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Effects of inertia on the diffusional deposition of small particles to spheres and cylinders at low Reynolds numbers

Published online by Cambridge University Press:  20 April 2006

J. Fernandez De La Mora  and
D. E. Rosner
J. Fernandez De La Mora
Affiliation:
Yale University, Department of Engineering and Applied Science. Chemical Engineering Section, New Haven, CT 06520, U.S.A.
D. E. Rosner
Affiliation:
Yale University, Department of Engineering and Applied Science. Chemical Engineering Section, New Haven, CT 06520, U.S.A.
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Abstract

A formalism that accounts for inertial and diffusive effects in the dynamics of a dilute gas-particle suspension is introduced. The treatment is purely deterministic away from a very thin Brownian diffusion sublayer, while, within the sublayer, inertial effects are small, permitting a near-equilibrium expansion in powers of the Stokes number (particle relaxation time divided by flow characteristic residence time). This expansion provides phenomenological expressions for the particle velocity including two terms : the standard Brownian diffusion, and an additional inertial drift velocity which is closely related to the pressure diffusion term of the Chapman-Enskog expansion. As an example, the general formalism is applied in detail to the case of Stokes flow about a sphere, and sketched for the similar case of a cylinder. Two competing mechanisms are seen to affect the total rate of particle capture by the sphere : (if the stagnation-point region is considerably enriched in particles owing to the high compressibility of the particle phase, which leads to locally enhanced deposition; (ii) centrifugal forces tend to deplete the Brownian diffusion sublayer of particles, reducing diffusion rates away from the stagnation point to the surface. The first effect is seen to dominate over the second except in a very narrow zone of small Stokes numbers. Our method bridges the gap between Levich's solution for the ‘pure-diffusion’ limit and Michael's treatment in the ‘pure-inertia’ limit.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 379 - 395
Copyright
© 1982 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Blaisdel.
Einstein, A. 1908 The elementary theory of the Brownian motion. Z. Elektrochemie 14, 235–239. (English transl. in Investigations on the Theory of the Brownian Movement, pp. 68–85. Dover 1956.)Google Scholar
Fernández De La Mora, J. 1980 Deterministic and diffusive mass transfer mechanisms in the capture of vapors and particles. Ph.D. dissertation, Yale University.
Fernández De La Mora, J. 1982 Inertial nonequilibrium in strongly decelerated gas mixtures of disparate molecular weights. Phys. Rev. A 25, 1108–1122.Google Scholar
Fernández De La Mora, J. & Rosner, D. E. 1981 Inertial deposition of particles revisited: Eulerian approach to a traditionally Lagrangian problem. Physicochem. Hydrodyn. 2, 1–21.Google Scholar
Frank-Kamanetskii, D. A. 1969 Diffusion and Heat Transfer in Chemical Kinetics. Plenum.
Friedlander, S. K. 1977 Smoke, Dust and Haze. Wiley.
Fuchs, N. A. 1964 The Mechanics of Aerosols. Pergamon.
Landau, L. & Lifshitz, E. 1971 Mecanique des Fluides. M.I.R.
Lee, K. W. 1977 Brownian diffusion and filtration. Ph.D. dissertation, University of Minnesota.
Lee, K. W. & Gieseke, J. 1979 Collection of aerosol particles by packed beds. Environ. Sci. Tech. 13, 466.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.
Marble, F. E. 1970 Dynamics of dusty gases. Ann. Rev. Fluid Mech. 2, 397–446.Google Scholar
Michael, D. H. 1963 The stability of a plane Poiseuille flow of a dusty gas. J. Fluid Mech. 18, 19–32.Google Scholar
Michael, D. H. 1968 The steady motion of a sphere in a dusty gas. J. Fluid Mech. 31, 175–192.Google Scholar
Michael, D. H. & Norey, P. W. 1968 The laminar flow of a dusty gas between two rotating cylinders. Q. J. Mech. Appl. Math. 21, 375–388.Google Scholar
Michael, D. H. & Norey, P. W. 1970 Slow motion of a sphere in a two-phase medium. Can. J. Phys. 48, 1607–1616.Google Scholar
Morsi, S. A. & Alexander, A. J. 1972 An investigation of particle trajectories in two-phase flow systems. J. Fluid Mech. 55, 193–208.Google Scholar
Nag, S. R., Jana, R. N. & Datta, N. 1979 Couette flow of a dusty gas. Acta Mech. 33, 179–187.Google Scholar
Peddieson, J. 1976 Some unsteady parallel flows of particulate suspensions. Appl. Sci. Res. 32, 239–268.Google Scholar
Robinson, A. 1956 On the motion of small particles in a potential field flow. Communs Pure Appl. Math. 9. 69–84.Google Scholar
Singleton, R. E. 1965 The compressible gas–solid particle flow over a semi-infinite flat plate. Z. argew. Math. Phys. 16, 421–449.Google Scholar
Soo, S. L. 1967 The Fluid Dynamics of Multiphase Systems. Blaisdel.
Spielman, L. A. 1977 Particle capture from low-speed laminar flows. Ann. Rev. Fluid Mech. 9, 297–319.Google Scholar
Stechkina, I. B., Kirsh. A. A. & Fuchs, N. A. 1970 Effects of inertia on the capture coefficient of aerosol particles at cylinders at low Stokes numbers. Kolloidnyi Zh. 32, 467.Google Scholar
Stewart, W. E. 1977 Convective heat and mass transport in three-dimensional systems with small diffusivities. In Physicochemical Hydrodynamics (ed. D. B. Spalding), pp. 23–63. Advance.
Thuan, N. K. 1974 Ph.D. thesis, Princeton University.
Thuan, N. K. & Andres, R. P. 1979 Free jet deceleration: a scheme for separating gas species of disparate mass. In Proc. Rarefied Gas Dynamics, 11th Symposium (ed. R. Campargue), p. 667. CEA, Paris.
Truesdell, C. 1962 Mechanical basis of diffusion. J. Chem. Phys. 37, 2336–2344.Google Scholar
Yeh, H. C. & Liu, B. H. 1974 Aerosol filtration by fibrous filters: I. Theoretical: II. Experimental. J. Aerosol Sci. 5, 191–204, 205–207.Google Scholar
Yuu, S. & Jotaki, T. 1978 The calculation of particle deposition efficiency due to inertia diffusion and interception in a plane stagnation flow. Chem. Engng Sci. 33, 971–978.Google Scholar
Zung, L. B. 1969 Flow induced in fluid-particle suspension by an infinite rotating disk. Phys. Fluids 12, 18–23.Google Scholar