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Dispersed-phase stress tensor in flows of bubbly liquids at large Reynolds numbers

Published online by Cambridge University Press:  26 April 2006

A. S. Sangani  and
A. K. Didwania
A. S. Sangani
Affiliation:
Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, USA
A. K. Didwania
Affiliation:
Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, USA Present address: Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, CA 92093-0310, USA.
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Abstract

We derive averaged equations for large Reynolds number laminar flows of gas–liquid dispersions accounting for slowly varying spatial and temporal fields. In particular, we obtain an exact expression for the dispersed-phase stress tensor to be used in the force balance equation for gas bubbles and illustrate its application by evaluating the stress tensor for a few special cases. It is shown that the dispersed-phase stress tensor gradient with respect to the mean relative motion or the void fraction for the uniformly random bubbly liquids under conditions of large Reynolds number laminar flows is negative and thus has a destabilizing influence on the dynamics of void fraction waves in bubbly liquids.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 27 - 54
Copyright
© 1993 Cambridge University Press

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References

Batchelor, G. K. 1988 A new theory for the instability of a uniform fluidized bed. J. Fluid Mech. 193, 75.Google Scholar
Biesheuvel, A. & Gorissen, W. C. M. 1990 Void fraction disturbances in a uniform bubbly liquid. Intl J. Multiphase Flow 16, 211.Google Scholar
Biesheuvel, A. & Wijngaarden, L. van 1982 The motion of pairs of gas bubbles in a perfect liquid. J. Engng Maths 16, 348.Google Scholar
Biesheuvel, A. & Wijngaarden, L. van 1984 Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J. Fluid Mech. 148, 301.Google Scholar
Geurst, J. A. 1986 Variational principles and two-fluid hydrodynamics of bubbly liquid/gas mixture. Physica 135A, 455.Google Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317.Google Scholar
Ishii, M. 1975 Thermo-Fluid Dynamic Theory of Two-Phase Flow. Eyrolles.
Jenkins, J. T. & Richman, R. W. 1985 Kinetic theory for plane flows of a dense gas of identical, rough, inelastic circular disks. Phys. Fluids 28, 3485.Google Scholar
Koch, D. L. 1990 Kinetic theory for a monodisperse gas–solid suspension. Phys. Fluids A 2, 1711.Google Scholar
Kok, J. B. W. 1989 Dynamics of gas bubbles moving through liquid. Ph.D. thesis, University of Twente, Enschede, The Netherlands.
Nigmatulin, R. I. 1979 Spatial averaging in the mechanics of heterogeneous and dispersed systems. Intl J. Multiphase Flow 5, 353.Google Scholar
Prosperetti, A. & Jones, A. V. 1984 Pressure forces in disperse two-phase flow. Intl J. Multiphase Flow 10, 425.Google Scholar
Rice, S. A. & Gray, P. 1965 The Statistical Mechanics of Simple Liquids. John Wiley & Sons.
Sangani, A. S. 1991 A pairwise interaction theory for determining the linear acoustic properties of dilute bubbly liquids. J. Fluid Mech. 232, 221.Google Scholar
Sangani, A. S. & Acrivos, A. 1982 Slow flow through a periodic array of spheres. Intl J. Multiphase Flow 8, 343.Google Scholar
Sangani, A. S. & Acrivos, A. 1983 The effective conductivity of a periodic array of spheres. Proc. R. Soc. Lond. 386, 263.Google Scholar
Sangani, A. S. & Didwania, A. K. 1993 Dynamic simulations of flows of bubbly liquids at large Reynolds numbers. J. Fluid Mech. (in press), referred to herein as I.Google Scholar
Sangani, A. S., Zhang, D. Z. & Prosperetti, A. 1991 The added mass, Basset, and viscous drag coefficients in nondilute bubbly liquids undergoing small-amplitude oscillatory motion. Phys. Fluids A 3, 2955.Google Scholar
Wijngaarden, L. van & Kapteyn, C. 1990 Concentration waves in dilute bubble/liquid mixtures. J. Fluid Mech. 212, 111.Google Scholar