On the determination of yield surfaces in Herschel-Bulkley fluids

Journal of Rheology

Volumn 43, Issue 3, 1999, Pages 463-483

  Burgos, Gilmer R ^a   Alexandrou, Andreas N ^a   Entov, Vladimir ^b  

^a WORCESTER POLYTECHNIC INSTITUTE   (United States)

^b INSTITUTE FOR PROBLEMS IN MECHANICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000625943     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.550992     Document Type: Article

References (26)

1. Ahmed, A. and A. N. Alexandrou, "Processing of Semi-Solid materials using a Shear-Thickening Bingham Fluid Model," Proceeding of the 1994, ASME Fluids Engineering Division Summer Meeting, ASME, New York, 1994 FED-Vol. 179, pp. 83-87.
2. Atkinson, C. and K. El-Ali, "Some boundary-value problems for the Bingham model," J. Non-Newtonian Fluid Mech. 41, 339-363 (1992).
3. Azouz, I., S. A. Shirazi, A. Pilehvari, and J. J. Azar, "Numerical simulation of laminar flows of yield-powerlaw fluids in conduits of arbitrary cross-section," J. Fluids Eng. 115, 710-716 (1993).
4. Barenblatt, G. I., V. M. Entov, and V. M. Ryzhik, Theory of Fluid Flows Through Natural Rocks (Kluwer, Dordrecht, 1990).
5. Bercovier, M. and M. Engelman, "A finite element method for incompressible non-Newtonian flows," J. Comput. Phys. 36, 313-326 (1980).
6. Bernadiner, M. G. and V. M. Entov, Hydrodynamic Theory of Seepage Flow of Anomalous Fluids (Nauka, Moscow, 1975) (in Russian).
7. Beverly, C. R. and R. I. Tanner, "Numerical analysis of extrudate swell in viscoelastic materials with yield stress," J. Rheol. 33, 989-1009 (1989).
8. Bingham, E. C., Fluidity and Plasticity (McGraw-Hill, New York, 1922), pp. 215-218.
9. Bird, R. B., G. C. Dai, and B. J. Yarusso, "The Rheology and Flow of Viscoplastic Materials," Rev. Chem. Eng. 1, 1-70 (1983).
10. Blackery, J. and E. Mitsoulis, "Creeping motion of a sphere in tubes filled with a Bingham plastic material," J. Non-Newtonian Fluid Mech. 70, 59-77 (1997).
11. Carter, R. E. and R. C. Warren, "Extrusion Stresses, Die Swell, and Viscous Heating Effects in Double-Base Propellants," J. Rheol. 31, 151-173 (1987).
12. Covey, G. H. and B. R. Stanmore, "Use of parallel-plate plastometer for the characterization of viscous fluids with a yield stress," J. Non-Newtonian Fluid Mech. 8, 249-260 (1981).
13. Craster R. V., "Solutions for Herschel-Bulkley flows," Q. J. Mech. Appl. Math. 48, 343-374 (1995).
14. Craster R. V., "Yield surfaces for Herschel-Bulkley flow in complex geometries," IMA J. Appl. Math. 56, 253-276 (1996).
15. Elwood, K. R. J., G. C. Georgiou, T. C. Papanastasiou, and J. O. Wilkes, "Laminar jets of Bingham-plastic liquids," J. Rheol. 34, 787-811 (1990).
16. Entov, V. M. and T. A. Malakhova, "Filtration problems with a piecewise-linear resistance law," Fluid Dyn. (USSR) 9, 194-198 (1994).
17. Herschel, W. H. and R. Bulkley, "Konsistenzmessungen von Gummi-Benzol-Lösungen," Kolloid-Z. 39, 291-300 (1926).
18. Mitsoulis, E. and S. S. Abdali, "Flow Simulation of Herschel-Bulkley Fluids through Extrusion Dies," Can. J. Chem. Eng. 71, 147-160 (1993).
19. Mittal, S. and T. E. Tezduyar, "Direct Time-Integration Methods: Stabilized Space-Time Finite Element Formulation of Incompressible Flows," Solving Large-Scale Problems in Mechanics, edited by Manolis Papadrakakis (Wiley, New York, 1993), pp. 357-389.
20. O'Donovan, E. J. and R. I. Tanner, "Numerical study of the Bingham squeeze film problem," J. Non-Newtonian Fluid Mech. 15, 75-83 (1984).
21. Oldroyd, J. G., "A rational formulation of the equations of plastic flow for a Bingham solid," Proc. Cambridge Philos. Soc. 43, 100-105 (1947).
22. Papanastasiou, T. C., "Flows of Materials with Yield," J. Rheol. 31, 385-404 (1987).
23. Polubrinova-Kochina, P. Y., Theory of Ground Water Movement (Princeton University Press, Princeton, NJ, 1962).
24. Taylor, A. J. and S. D. R. Wilson, "Conduit flow of an incompressible, yield-stress fluid," J. Rheol. 41, 93-101 (1997).
25. Tsamopoulos, J. A., M. F. Chen, and A. V. Borkar, "On the spin coating of viscoplastic fluids," Rheol. Acta 35, 597-615 (1996).
26. Van Der Vorst, H., "Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 13, 631-644 (1992).