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Limiting behaviour of particles in Taylor–Couette flow

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Abstract

Negatively buoyant inertial particles are tracked in a steady Taylor vortex background flow with gravity acting along the axis of the cylinders. Particles are found to either fall through the apparatus due to gravity or to be within retention zones. The particles within these retention zones tend towards a limit orbit in the meridional plane. It is found that for particles with density close to that of the background fluid, the size of the retention zone is relatively large with the centre of the limit orbit being close to that of the Taylor vortex. As the particle density increases, the size of the retention zone decreases and the centre of the limit orbit moves away from the centre of the Taylor vortex. The effect of varying the fluid and particle parameters on the retention zone and orbit size is investigated.

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References

  1. Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Phil Trans R Soc Lond A 223: 289–343

    Article  ADS  Google Scholar 

  2. Davey A, Di Prima RC, Stuart JT (1968) On the instability of Taylor vortices. J Fluid Mech 31: 17–52

    Article  MATH  ADS  Google Scholar 

  3. Jones CA (1981) Nonlinear Taylor vortices and their stability. J Fluid Mech 102: 249–261

    Article  MATH  ADS  Google Scholar 

  4. Fenstermacher PR, Swinney HL, Gollub JP (1979) Dynamical instabilities and the transition to chaotic Taylor vortex flow. J Fluid Mech 94: 103–128

    Article  ADS  Google Scholar 

  5. Lueptow RM (1995) Fluid mechanics of a rotating filter separator. In: Choi KJ (ed) Advances in filtration and separation technology, vol 9. American Filtration and Separations Society, pp 283–291

  6. Holeschovsky UB, Cooney CL (1991) Quantitative description of a ultrafiltration in a rotating filtration device. AIChE J 37: 1219–1226

    Article  Google Scholar 

  7. Belfort G, Mikulasek P, Pimbley JM, Chung KY (1993) Diagnosis of membrane fouling using a rotating annular filter. 2. Dilute particle suspensions of known particle-size. J Memb Sci 77: 23–39

    Article  Google Scholar 

  8. Ohashi K, Tashiro K, Kushiya F, Matsumoto T, Yoshida S, Endo M, Horio T, Ozawa K, Sakai K (1988) Rotation-induced Taylor vortex enhances filtrate flux in plasma separation. Trans Am Soc Artif Intern Organs 34: 300–307

    Google Scholar 

  9. Dutta PK, Ray AK (2004) Experimental investigation of Taylor vortex photocatalytic reactor for water purification. Chem Eng Sci 59: 5249–5259

    Article  Google Scholar 

  10. Haut B, Ben Amor H, Coulon L, Jacquet A, Halloin V (2003) Hydrodynamics and mass transfer in a Couette-Taylor bioreactor for the culture of animal cells. Chem Eng Sci 58: 777–784

    Article  Google Scholar 

  11. Vedantam S, Joshi JB (2006) Annular centrifugal contractors—a review. Chem Eng Res Des 84: 522–542

    Article  Google Scholar 

  12. Maxey MR, Riley JJ (1983) Equation of motion for a small rigid sphere in a nonuniform flow. Phys Fluids 26: 883–889

    Article  MATH  ADS  Google Scholar 

  13. Michaelides EE (1997) Review—the transient equation of motion for particles, bubbles and droplets. J Fluids Eng 119: 233–247

    Article  Google Scholar 

  14. Rudman M (1994) Particle shear-rate history in a Taylor-Couette column. Liquid-solid flows. ASME 189: 23–30

    Google Scholar 

  15. Rudman M (1998) Mixing and particle dispersion in the wavy vortex regime of Taylor-Couette flow. AIChE J 44: 1015–1026

    Article  Google Scholar 

  16. Wereley ST, Lueptow RM (1999) Velocity field for Taylor-Couette flow with an axial flow. Phys Fluids 11: 325–333

    Article  MATH  ADS  Google Scholar 

  17. Davey A (1962) The growth of Taylor vortices in flow between rotating cylinders. J Fluid Mech 14: 336–368

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. Henderson KL, Gwynllyw DRh, Barenghi CF (2007) Particle tracking in Taylor Couette flow. Eur J Mech B Fluids 26: 738–748

    Article  MATH  MathSciNet  Google Scholar 

  19. Henderson KL, Barenghi CF (1995) Numerical methods for helium’s two fluid model. J Low Temp Phys 98: 351–381

    Article  ADS  Google Scholar 

  20. Auton TR, Hunt JCR, Prud’homme M (1988) The force exerted on a body in inviscid unsteady non-uniform rotational flow. J Fluid Mech 197: 241–257

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. Mei RW (1994) Flow due to an oscillating sphere and an expression for unsteady drag on the sphere at finite Reynolds number. J Fluid Mech 270: 133–174

    Article  MATH  ADS  Google Scholar 

  22. Gwynllyw DRh, Phillips TN (2005) Some issues regarding spectral element meshes for moving journal bearing system. Int J Numer Methods Fluids 48: 423–454

    Article  MATH  MathSciNet  Google Scholar 

  23. Jones CA (1985) The transition to wavy Taylor vortices. J Fluid Mech 157: 135–162

    Article  ADS  Google Scholar 

  24. Kawai H, Kudo H, Takahashi H (2007) Visualization of a limit cycle orbit in a Taylor vortex flow with a short annulus. J Chem Eng Jpn 40: 944–950

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of the West of England, Bristol, BS16 1QY, UK

    Karen L. Henderson & D. Rhys Gwynllyw

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  1. Karen L. Henderson
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  2. D. Rhys Gwynllyw
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Correspondence to Karen L. Henderson.

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Henderson, K.L., Gwynllyw, D.R. Limiting behaviour of particles in Taylor–Couette flow. J Eng Math 67, 85–94 (2010). https://doi.org/10.1007/s10665-009-9321-z

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  • DOI: https://doi.org/10.1007/s10665-009-9321-z

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