Linear stability involving the Bingham model when the yield stress approaches zero

Physics of Fluids

Volumn 17, Issue 10, 2005, Pages

  Metivier C ^a   Nouar, C ^a   Brancher, J P ^a  

^a NANCY UNIVERSITÉ   (France)

Author keywords

Channel flow; Non Newtonian flow; Non Newtonian fluids; Poiseuille flow; Rayleigh Benard instability

Indexed keywords

CHANNEL FLOW; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; NON NEWTONIAN FLOW; RIGIDITY; YIELD STRESS;

BINGHAM MODEL; LINEAR STABILITY; POISEUILLE FLOW; RAYLEIGH-BENARD INSTABILITY;

FLUID DYNAMICS;

CHANNEL FLOW; CONVERGENCE OF NUMERICAL METHODS; FLUID DYNAMICS; MATHEMATICAL MODELS; NON NEWTONIAN FLOW; RIGIDITY; YIELD STRESS;

EID: 33645781324     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2101007     Document Type: Article

References (20)

1. J. G. Oldroyd, "Two-dimensional plastic flow of a Bingham solid," Proc. Cambridge Philos. Soc. 43, 383 (1947). pcx PCPSA4 0068-6735
2. A. N. Beris, J. A. Tsamopoulos, R. C. Armstrong, and R. A. Brown, "Creeping motion of a sphere through a Bingham plastic," J. Fluid Mech. 158, 219 (1985). jfl JFLSA7 0022-1120
3. P. Coussot, "Saffman-Taylor instability in yield stress fluids," J. Fluid Mech. 380, 363 (1998). jfl JFLSA7 0022-1120 10.1017/S002211209800370X
4. I. A. Frigaard, S. D. Howison, and I. J. Sobey, "On the stability of Poiseuille flow of a Bingham fluid," J. Fluid Mech. 263, 133 (1994). jfl JFLSA7 0022-1120
5. R. R. Huilgol, "Variational inequalities in the flows of yield stress fluids including inertia: Theory and applications," Phys. Fluids 14, 1269 (2002). phf PHFLE6 1070-6631 10.1063/1.1448347
6. P. Carrière and P. Monkewitz, "Convective versus absolute instability in mixed Rayleigh-Bénard-Poiseuille convection," J. Fluid Mech. 43, 384 (1999). jfl JFLSA7 0022-1120
7. 3).
8. X. Nicolas, J.-M. Luijkx, and J.-K. Platten, "Linear stability of mixed convection flows in horizontal rectangular channels of finite transversal extension heated from below" Int. J. Heat Mass Transfer 43, 589 (2000). ijh IJHMAK 0017-9310 10.1016/S0017-9310(99)00099-X
9. G.S. Gershumi and E.M. Zhudhovitskii, Convective Stability of Incompressible Fluids (Keter, Jerusalem, 1976).
10. P.G. Drazin and W.H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
11. S. A. Orszag, "Accurate solution of the Orr-Sommerfeld stability equation," J. Fluid Mech. 50, 689 (1971). jfl JFLSA7 0022-1120
12. M. C. Potter, "Stability of plane Couette-Poiseuille flow," J. Fluid Mech. 24, 609 (1966). jfl JFLSA7 0022-1120
13. B. O. A. Hedström, "Flow of plastics materials in pipes," Ind. Eng. Chem. 44, 652 (1951). ich IECHAD 0019-7866
14. R. W. Hanks, "The laminar-turbulent transition for fluids with a yield stress," AIChE J. 9, 306 (1963). aic AICEAC 0001-1541 10.1002/ aic.690090307
15. J. T. Park, R. J. Mannheimer, T. A. Grimley, and T. B. Morrow, "Pipe flow measurements of a transparent non-Newtonian slurry" ASME J. Fluids Eng. 111, 331 (1989). 97k JFEGA4 0098-2202
16. M. P. Escudier and F. Presti, "Pipe flow of a thixotropic liquid," J. Non-Newtonian Fluid Mech. 62, 221 (1996). jnf JNFMDI 0377-0257
17. R. M. Turian, T.-W. Ma, F.-L. G. Hsu, and D.-J. Sung, "Flow of concentrated non-Newtonian slurries: 1. Friction losses in laminar, turbulent and transition flow through straight pipe," Int. J. Multiphase Flow 24, 225 (1998). iny IJMFBP 0301-9322 10.1016/ S0301-9322(97)00038-4
18. T. C. Papanastasiou," Flows of materials with yield," J. Rheol. 31, 385 (1987). jor JORHD2 0148-6055 10.1122/1.549926
19. M. Bercovier and M. Engelman, "A finite element method for incompressible non-Newtonian flows," J. Comput. Phys. 36, 313 (1980). jct JCTPAH 0021-9991 10.1016/0021-9991(80)90163-1
20. E. J. O'Donovan and R. I. Tanner, "Numerical study of the Bingham squeeze film problem," J. Non-Newtonian Fluid Mech. 15, 75 (1984). jnf JNFMDI 0377-0257 10.1016/0377-0257(84)80029-4