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Simultaneous sedimentation and coalescence of a dilute dispersion of small drops

Published online by Cambridge University Press:  26 April 2006

Hua Wang  and
Robert H. Davis
Hua Wang
Affiliation:
Department of Chemical Engineering, University of Colorado, Boulder, CO 80309-0424, USA Present address: Department of Chemical Engineering, MIT, Cambridge, MA 02139, USA.
Robert H. Davis
Affiliation:
Department of Chemical Engineering, University of Colorado, Boulder, CO 80309-0424, USA
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Abstract

Macroscopic phase separation and the evolution of the drop size distribution for non-homogeneous dispersions, in which buoyancy-driven settling and coalescence of drops cause spatial as well as temporal variations of the drop size distribution, was analysed by numerical solution of the population dynamics equations. Collision efficiencies based on detailed hydrodynamic interactions of spherical drops with clean interfaces were incorporated in the description of the pairwise drop coalescence rates. A dimensionless parameter that characterizes the relative importance of settling and coalescence was identified. For finite values of this parameter, the phase separation rates and average drop size initially increase owing to coalescence, and then decrease owing to the larger drops settling out of the dispersion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 295 , 25 July 1995 , pp. 247 - 261
Copyright
© 1995 Cambridge University Press

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References

Berry, E. X. & Reinhardt, R. L. 1974 An analysis of cloud drop growth by collection: Part I. Double distributions. J. Atmos. Sci. 31, 1814–1824.Google Scholar
Clark, T. L. 1973 Numerical modeling of the dynamics and microphysics of warm cumulus convection. J. Atmos. Sci. 30, 857–878.Google Scholar
Clark, T. L. & Hall, W. D. 1979 A numerical experiment on stochastic condensation theory. J. Atmos. Sci. 36, 470–483.Google Scholar
Crowley, W. P. 1968 Numerical advection experiments. Mon. Weather Rev. 96, 1–11.Google Scholar
Davis, R. H. & Acrivos, A. 1985 Sedimentation of noncolloidal particles at low Reynolds numbers. Ann. Rev. Fluid Mech. 17, 91–118.Google Scholar
Davis, R. H., Schonberg, J. A. & Rallison, J. M. 1989 The lubrication force between two viscous drops. Phys. Fluids A 1, 77–81.Google Scholar
Fletcher, C. A. J. 1991 Computational Techniques for Fluid Dynamics 1: Fundamentals and General Techniques. Springer.
Hadamard, J. S. 1911 Mouvement permenent lent d'une sphere liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. Paris 152, 1735.Google Scholar
Hall, W. D. 1980 A detailed microphysical model within a two-dimensional dynamic framework: Model description and preliminary results. J. Atmos. Sci. 37, 2486–2507.Google Scholar
Lax, P. D. & Wendroff, B. 1960 Systems of conservation laws. Commun. Pure Appl. Maths 13, 217–237.Google Scholar
Parsegian, V. A. & Weiss, G. H. 1981 Spectroscopic parameters for computation of van der Waals forces. J. Colloid Interface Sci. 81, 285–289.Google Scholar
Reddy, S. R., Melik, D. H. & Fogler, H. S. 1981 Emulsion stability-theoretical studies on simultaneous flocculation and creaming. J. Colloid Interface Sci. 82, 116–127.Google Scholar
Rogers, J. R. & Davis, R. H. 1990a Modeling of collision and coalescence of droplets in micro-gravity processing of Zn—Bi immiscible alloys. Metall. Trans 21A, 59–98.Google Scholar
Rogers, J. R. & Davis, R. H. 1990b The effects of van der Waals attractions on cloud growth by coalescence. J. Atmos. Sci. 47, 1075–1080.Google Scholar
Rybczynski, W. 1911 Uber die fortschreitende bewegung einer flussigen kugel in einem zahen medium. Bull. Acad. Sci. Cracovie, A 40.Google Scholar
Satrape, J. V. 1992 Interactions and collisions of bubbles in thermocapillary motion. Phys. Fluids A 4, 1883–1900.Google Scholar
Smithells, C. J. 1962 Metals-Reference Book, p. 698. Butterworths.
Wang, H. & Davis, R. H. 1993 Droplet growth due to Brownian, gravitational, or thermocapillary motion and coalescence in dilute dispersions. J. Colloid Interface Sci. 159, 108–118.Google Scholar
Zhang, X. & Davis, R. H. 1991 The rate of collisions due to Brownian or gravitational motion of small drops. J. Fluid Mech. 230, 479–504.Google Scholar
Zhang, X., Wang, H. & Davis, R. H. 1993 Collective effects of temperature gradients and gravity on droplet coalescence. Phys. Fluids A 5, 1602–1613.Google Scholar