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Steady flows inside and around a fluid sphere at low Reynolds numbers

Published online by Cambridge University Press:  20 April 2006

D. L. R. Oliver  and
J. N. Chung
D. L. R. Oliver
Affiliation:
Department of Mechanical Engineering, Washington State University. Pullman, Washington 99164-2920
J. N. Chung
Affiliation:
Department of Mechanical Engineering, Washington State University. Pullman, Washington 99164-2920
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Abstract

The effects of internal circulation in bubbles and droplets have been analysed by means of a semi-analytical series-truncation method. The equations of motion are transformed into a series of coupled, ordinary, nonlinear differential equations by use of orthogonal sets. These infinite-series equations are then truncated adequately and solved numerically. Using this series-truncation method, we have evaluated the effects of different ratios (between the continuous and dispersed phases) of both density and viscosity for the flows of low Reynolds numbers. For all the density ratios investigated, the density difference has almost no effect on the drag coefficient at low Reynolds numbers. The shear stress and the drag coefficient increase with increasing viscosity ratio of droplet to ambience and decrease with increasing Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 154 , May 1985 , pp. 215 - 230
Copyright
© 1985 Cambridge University Press

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References

Abdel-Alim, A. H. & Hamielec, A. E. 1975 Ind. Engng Chem. Fund. 14, 308.
Beard, K. V. & Pruppacher, H. R. 1969 J. Atmos. Sci. 26, 1066.
Brabston, D. C. 1974 Numerical solution of steady viscous flow past spheres and gas bubbles. Ph. D. thesis, Calif. Inst. of Tech.
Brabston, D. C. & Keller, H. B. 1975 J. Fluid Mech. 69, 179.
Chao, B. T. 1962 Phys. Fluids 5, 69.
Chester, W. & Breach, D. K. 1969 J. Fluid Mech. 37, 751.
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles, Chap. 3 and 5. Academic.
Dennis, S. C. R. & Walker, J. D. A. 1971 J. Fluid Mech. 48, 771.
Dennis, S. C. R., Walker, J. D. A. & Hudson, J. D. 1973 J. Fluid Mech. 60, 273.
Dennis, S. C. R. & Walker, M. S. 1964 Aero. Res. Counc. no. 26, 105.
Hadamard, J. 1911 C.K. Acad. Sci. 152, 1735.
Hamielec, A. E., Hoffman, T. Q. & Ross, L. L. 1967 AICHE J. 12, 212.
Hamielec, A. E. & Johnson, A. I. 1962 Can. J. Chem. Engng 40, 246.
Hamielec, A. E., Storey, A. E. & Whitehead, J. M. 1963 Can. J. Chem. Engng 41, 246.
Harper, J. F. 1972 Adv. Appl. Mech. 12, 59.
Harper, J. F. & Moore, D. W. 1968 J. Fluid Mech. 32, 369.
Leclair, B. P., Hamielec, A. E. & Pruppacher, H. R. 1970 J. Atmos. Sci. 27, 308.
Mcdonald, J. E. 1954 J. Met. 11, 478.
Maxworthy, T. 1965 J. Fluid Mech. 23, 369.
Moore, D. W. 1963 J. Fluid Mech. 16, 161.
Nakano, Y. & Tien, C. 1963 Can. J. Chem. Engng 41, 135.
Prakash, S. & Sirignano, W. A. 1980 Intl J. Heat Mass Transfer 21, 885.
Proudman, I. & Pearson, J. R. A. 1957 J. Fluid Mech. 2, 237.
Pruppacher, H. R. & Beard, K. V. 1970 Q. J. R. Met. Soc. 96, 247.
Pruppacher, H. R. & Klett, J. D. 1978 Microphysics of the Clouds and Circulation. Reidel.
Pruppacher, H. R., LeClair, B. P. & Hamielec, A. E. 1970 J. Fluid Mech. 44, 781.
Pruppacher, H. R. & Steinberger, E. H. 1968 J. Appl. Phys. 39, 4129.
Rivkind, V. Ya. & Ryskin, G. M. 1976 Fluid Dyn. 11, 5.
Rivkind, V. Ya., Ryskin, G. M. & Fishbein, G. A. 1976 Appl. Math. Mech. 40, 687.
Rottenberg, M., Bivins, R., Metropolis, N. & Wooten, J. K. 1959 The 3-J and 6-J Symbols. MIT, Cambridge: The Technology Press.
Rybcznski, W. 1911 Bull. Int. Acad. Pol. Sci. Lett. Cl. Sci. Math. Natur., Ser. A, 40.
Talman, J. D. 1968 Special Functions. Benjamin.
Taylor, T. D. & Acrivos, A. 1964 J. Fluid Mech. 18, 466.
Underwood, R. L. 1969 J. Fluid Mech. 37, 95.
Van Dyke, M. D. 1965 Stanford University SUDAER 247.
Winnikow, S. & Chao, B. T. 1965 Phys. Fluids 9, 50.