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Physics of Fluids / Volume 14 / Issue 12 / ARTICLES

Phys. Fluids 14, 4352 (2002); http://dx.doi.org/10.1063/1.1517603 (10 pages)

A model for preferential concentration

H. Sigurgeirsson1 and A. M. Stuart2

1SCCM Program, Stanford University, Stanford, California 94305
2Mathematics Institute, Warwick University, Coventry, CV4 7AL, England

(Received 8 May 2002; accepted 9 September 2002; published online 6 November 2002)

The preferential concentration of inertial particles in a turbulent velocity field occurs when the particle and fluid time constants are commensurate. We propose a straightforward mathematical model for this phenomenon and use the model to study various scaling limits of interest and to study numerically the effect of interparticle collisions. The model comprises Stokes’ law for the particle motions, and a Gaussian random field for the velocity. The primary advantages of the model are its amenability to mathematical analysis in various interesting scaling limits and the speed at which numerical simulations can be performed. The scaling limits corroborate experimental evidence about the lack of preferential concentration for a large and small Stokes number and make new predictions about the possibility of preferential concentration at large times and lead to stochastic differential equations governing this phenomenon. The effect of collisions is found to be negligible for the most part, although in some cases they have an interesting antidiffusive effect. © 2002 American Institute of Physics.

© 2002 American Institute of Physics

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KEYWORDS and PACS

Keywords

turbulence, velocity, stochastic processes, differential equations, flow simulation

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.1517603

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

    References

  1. J. K. Eaton and J. R. Fessler, "Preferential concentration of particles by turbulence," Int. J. Multiphase Flow 20, 169 (1994).
  2. K. D. Squires and J. K. Eaton, "Particle response and turbulence modification in isotropic turbulence," Phys. Fluids A 2, 1191 (1990)PFADEB000002000007001191000001.
  3. J. R. Fessler, J. D. Kulick, and J. K. Eaton, "Preferential concentration of heavy particles in a turbulent channel flow," Phys. Fluids 6, 3742 (1994)PHFLE6000006000011003742000001.
  4. A. J. Majda, I. Timofeyev, and E. Vanden Eijnden, "A mathematical framework for stochastic climate models," Commun. Pure Appl. Math. 54, 891 (2001). [ISI]
  5. P. Kramer and A. J. Majda, "Stochastic mode elimination applied to simulation methods for complex microfluid systems," SIAM J. Appl. Math. (in press).
  6. K. D. Squires and J. K. Eaton, "Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence," J. Fluid Mech. 226, 1 (1991). [Inspec] [ISI]
  7. K. D. Squires and J. K. Eaton, "Preferential concentration of particles by turbulence," Phys. Fluids A 3, 1169 (1991)PFADEB000003000005001169000001.
  8. R. C. Hogan, J. N. Cuzzi, and A. R. Dobrovolskis, "Scaling properties of particle density fields formed in simulated turbulent flows," Phys. Rev. E 60, 1674 (1999). [ISI] [MEDLINE]
  9. T. Elperin, N. Kleeorin, and I. Rogachevskii, "Self-excitation of fluctuations of inertial particle concentration in turbulent fluid flow," Phys. Rev. Lett. 77, 5373 (1996). [MEDLINE]
  10. T. Elperin, N. Kleeorin, and I. Rogachevskii, "Dynamics of particles advected by fast rotating turbulent fluid flow: Fluctuations and large scale structures," Phys. Rev. Lett. 81, 2898 (1998). [ISI]
  11. A. Crisanti, M. Falcioni, A. Provenzale, and A. Vulpiani, "Passive advection of particles denser than the surrounding fluid," Phys. Lett. A 150, 79 (1990). [Inspec] [ISI]
  12. S. Sundaram and L. R. Collins, "Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations," J. Fluid Mech. 335, 75 (1997).
  13. A. Bracco, P. H. Chavanis, A. Provenzale, and E. A. Spiegel, "Particle aggregation in a turbulent Keplerian flow," Phys. Fluids 11, 2280 (1999)PHFLE6000011000008002280000001.
  14. M. R. Maxey, "Gravitational settling of aerosol particles in homogeneous turbulence and random flow fields," J. Fluid Mech. 174, 441 (1987).
  15. R. H. Kraichnan, "Diffusion by a random velocity field," Phys. Fluids 13, 22 (1970)PFLDAS000013000001000022000001.
  16. A. Careta, F. Sagueés, and J. M. Sancho, "Stochastic generation of homogeneous isotropic turbulence with well-defined spectra," Phys. Rev. E 48, 2279 (1993). [ISI] [MEDLINE]
  17. A. C. Martí, J. M. Sancho, F. Sagués, and A. Careta, "Langevin approach to generate synthetic turbulent flows," Phys. Fluids 9, 1078 (1997)PHFLE6000009000004001078000001.
  18. A. Juneja, D. P. Lathrop, K. R. Sreenivasan, and G. Stolovitzky, "Synthetic turbulence," Phys. Rev. E 49, 5179 (1994). [ISI] [MEDLINE]
  19. J. García-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (Springer-Verlag, New York, 1999).
  20. G. I. Taylor, "Diffusion by continuous movements," Proc. London Math. Soc. 20, 196 (1921).
  21. A. Fannjiang and T. Komorowski, "Diffusions in long-range correlated Ornstein–Uhlenbeck flows," Elect. J. Prob. 7, 1 (2002).
  22. T. Komorowski and G. Papanicolaou, "Motion in a Gaussian, incompressible flow," Ann. Prob. 7, 229 (1997).
  23. R. Carmona and L. Xu, "Homogenization for time dependent 2D incompressible Gaussian flows," Ann. Appl. Probab. 7, 265 (1997).
  24. R. Carmona, S. Grishin, S. A. Molchanov, and L. Xu, "Surface stretching for Ornstein Uhlenbeck velocity fields," Electron. Comm. Probab. 2, 1 (1997).
  25. A. J. Majda and P. R. Kramer, "Simplified models for turbulent diffusion: Theory, numerical modeling, and physical phenomena," Phys. Rep. 314, 237 (1999).
  26. H. Kunita, Stochastic Flows and Stochastic Differential Equations (Wiley, New York, 1978).
  27. A. Fannjiang, L. Ryzhik, and G. Papanicolaou, "Evolution of trajectory correlations in steady random flows," Proc. Symp. Appl. Math. 54, 105 (1998).
  28. H. Kesten and G. Papanicolaou, "A limit theorem in turbulent diffusion." Commun. Math. Phys. 65, 97 (1979). [Inspec] [ISI]
  29. H. Sigurgeirsson, A. M. Stuart, and W.-L. Wan, "Algorithms for particle-field simulations with collisions," J. Comput. Phys. 172, 766 (2001). [Inspec] [ISI]
  30. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967).
  31. R. Clift, J. R. Grace, and M. E. Weber, Bubbles, Drops, and Particles (Academic, New York, 1978).
  32. H. Sigurgeirsson and A. M. Stuart, "Inertial particles in a random field," Stochastics Dyn. 2, 295 (2002).
  33. T. Kurtz, "A limit theorem for perturbed operator semigroups with applications to random evolutions," J. Funct. Anal. 12, 55 (1973).
  34. R. M. Dowell, "Differentiable approximation to Brownian motion on manifolds," Ph.D. thesis, University of Warwick, 1980.


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