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Collective hydrodynamics of deformable drops and bubbles in dilute low Reynolds number suspensions

Published online by Cambridge University Press:  26 April 2006

Michael Manga  and
H. A. Stone
Michael Manga
Affiliation:
Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA
H. A. Stone
Affiliation:
Division of Applied Sciences, Harvard University, Cambridge, MA 02138, USA
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Abstract

Deformation due to hydrodynamic interactions between two deformable buoyant drops may result in the alignment and coalescence of horizontally offset drops. Three-dimensional boundary integral calculations are presented for systems containing two, three or four drops and it is argued that the interactions which occur between three drops or four drops may be characterized qualitatively by the two-drop interactions. In a dilute monodisperse suspension, the rate of coalescence of deformable drops is calculated using far-field analytical results and is found to be proportional to the Bond number. The rate of coalescence in a dilute polydisperse suspension of bubbles in corn syrup is determined by performing a large number of laboratory experiments for Bond numbers based on the larger bubble radius 15 < [Bscr ] < 120. The rate of coalescence is enhanced (by a factor of 10 for [Bscr ] = 10), owing to the effects of deformation, compared to the predictions of models which include hydrodynamic interactions and van der Waals forces among spherical bubbles. The rate of coalescence is greater than the rate predicted by the Smoluchowski model which ignores all hydrodynamic interactions. The experimental results are used to calculate the evolution of the bubble size distribution in suspensions using a standard one-dimensional population dynamics model; deformation affects the size distribution in suspensions, resulting in a wider range of bubble sizes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 300 , 10 October 1995 , pp. 231 - 263
Copyright
© 1995 Cambridge University Press

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References

Davis, R. H. 1984 The rate of coagulation of a dilute polydisperse system of sedimenting spheres. J. Fluid Mech. 145, 179–199.Google Scholar
Debruijn, R. A. 1989 Deformation and breakup of drops in simple shear flows. PhD thesis, Technical University at Eindhoven.
Durlofsky, L., Brady, J. F. & Bossis, G. 1987 Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180, 21–49.Google Scholar
Friedlander, S. K. 1977 Smoke, Dust and Haze: Fundamentals of Aerosol Behavior John Wiley & Sons.
Hocking, L. M. 1964 The behaviour of clusters of spheres falling in a viscous fluid. Part 2. Slow motion theory. J. Fluid Mech. 20, 129–139.Google Scholar
Kennedy, M. R., Pozrikidis, C. & Skalak, R. 1994 Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow. Computers Fluids 23, 251–278.Google Scholar
Koch, D. L. & Shaqfeh, E. S. G. 1989 The instability of a dispersion of sedimenting spheroids. J. Fluid Mech. 209, 521–542.Google Scholar
Manga, M. 1994 The motion of deformable drops and bubbles at low Reynolds numbers: Applications to selected problems in geology and geophysics. PhD thesis, Harvard University.
Manga, M. & Stone, H. A. 1993 Buoyancy-driven interactions between deformable drops at low Reynolds numbers. J. Fluid Mech. 256, 647–683.Google Scholar
Manga, M. & Stone, H. A. 1994 Interactions between bubbles in magmas and lavas: Effects of deformation. J. Volcanol. Geothermal Res. 63, 269–281.Google Scholar
Nevers, N. DE & Wu, J.-L. 1971 Bubble coalescence in viscous fluids. AIChE J. 17, 182–186.Google Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow Cambridge University Press.
Pozrikidis, C. 1994 Effects of surface viscosity on the finite deformation of a liquid drop and the rheology of dilute emulsions in simple shearing flow. J. Non-Newtonian Fluid Mech. 51, 161–178.Google Scholar
Rallison, J. M. 1981 A numerical study of the deformation and burst of a viscous drop in general shear flows. J. Fluid Mech. 109, 465–482.Google Scholar
Sahagian, D. L. 1985 Bubble migration and coalescence during the solidification of basaltic lava flows. J. Geol. 93, 205–211.Google Scholar
Satrape, J. V. 1992 Interactions and collisions of bubbles in thermocapillary motion. Phys. Fluids A 4, 1883–1900.Google Scholar
Tanzosh, J., Manga, M. & Stone, H. A. 1992 Boundary element methods for viscous freesurface flow problems: Deformation of single and multiple fluid-fluid interfaces. In Boundary Element Technolgies (ed. C.A. Brebbia & M.S. Ingber), pp. 19–39. Computational Mechanics Publications and Elsevier Applied Science, Southampton.
Unverdi, S. O. & Tryggvason, G. 1992 A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 25–37.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
Zinchenko, A. Z. 1982 Calculations of the effectiveness of gravitational coagulation of drops with allowance for internal circulation. Prikl. Mat. Mech. 46, 58–65.Google Scholar