Abstract
The centrifugal separation of foreign inclusions (particles) in a rotating spherical volume of a self-gravitating medium is considered in the hydrodynamic approximation. Using the full Lagrangian approach, the particle trajectories and radial concentration profiles are studied for a rigid-body velocity distribution in the carrier phase. The regimes of continuum and free-molecular flow around the particles are considered. The cases of a “heavy” (with density greater than that of the carrier phase and traveling toward the center) and a “light-weight” (traveling toward the periphery) admixture are investigated. Analytical and numerical solutions corresponding to steady-state spherically symmetric boundary conditions for the dispersed phase are found. It is shown that the presence of rotation may result in a significant angular anisotropy of the radial particle concentration distributions and, in particular, in the formation of ring-shaped accumulation zones of “heavy” inclusions in the equatorial plane. The solutions obtained can be used to explain the mechanisms of onset of density nonuniformities in planet cores, the formation of planetary systems from gas-particle clouds, and the behavior of aerosol particles in atmospheric vortices.
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REFERENCES
A. Morelli, A. M. Dziewonski, and J. H. Woodhouse, “Anisotropy of the inner core inferred from PKIPKP travel times,” Geophys. Res. Lett., 13, 1545–1548(1986).
J. H. Woodhouse, D. Giardini, and X.-D. Li,“Evidence for inner-core anisotropy from splitting in free oscillation data,” Geophys. Res. Lett., 13, 1549–1552(1986).
J. Tromp, “Inner-core anisotropy and rotation,” Annu. Rev. Earth Planet Sci. 29, 47–69(2001).
S. C. Singh, M. A. Taylor, and J. P. Montagner, “On the presence of liquid in Earth’s inner core,” Science, 287, 2471–2474(2000).
F. E. Marble, “Dynamics of dusty gases,” Annu. Rev. Fluid Mech., 2, 397–446(1970).
A. N. Osiptsov, “Lagrangian modelling of dust admixture in gas flows,” Astrophys. Space Sci., 274, 377–386(2000).
M. R. Maxey and J. R. Riley, “Equation of motion of a small rigid sphere in a non-uniform flow,” Phys. Fluids, 26, 883–889(1983).
N. Raju and E. Meiburg, “Dynamics of small, spherical particles in vortical and stagnation point flow fields,” Phys. Fluids, 9, No. 2, 299–314(1997).
P. M. Lovalenti and J. F. Brady, “The force on a bubble, drop, or particle in arbitrary time-dependent motion at small Reynolds number,”Phys. Fluids A, 5, 2104–2116(1993).
E. N. Bondarev, V. T. Dubasov, Yu. A. Ryzhov, et al., Aerohydromechanics[in Russian], Mashinostroenie, Moscow (1993).
A. N. Osiptsov, “Investigation of the zones of unbounded growth of particle concentration in disperse flows,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 46–52(1984).
Handbook of Mathematical Functions(Eds. M. Abramowitz and I. A. Stegun), National Bureau of Standards, Appl. Math. Series – 55 (1964).
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Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 86–100.Original Russian Text Copyright © 2004 by Ahuja, Belonoshko, Johansson, and Osiptsov.
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Ahuja, R., Belonoshko, A.B., Johansson, B. et al. Inertial phase separation in rotating self-gravitating media. Fluid Dyn 39, 920–932 (2004). https://doi.org/10.1007/s10697-004-0008-x
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DOI: https://doi.org/10.1007/s10697-004-0008-x