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Faxén-like relations for a nonuniform suspension

Phys. Fluids 16, 2483 (2004); doi:10.1063/1.1734951

Published 2 June 2004

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Kengo Ichiki
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218

Andrea Prosperetti
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218
Faculty of Applied Physics, Twente Institute of Mechanics and Burgerscentrum, University of Twente, AE 7500 Enschede, The Netherlands
The first part of the paper shows how ensemble averages that correspond to a prescribed statistically nonuniform spatial distribution of particles can be evaluated starting from a statistically uniform ensemble. The method consists of attributing to each realization of the uniform ensemble a suitable weight which is explicitly constructed. As an application of this general procedure, in the second part of the paper, the behavior of particles subjected to force or torque in a statistically nonuniform suspension and the behavior of a suspension subjected to a uniform shear are studied. In particular, it is shown how the average translational and angular velocities of the particles with respect to the mixture satisfy Faxén-like relations. Furthermore, it is pointed out that several quantities which vanish in an identical way in the case of a uniform suspension are nonzero in the presence of spatial nonuniformities. ©2004 American Institute of Physics.
History: Received 22 October 2003; accepted 17 February 2004; published 2 June 2004
Permalink: http://link.aip.org/link/?PHFLE6/16/2483/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.55.Kf
    Multiphase and particle-laden flows
  • 47.20.Ft
    Instability of shear flows
  • YEAR: 2004

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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REFERENCES (42)
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  1. G. K. Batchelor, "Sedimentation in a dilute dispersion of spheres," J. Fluid Mech. 52, 245 (1972).
  2. G. K. Batchelor and J. T. Green, "The determination of the bulk stress in a suspension of spherical particles to order c2," J. Fluid Mech. 56, 401 (1972).
  3. H. Brenner, "Suspension rheology in the presence of rotary Brownian motion and external couples: Elongational flow of dilute suspensions," Chem. Eng. Sci. 27, 1069 (1972).
  4. M. Zuzovsky, P. M. Adler, and H. Brenner, "Spatially periodic suspensions of convex particles in linear shear flows. III. Dilute arrays of spheres suspended in Newtonian fluids," Phys. Fluids 26, 1714 (1983).
  5. H. Brenner, "Antisymmetric stress induced by the rigid-body rotation of dipolar suspensions," Int. J. Eng. Sci. 22, 645 (1984).
  6. P. Mazur, "On the motion and Brownian motion of n spheres in a viscous fluid," Physica A 110, 128 (1982).
  7. P. Mazur and W. van Saarlos, "Many-sphere hydrodynamic interactions and mobilities in a suspension," Physica A 115, 21 (1982).
  8. J. F. Brady and G. Bossis, "Stokesian dynamics," Annu. Rev. Fluid Mech. 20, 111 (1988).
  9. A. S. Sangani and A. Acrivos, "Slow flow through a periodic array of spheres," Int. J. Multiphase Flow 8, 343 (1982).
  10. A. J. C. Ladd, "Hydrodynamic transport coefficients of random dispersions of hard spheres," J. Chem. Phys. 93, 3484 (1990).
  11. A. J. C. Ladd, "Sedimentation of homogeneous suspensions of non-Brownian spheres," Phys. Fluids 9, 491 (1997).
  12. A. S. Sangani and G. Mo, "An O(N) algorithm for Stokes and Laplace interactions of particles," Phys. Fluids 8, 1990 (1996).
  13. A. Sierou and J. F. Brady, "Accelerated Stokesian dynamics simulations," J. Fluid Mech. 448, 115 (2001).
  14. C. C. Chang and R. L. Powell, "The rheology of bimodal hard-sphere dispersions," Phys. Fluids 6, 1628 (1994).
  15. R. J. Phillips, J. F. Brady, and G. Bossis, "Hydrodynamic transport properties of hard-sphere dispersions. I. Suspensions of freely mobile particles," Phys. Fluids 31, 3462 (1988).
  16. J. F. Brady and L. Durlofsky, "The sedimentation rate of disordered suspensions," Phys. Fluids 31, 717 (1988).
  17. P. R. Nott and J. F. Brady, "Pressure-driven flow of suspensions: Simulation and theory," J. Fluid Mech. 275, 157 (1994).
  18. J. F. Morris and J. F. Brady, "Pressure-driven flow of a suspension: Buoyancy effects," Int. J. Multiphase Flow 24, 105 (1998).
  19. M. P. Brenner, "Screening mechanisms in sedimentation," Phys. Fluids 11, 754 (1999).
  20. F. Feuillebois, "Sedimentation in a dispersion with vertical inhomogeneities," J. Fluid Mech. 139, 145 (1984).
  21. D. Lhuillier, "Ensemble averaging in slightly non-uniform suspensions," Eur. J. Mech. B/Fluids 11, 649 (1992).
  22. M. Marchioro, M. Tanksley, W. Wang, and A. Prosperetti, "Flow of spatially non-uniform suspensions. Part II: Systematic derivation of closure relations," Int. J. Multiphase Flow 27, 237 (2001).
  23. D. Leighton and A. Acrivos, "The shear-induced migration of particles in concentrated suspensions," J. Fluid Mech. 181, 415 (1987).
  24. M. Marchioro and A. Acrivos, "Shear-induced particle diffusivities from numerical simulations," J. Fluid Mech. 443, 101 (2001).
  25. J. H. C. Luke, "Decay of velocity fluctuations in a stably stratified suspension," Phys. Fluids 12, 1619 (2000).
  26. P. N. Segré, F. Liu, P. Umbanhovar, and D. A. Weitz, "An effective gravitational temperature for sedimentation," Nature (London) 409, 594 (2001).
  27. M. Marchioro, M. Tanksley, and A. Prosperetti, "Flow of spatially non-uniform suspensions. Part I: Phenomenology," Int. J. Multiphase Flow 26, 783 (2000).
  28. W. Wang and A. Prosperetti, "Flow of spatially non-uniform suspensions. Part III: Closure relations for porous media and spinning particles," Int. J. Multiphase Flow 27, 1627 (2001).
  29. M. Tanksley and A. Prosperetti, "Average pressure and velocity fields in non-uniform suspensions of spheres in Stokes flow," J. Eng. Math. 41, 275 (2001).
  30. J. F. Brady, R. J. Phillips, J. C. Lester, and G. Bossis, "Dynamic simulation of hydrodynamically interacting suspensions," J. Fluid Mech. 195, 257 (1988).
  31. G. Mo and A. S. Sangani, "A method for computing Stokes flow interactions among spherical objects and its application to suspensions of drops and porous particles," Phys. Fluids 6, 1637 (1994).
  32. K. Ichiki, "Improvement of the Stokesian dynamics method for systems with finite number of particles," J. Fluid Mech. 452, 231 (2002).
  33. J. Happel and H. Brenner, Low-Reynolds Number Hydrodynamics (Prentice–Hall, Englewood Cliffs, NJ, 1965).
  34. S. Kim and S. J. Karrila, Microhydrodynamics (Butterworth–Heinemann, Boston, 1991).
  35. O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, 2nd ed. (Gordon and Breach, New York, 1969).
  36. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, 1992).
  37. H. Hasimoto, "On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres," J. Fluid Mech. 5, 317 (1959).
  38. J. K. Percus and G. J. Yevick, "Analysis of classical statistical mechanics by means of collective coordinates," Phys. Rev. 110, 1 (1958).
  39. M. S. Wertheim, "Exact solution of the Percus–Yevick integral equation for hard spheres," Phys. Rev. Lett. 10, 321 (1963).
  40. E. Thiele, "Equation of state for hard spheres," J. Chem. Phys. 39, 474 (1963).
  41. P. G. Saffman, "On the settling speed of free and fixed suspensions," Stud. Appl. Math. 52, 115 (1973).
  42. U. Geigenmüller and P. Mazur, "Sedimentation of homogeneous suspensions in finite vessels," J. Stat. Phys. 53, 137 (1988).

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