Skip to main content Accessibility help
×
Home

Dynamic simulations of flows of bubbly liquids at large Reynolds numbers

  • A. S. Sangani (a1) and A. K. Didwania (a1) (a2)

Abstract

Results of dynamic simulations of bubbles rising through a liquid are presented. The Reynolds number of the flow based on the radius and the terminal speed of bubbles is large compared to unity, and the Weber number, which is the ratio of inertial to surface tension forces, is small. It is assumed that the bubbles do not coalesce when they approach each other but rather bounce instantaneously, conserving the momentum and the kinetic energy of the system. The flow of the liquid is assumed to be irrotational and is determined by solving the many-bubble interaction problem exactly. The viscous force on the bubbles is estimated from the rate of viscous energy dissipation. It is shown that the random state of bubbly liquids under these conditions is unstable and that the bubbles form aggregates in planes transverse to gravity. These aggregates form even when the size distribution of the bubbles is non-uniform. While the instability results primarily from the nature of inertial interaction among pairs of bubbles, which causes them to be attracted toward each other when they are aligned in the plane perpendicular to gravity, it is shown that the presence of viscous forces facilitates the process.

Copyright

References

Hide All
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Biesheuvel, A. & Wijngaarden, L. van 1982 The motion of pairs of gas bubbles in a perfect liquid. J. Engng Maths 16, 349.
Davis, R. H., Schonberg, J. A. & Rallison, J. M. 1989 The lubrication force between two viscous drops. Phys. Fluids A 1, 77.
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.
Kang, I. S. & Leal, L. G. 1988 The drag coefficient for a spherical bubble in a uniform streming flow. Phys. Fluids 31, 233.
Kok, J. B. W. 1989 Dynamics of gas bubbles moving through liquid. Doctoral thesis, University of Twenty, Enschede, The Netherlands.
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.
Moore, D. W. 1963 The boundary layer on a special gas bubble. J. Fluid Mech. 16, 161.
Prosperetti, A. 1977 On the stability of spherically symmetric flows. Atti della Accademia Nazionale dei Lincei, Rendiconti della Classe di Scienze fisiche, mathematiche e naturali, vol. 62, p. 196.
Sangani, A. S. 1991 A pairwise interaction theory for determining the linear acoustic properties of dilute bubbly liquids. J. Fluid Mech. 232, 221.
Sangani, A. S. & Didwania, A. K. 1993 Dispersed-phase stress tensor in flows of bubbly liquids at large Reynolds numbers. J. Fluid Mech. 248, 27.
Sangani, A. S. & Yao, C. 1988 Bulk thermal conductivity of composites with spherical inclusions. J. Appl. Phys. 63, 1334.
Sangani, A. S., Zhang, D. Z. & Prosperetti, A. 1991 The added mass, Basset, and viscous drag coefficients in non-dilute bubbly liquids undergoing small-amplitude oscillatory motion. Phys. Fluids A 3, 2955.
Tam, P. D. 1981 The unsteady drag on a spherical bubble at large Reynolds numbers. Appl. Sci. Res. 38, 245.
Wijngaarden, L. van & Kapteyn, C. 1990 Concentration waves in dilute bubble/liquid mixtures. J. Fluid Mech. 212, 111.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Related content

Powered by UNSILO

Dynamic simulations of flows of bubbly liquids at large Reynolds numbers

  • A. S. Sangani (a1) and A. K. Didwania (a1) (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.