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Particle dynamics and pattern formation in a rotating suspension

Published online by Cambridge University Press:  19 April 2007

JONGHOON LEE  and
ANTHONY J. C. LADD
JONGHOON LEE
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611-6005
ANTHONY J. C. LADD
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611-6005
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Abstract

A rotating suspension of non-neutrally buoyant particles, confined by a horizontal cylinder, can be unstable to axial perturbations in concentration. A highly regular pattern of particle density and fluid flow then coexists in a non-equilibrium stationary state. The density profile along the cylinder axis is roughly sinusoidal, with a well-defined wavelength close to the cylinder diameter, and has a magnitude of approximately 30% of the average number density. We have used numerical simulations within the Stokes-flow approximation to investigate the mechanism underlying axial-band formation. Our results show that bands develop from an inhomogeneous particle distribution in the radial plane, which is itself driven by the competition between gravity and the viscous drag of the rotating fluid. We have discovered that the mean angular velocity of the particles is an order parameter which distinguishes between a low-frequency segregated phase and a high-frequency dispersed phase, where the particles fill the whole volume uniformly. The order parameter is a function of a single dimensionless frequency, with a characteristic length that is the mean interparticle separation. As the rotational frequency increases, the particle distribution becomes more homogeneous and the band structure disappears. Hydrodynamic diffusion stabilizes the suspension against centrifugal forces, allowing for a uniformly dispersed phase that can be used to grow three-dimensional cell cultures in an artificial microgravity environment.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 577 , 25 April 2007 , pp. 183 - 209
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1972 Handbook of mathematical functions. Dover.Google Scholar
Acrivos, A. & Herbolzheimer, E. 1979 Enhanced sedimentation in settling tanks with inclined walls. J. Fluid Mech. 92, 435–457.CrossRefGoogle Scholar
Blake, J. A. 1971 A note on the image system for a Stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303.Google Scholar
Botchwey, E. A., Pollack, S. R., Levine, E. M., Johnston, E. D. & Laurencin, C. T. 2004 Quantitative analysis of three-dimensional fluid flow in rotating bioreactors for tissue engineering. J. Biomed. Mater. Res. 69A, 205–215.Google Scholar
Breu, A. P. J., Kruelle, C. A. & Rehberg, I. 2003 Pattern formation in a rotating aqueous suspension. Europhys. Lett. 62, 491–497.Google Scholar
Caflisch, R. E. & Luke, J. H. C. 1985 Variance in the sedimentation speed of a suspension. Phys. Fluids 28, 759.CrossRefGoogle Scholar
Crowley, J. M. 1971 Viscosity-induced instability of a one-dimensional lattice of falling spheres. J. Fluid Mech. 45, 151–159.Google Scholar
Hammond, T. G. & Hammond, J. M. 2001 Optimized suspension culture: the rotating-wall vessel. Am. J. Physiol. Renal Physiol. 281, F12–F15.CrossRefGoogle ScholarPubMed
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.Google Scholar
Higdon, J. J. L. & Muldowney, G. P. 1995 Resistance functions for spherical particles, droplets and bubbles in cylindrical tubes. J. Fluid Mech. 298, 193–210.Google Scholar
Hirschfeld, B. R., Brenner, H. & Falade, A. 1984 First and second order wall effects upon the slow viscous asymmetric motion of an arbitrarily shaped, positioned and oriented particle within a circular cylinder. Physiochem. Hydrodyn. 5, 99–133.Google Scholar
Jain, N., Khakhar, D. V., Lueptow, R. M. & Ottino, J. M. 2001 Self-organization in granular slurries. Phys. Rev. Lett. 86, 3771–3774.CrossRefGoogle ScholarPubMed
Kynch, G. J. 1952 A theory of sedimentation. Trans. Farad. Soc. 48, 166–176.Google Scholar
Lee, J. & Ladd, A. J. C. 2002 Axial segregation in a cylindrical centrifuge. Phys. Rev. Lett. 89, 104301.CrossRefGoogle Scholar
Lee, J. & Ladd, A. J. C. 2005 Axial segregation of a settling suspension in a rotating cylinder. Phys. Rev. Lett. 95, 048001.CrossRefGoogle Scholar
Lipson, S. G. & Seiden, G. 2002 Particle banding in rotating fluids: a new pattern-forming system. Physica A 314, 272–277.Google Scholar
Liron, N. & Shahar, R. 1978 Stokes flow due to a Stokeslet in a pipe. J. Fluid Mech. 86, 727–744.CrossRefGoogle Scholar
Matson, W. R., Ackerson, B. J. & Tong, P. 2003 Pattern formation in a rotating suspension of non-Brownian settling particles. Phys. Rev. E 67, 050301(R).CrossRefGoogle Scholar
Matson, W. R., Ackerson, B. J. & Tong, P. 2006 Dynamics of rotating suspensions. Solid State Commun. 139, 605–616.CrossRefGoogle Scholar
Matson, W. R., Kalyankar, M., Ackerson, B. J. & Tong, P. 2005 Concentration and velocity patterns in a horizontal rotating suspension of non-Brownian settling particles. Phys. Rev. E 71, 031401.Google Scholar
Maul, C. & Kim, S. 1994 Image systems for a Stokeslet inside a rigid spherical container. Phys. Fluids 6, 2221–2223.Google Scholar
Ottino, J. M. & Khakhar, D. V. 2000 Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32, 55–91.CrossRefGoogle Scholar
Pouliquen, O., Delour, J. & Savage, S. B. 1997 Fingering in granular flows. Nature 386, 816–817.Google Scholar
Roberts, G. O., Kornfeld, D. M. & Fowlis, W. W. 1991 Particle orbits in a rotating liquid. J. Fluid Mech. 229, 555–567.CrossRefGoogle Scholar
Shen, A. Q. 2002 Granular fingering patterns formation in horizontal rotating cylinders. Phys. Fluids 14, 462–470.Google Scholar
Tirumkudulu, M., Mileo, A. & Acrivos, A. 2000 Particle segregation in monodisperse sheared suspensions in a partially filled rotating horizontal cylinder. Phys. Fluids 12, 1615.Google Scholar
Völtz, C., Pesch, W. & Rehberg, I. 2002 Rayleigh-Taylor instability in a sedimenting suspension. Phys. Rev. E 65, 011404.Google Scholar
Zik, O., Levine, D., Lipson, S. G., Shtrikman, S. & Stavans, J. 1994 Rotationally induced segregation of granular materials. Phys. Rev. Lett. 73, 644–647.Google Scholar