Hydrodynamic stability of flow between rotating porous cylinders with radial and axial flow

Physics of Fluids

Volumn 9, Issue 12, 1997, Pages 3687-3696

  Johnson, Eric C ^a   Lueptow, Richard M ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001006157     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869506     Document Type: Article

References (48)

1. G. I. Taylor, "Stability of a viscous liquid contained between two rotating cylinders," Philos. Trans. A 223, 289 (1923).
2. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, 1961).
3. R. C. DiPrima and H. L. Swinney, "Instabilities and transition in flow between concentric rotating cylinders," in Topics in Applied Physics, Hydrodynamic Instabilities and the Transition to Turbulence, edited by H. L. Swinney and J. P. Gollub (Springer-Verlag, Berlin, 1985), pp. 139-180.
4. K. Kataoka, "Taylor vortices and instabilities in circular Couette flows," in Encyclopedia of Fluid Mechanics, edited by N. P. Cheremisinoff (Gulf Publishing Company, Houston, 1986), Vol. 1, pp. 237-273.
5. E. L. Koschmieder, Benard Cells and Taylor Vortices (Cambridge University Press, Cambridge, 1993).
6. J. Kaye and E. C. Elgar, "Modes of adiabatic and diabatic fluid flow in an annulus with an inner rotating cylinder," Trans. ASME 80, 753 (1958).
7. S. Chandrasekhar, "The hydrodynamic stability of viscid flow between coaxial cylinders," Proc. Natl. Acad. Sci. USA 46, 141 (1960).
8. R. C. DiPrima, "The stability of a viscous fluid between rotating cylinders with an axial flow," J. Fluid Mech. 9, 621 (1960).
9. K. C. Chung and K. N. Astill, "Hydrodynamic instability of viscous flow between rotating coaxial cylinders with fully developed axial flow," J. Fluid Mech. 81, 641 (1977).
10. M. A. Hasoon and B. W. Martin, "The stability of viscous axial flow in an annulus with a rotating inner cylinder," Proc. R. Soc. London. Ser. A 352, 351 (1977).
11. N. Gravas and B. W. Martin, "Instability of viscous axial flow in annuli having a rotating inner cylinder," J. Fluid Mech. 86, 385 (1978).
12. B. S. Ng and E. R. Turner, "On the linear stability of spiral flow between rotating cylinders," Proc. R. Soc. London. Ser. A 382, 83 (1982).
13. K. L. Babcock, G. Ahlers, and D. S. Cannell, "Noise-sustained structure in Taylor-Couette flow with through flow," Phys. Rev. Lett. 67, 3388 (1991).
14. R. C. DiPrima and A. Pridor, "The stability of viscous flow between rotating concentric cylinders with an axial flow," Proc. R. Soc. London, Ser. A 366, 555 (1979).
15. D. I. Takeuchi and D. F. Jankowski, "A numerical and experimental investigation of the stability of spiral Poiseuille flow," J. Fluid Mech. 102, 101 (1981).
16. R. M. Lueptow, A. Docter, and K. Min, "Stability of axial flow in an annulus with a rotating inner cylinder," Phys. Fluids A 4, 2446 (1992).
17. H. A. Snyder, "Experiments on the stability of spiral flow at low axial Reynolds numbers," Proc. R. Soc. London, Ser. A 265, 198 (1962).
18. K. Bühler, "Instabilitaten spiralformiger stromungen im zylinderspalt," Z. Angew. Math. Mech. 64, T180 (1984).
19. K. Bühler and N. Polifke, "Dynamical behavior of Taylor vortices with superimposed axial flow," in Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems, Vol. Series B: Physics edited by F. H. Busse and L. Kramer (Plenum Press, New York, 1990), Vol. 225, pp. 21-29.
20. A. Recktenwald, M. Lücke, and H. W. Müller, "Taylor vortex formation in axial through-flow: Linear and weakly nonlinear analysis," Phys. Rev. E 48, 4444 (1993).
21. A. Tsameret, G. Goldner, and V. Steinberg, "Experimental evaluation of the intrinsic noise in the Couette-Taylor system with an axial flow," Phys. Rev. E 49, 1309 (1994).
22. P. Büchel, M. Lücke, D. Roth, and R. Schmitz, "Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow," Phys. Rev. A 53, 4764 (1996).
23. T. S. Chang and W. K. Sartory, "Hydromagnetic stability of dissipative flow between rotating permeable cylinders," J. Fluid Mech. 27, 65 (1967).
24. T. S. Chang and W. K. Sartory, "Hydromagnetic stability of dissipative. flow between rotating permeable cylinders," Part 2. Oscillatory critical modes and asymptotic results," J. Fluid Mech. 36, 193 (1969).
25. S. K. Bahl, "Stability of viscous flow between two concentric rotating porous cylinders," Def. Sci. J. 20, 89 (1970).
26. K. Bühler, "Taylor vortex flow with superimposed radial mass flux," in Ordered and Turbulent Patterns in Taylor-Couette Flow, edited by E. D. Andereck and F. Hayot (Plenum Press, New York, 1992), pp. 197-203.
27. K. Min and R. M. Lueptow, "Hydrodynamic stability of viscous flow between rotating porous cylinders with radial flow," Phys. Fluids 6, 144 (1994).
28. K. Min and R. M. Lueptow, "Circular Couette flow with pressure-driven axial flow and a porous inner cylinder," Exp. Fluids 17, 190 (1994).
29. K. H. Kroner, V. Nissinen, and H. Ziegler, "Improved dynamic filtration of microbial suspension," Bio/Technology 5, 921 (1987).
30. K. H. Kroner and V. Nissinen, "Dynamic filtration of microbial suspensions using an axially rotating filter," J. Membrane Sci. 36, 85 (1988).
31. G. Beaudoin and M. Y. Jaffrin, "Plasma filtration in Couette flow membrane devices," Artif. Organs 13, 43 (1989).
32. S. Wronski, E. Molga, and L. Rudniak, "Dynamic filtration in biotechnology," Bioproc. Eng. 4, 99 (1989).
33. U. B. Holeschovsky and C. L. Cooney, "Quantitative description of ultrafiltration in a rotating filtration device," AIChE J. 37, 1219 (1991).
34. G. Belfort, J. M. Pimbley, A. Greiner, and K. Y. Chung, "Diagnosis of membrane fouling using a rotating annular filter. 1. Cell culture media," J. Membrane Sci. 77, 1 (1993).
35. G. Belfort, P. Mikulasck, J. M. Pimbley, and K. Y. Chung, "Diagnosis of membrane fouling using a rotating annular filter. 2. Dilute particle suspensions of known particle size," J. Membrane Sci. 77, 23 (1993).
36. H. B. Winzeler and G. Belfort, "Enhanced performance for pressure-driven membrane processes: The argument for fluid instabilities," J. Membrane Sci. 80, 35 (1993).
37. R. M. Lueptow and A. Hajiloo, "Flow in a rotating membrane plasma separator," ASAIO J. 41, 182 (1995).
38. J. R. Hildebrandt and J. B. Saxton, "The use of Taylor vortices in protein processing to enhance membrane filtration performance," in Bioprocess Engineering Colloquium, edited by R. C. Dean Jr. and R. M. Nerem (The American Society of Mechanical Engineers, New York, 1987), pp. 93-95.
39. R. M. Lueptow, "Fluid mechanics of a rotating filter separator," Advances in Filtration and Separation Technology, Nashville, TN, American Filtration and Separations Society, 1995, pp. 283-291.
40. S. K. Bahl and K. M. Kapur, "The stability of a viscous flow between two concentric rotating porous cylinders with an axial flow," Def. Sci. J. 25, 139 (1975).
41. A. Kolyshkin and R. Vaillancourt, "Convective instability boundary of Couette flow between rotating porous cylinders with axial and radial flow," Phys. Fluids 9, 910 (1997).
42. F. Marques, J. Sanchez, and P. D. Weidman, "Generalized Couette-Poiseuille flow with boundary mass transfer," submitted to J. Fluid Mech.
43. S. Wolfram, Mathematica: A System for Doing Mathematics by Computer (Addison-Wesley, Redwood City, CA, 1991).
44. A. Tsameret and V. Steinberg, "Noise-modulated propagating pattern in a convectively unstable system," Phys. Rev. Lett. 67, 3392 (1991).
45. E. M. Sparrow, W. D. Munro, and V. K. Jonsson, "Instability of the flow between rotating cylinders: The wide-gap problem," J. Fluid Mech. 20, 35 (1964).
46. P. H. Roberts, "Appendix: The solution of the characteristic value problems," Proc. R. Soc. London. Ser A 283, 550 (1965).
47. W. Tobler, "Dynamic filtration: Principle and application of shear filtration in an annular gap," Filtr. Sep. 19, 329 (1982).
48. K. Ohashi, K. Tashiro, F. Kushiya, T. Matsumoto, S. Yoshida, M. Endo, T. Horio, K. Ozawa, and K. Sakai, "Rotation-induced Taylor vortex enhances filtrate flux in plasma separation," Trans. Am. Soc. Artif. Intern. Organs 34, 300 (1988).