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The motion of a prolate ellipsoid in a rotating Stokes flow

Published online by Cambridge University Press:  04 July 2007

J. R. T. SEDDON  and
T. MULLIN
J. R. T. SEDDON
Affiliation:
Manchester Centre for Nonlinear Dynamics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
T. MULLIN
Affiliation:
Manchester Centre for Nonlinear Dynamics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
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Abstract

Results are presented from experimental investigations into the motion of a heavy ellipsoid in a horizontal rotating cylinder, which has been completely filled with highly viscous fluid. The motion can be conveniently classified using the ratio between the maximum radius of curvature of the ellipsoid κmax and the radius of the drum Rd. If κmax < Rd the ellipsoid adopts a fixed position adjacent to the rising wall for a given cylinder rotation rate. The dependence of this position on wall speed is, surprisingly, independent of the ellipsoid's length, and a Stokes flow model has been developed which predicts both this independence and the speed for the limiting case of an ellipsoid adjacent to a vertical wall. If κ max < Rd the ellipsoid must tilt in order to maintain the maximum surface area in close proximity to the wall. Once tilted, a component of the viscous drag acts to laterally translate the ellipsoid from end to end of the drum. The ellipsoid with κmax = Rd adopts a series of fixed positions for most drum rotational rates but, between two regions of fixed-point behaviour, it undergoes a transition to oscillatory motion.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 123 - 132
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Albertano, P., Somma, D. Di & Capucci, E. 1997 Cyanobacterial picoplankton from the Central Baltic Sea: cell size classification by image-analyzed fluorescence microscopy. J. Plankton Res. 19, 1405–1416.CrossRefGoogle Scholar
Ashmore, J., delPino, C. Pino, C. & Mullin, T. 2005 Cavitation in a lubricating flow between a moving sphere and a boundary. Phys. Rev. Lett. 94, 124501.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bluemink, J. J., vanNierop, E. A. Nierop, E. A., Luther, S., Deen, N. G., Magnaudet, J., Prosperetti, A. & Lohse, S. 2005 Asymmetry-induced particle drift in a rotating flow. Phys. Fluids 17, 072106.CrossRefGoogle Scholar
Brenner, H. & Gajdos, L. J. 1981 London – van der waals forces and torques exerted on an ellipsoidal particle by a nearby semi-infinite slab. Can. J. Chem. 59, 2004–2018.CrossRefGoogle Scholar
Bujalowski, W., Klonowska, M. M. & Jezewska, M. J. 1994 Oligomeric structure of Escherichia coli primary replicative helicase DnaB protein. J. Biol. Chem. 269, 31350–31358.CrossRefGoogle ScholarPubMed
Goldman, A. J., Cox, R. G. & Brenner, H. 1967 Slow viscous motion of a sphere parallel to a plane wall-I Motion through a quiescent fluid. Chem. Engng Sci. 22, 637–651.CrossRefGoogle Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn.Cambridge University Press.Google Scholar
Mody, N. A. & King, M. R. 2005 Three-dimensional simulations of a platelet-shaped spheroid near a wall in shear flow. Phys. Fluids 17, 113302.CrossRefGoogle Scholar
Oberbeck, A. 1876 Ueber stationäre flüssigkeitsbewegungen mit berücksichtigung der inneren reibung. Crelles J. 81, 62–80.Google Scholar
Seddon, J. R. T. & Mullin, T. 2006 Reverse rotation of a cylinder near a wall. Phys. Fluids 18, 041703.CrossRefGoogle Scholar
Taylor, G. I. 1923 The motion of ellipsoidal particles in a viscous fluid. Proc. R. Soc. Lond. A 103, 58–61.Google Scholar
Wakiya, S. 1957 Viscous flows past a spheroid. J. Phys. Soc. Japan 12, 1130–1141.CrossRefGoogle Scholar
Yang, L., Seddon, J. R. T., Mullin, T., delPino, C. Pino, C. & Ashmore, J. 2006 The motion of a rough particle in a stokes flow adjacent to a boundary. J. Fluid Mech. 557, 337–346.CrossRefGoogle Scholar
Yarin, A. L., Gottlieb, O. & Roisman, I. V. 1997 Chaotic rotation of triaxial ellipsoids in simple shear flow. J. Fluid Mech. 340, 83–100.CrossRefGoogle Scholar