fluid. Izvestiya Akademii Nauk-Mekhanika Zhidkosti i Gaza 9(6):996–998MATH

31.

Thual O, Lacaze L (2010) Fluid boundary of a viscoplastic Bingham flow for finite solid deformations. J Non-Newton Fluid Mech 165(3):84–87CrossRefMATH

32.

Huilgol RR (2015) Fluid mechanics of viscoplasticity. Springer, BerlinCrossRefMATH

33.

Lecampion B, Garagash DI (2014) Confined flow of suspensions modelled by a frictional rheology. J Fluid Mech 759:197–235CrossRef

34.

Oh S, Song Y, Garagash DI, Lecampion B, Desroches J (2015) Pressure-driven suspension flow near jamming. Phys Rev Lett 114(8):088301

35.

Vazquez-Quesada A, Ellero M (2016) Rheology and microstructure of non-colloidal suspensions under shear studied with smoothed particle hydrodynamics. J Non-Newton Fluid Mech 233:37–47MathSciNetCrossRef

36.

Gadala-Maria F, Acrivos A (1980) Shear-induced structure in a concentrated suspension of solid spheres. J Rheol 24(6):799–814CrossRef

37.

Prosperetti A, Jones AV (1987) The linear stability of general two-phase flow models-II. Int J Multiph Flow 13(2):161–171CrossRefMATH

38.

Stewart HB (1979) Stability of two-phase flow calculation using two-fluid models. J Comput Phys 33(2):259–270CrossRefMATH

39.

Carpio A, Chapmann SJ, Velazques JLL (2001) Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals. SIAM J Appl Math 61:2168–2199MathSciNetCrossRef

40.

Bell JB, Trangenstein JA, Shubin GR (1986) Conservation laws of mixed type describing three-phase flow in porous media. SIAM J Appl Math 46:1000–1023MathSciNetCrossRefMATH

41.

Zhou J, Dupuy B, Bertozzi A, Hosoi A (2005) Theory for shock dynamics in particle-laden thin films. Phys Rev Lett 94(11):117803CrossRef

42.

Cook BP, Bertozzi AL, Hosoi AE (2008) Shock solutions for particle-laden thin films. SIAM J Appl Math 68(3):760–783MathSciNetCrossRefMATH

Titel: Stability of concentrated suspensions under Couette and Poiseuille flow
verfasst von: Tobias Ahnert
Andreas Münch
Barbara Niethammer
Barbara Wagner
Publikationsdatum: 21.02.2018
Verlag: Springer Netherlands
Erschienen in: Journal of Engineering Mathematics / Ausgabe 1/2018
Print ISSN: 0022-0833
Elektronische ISSN: 1573-2703
DOI: https://doi.org/10.1007/s10665-018-9954-x

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1/2018

Drop spreading and drifting on a spatially heterogeneous film: capturing variability with asymptotics and emulation

Pressure-driven plug flows between superhydrophobic surfaces of closely spaced circular bubbles

Streamwise-travelling viscous waves in channel flows

Fast evaluation of the fundamental singularities of two-dimensional doubly periodic Stokes flow

Performance analysis of a water tank with oscillating walls for wave energy harvesting

Selective withdrawal from an intake channel connected to a reservoir

Premium Partner

Marktübersichten