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The effect of weak gravitational force on Brownian coagulation of small particles

Published online by Cambridge University Press:  26 April 2006

Y. G. Wang  and
C. S. Wen
Y. G. Wang
Affiliation:
Department of Physics, Nankai University, Tianjin, China Institute of Atmospheric Physics, the Chinese Academy of Sciences, Beijing, China.
C. S. Wen
Affiliation:
Department of Physics, Nankai University, Tianjin, China
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Abstract

The coagulation rate of a dilute polydisperse suspension of particles is considered for small Péclet number, which provides a measure of the ratio of the relative gravity-induced motion to Brownian motion between two rigid spheres. In particular, a fourterm expansion for the dimensionless coagulation rate (Nusselt number) as function of the Péclet number is developed by making use of a singular perturbation method. In the limit of the radius of one of the two spheres becoming small, the result agrees with Acrivos & Taylor's (1962) work on mass transfer to spheres at small Péclet number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 599 - 610
Copyright
© 1990 Cambridge University Press

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References

Brown, W. B. 1962 Exact numerical solutions of the complete linearized equations for the stability of compressible boundary layers. Norair Rep. NOR-62–15. Northrop Aircraft Inc., Hawthorne, LA.Google Scholar
Bush, W. B. 1976 Axial incompressible viscous flow past a slender body of revolution. Rocky Mountain J. Maths 6, 527.Google Scholar
Duck, P. W. & Bodonyi, R. J. 1986 The wall jet on an axisymmetric body. Q. J. Mech. Appl. Maths 39, 407.Google Scholar
Duck, P. W. & Hall, P. 1989 On the interaction of axisymmetric Tollmien–Schlichting waves in supersonic flow. Q. J. Mech. Appl. Maths 42, 115 (also ICASE Rep. 88–10).Google Scholar
Duck, P. W. & Hall, P. 1990 Non-axisymmetric viscous lower branch modes in axisymmetric supersonic flows. J. Fluid Mech. 213, 191–201. (Also ICASE Rep. 88–42).Google Scholar
Gaster, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances and hydrodynamic stability. J. Fluid Mech. 14, 222.Google Scholar
Glauert, M. B. & Lighthill, M. J. 1955 The axisymmetric boundary layer on a long thin cylinder.. Proc. R. Soc. Lond. A 230, 188.Google Scholar
Küchemann, D. 1938 Störungsbewegunyen in einer Gasstromung mit Grentschicht. Z. Angew. Math. Mech. 18, 207.Google Scholar
Lees, L. 1947 The stability of the laminar boundary layer in a compressible fluid. NACA Tech. Rep. 876.Google Scholar
Lees, L. & Lin, C. C. 1946 Investigation of the stability of the laminar boundary layer in a compressible fluid. NACA Tech. Note 1115.Google Scholar
Lin, C. C. 1945a On the stability of two-dimensional parallel flows, part I. Q. Appl. Maths 3, 117.Google Scholar
Lin, C. C. 1945b On the stability of two-dimensional parallel flows, part II. Q. Appl. Maths 3, 218.Google Scholar
Lin, C. C. 1945c On the stability of two-dimensional parallel flows, part III. Q. Appl. Maths 3, 277.Google Scholar
Mack, L. M. 1963 The inviscid stability of the compressible laminar boundary layer. In Space Programs Summary, no. 37–23, p. 297. JPL, Pasadena, CA.
Mack, L. M. 1964 The inviscid stability of the compressible laminar boundary layer: Part II. In Space Programs Summary, no. 37–26, vol. IV, p. 165. JPL Pasadena, CA.
Mack, L. M. 1965a Stability of the compressible laminar boundary layer according to a direct numerical solution. AGARDograph, vol. 97, part I, p. 329.Google Scholar
Mack, L. M. 1965b Computation of the stability of the laminar boundary layer. In Methods in Computational Physics (ed. B. Alder, S. Fernbach & M. Rotenberg), vol. 4, p. 247. Academic.
Mack, L. M. 1969 Boundary-layer stability theory. Document 900–277, Rev. A. JPL, Pasadena, CA.Google Scholar
Mack, L. M. 1984 Boundary-layer linear stability theory. I. Special Course on Stability and Transition of Laminar Flow, AGARD Rep. 709, p. 3–1.Google Scholar
Mack, L. M. 1987 Review of compressible stability theory. In Proc. ICASE Workshop on the Stability of Time Dependent and Spatially Varying Flows. Springer.
Michalke, A. 1971 Instabilität eines Kompressiblen rundens Freistrahls unter Berucksichtingung des Einflusses den Strahlgrenzschtdicke. Z. Flugwiss. 19, 319.Google Scholar
Moore, F. K. 1955 Unsteady laminar boundary layer flow. NACA Tech. Note 2471.Google Scholar
Reshotko, E. 1962 Stability of three-dimensional compressible boundary layers. NASA Tech. Note D-1220.Google Scholar
Seban, R. A. & Bond, R. 1951 Skin friction and heat transfer characteristics of laminar boundary layer of a cylinder in axial incompressible flow. J. Aero. Sci. 10, 671.Google Scholar
Stewartson, K. 1951 On the impulsive motion of a flat plate in a viscous fluid. Q. J. Mech. Appl. Maths 4, 182.Google Scholar
Stewartson, K. 1955 The asymptotic boundary layer on a circular cylinder in axial incompressible flow. Q. Appl. Maths 13, 113.Google Scholar
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids. Oxford University Press.
Thompson, P. A. 1972 Compressible Fluid Dynamics. McGraw-Hill.
Zaat, J. A. 1958 Numerische Beiträge zur Stabilitätstheoric de Grenzschichten. Grenzschichtforschung Symp., IUTAM, p. 127. Springer.