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The collision rate of small drops in linear flow fields

Published online by Cambridge University Press:  26 April 2006

Hua Wang ,
Alexander Z. Zinchenko  and
Robert H. Davis
Hua Wang
Affiliation:
Department of Chemical Engineering, University of Colorado, Boulder, CO 80309–0424, USA
Alexander Z. Zinchenko
Affiliation:
Department of Chemical Engineering, University of Colorado, Boulder, CO 80309–0424, USA
Robert H. Davis
Affiliation:
Department of Chemical Engineering, University of Colorado, Boulder, CO 80309–0424, USA
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Abstract

A dilute dispersion containing small, force-free drops of one fluid dispersed in a second, immiscible in a linear flow field is considered for small Reynolds numbers and large Péclet numbers under isothermal conditions. The emphasis of our analysis is on the effects of pairwise drop interactions on their collision rate, as described by the collision efficiency, using a trajectory analysis. Simple shear flow and uniaxial extensional or compressional flow are considered. For both flows, the collision efficiency decreases with increasing drop viscosity due to the effects of hydrodynamic interactions. It also decreases as the ratio of the smaller drop radius to the larger radius decreases. For uniaxial flow, finite collision rates are predicted in the absence of interdroplet forces for all finite values of the drop size ratio and the ratio of the viscosities of the drop and suspending medium. In contrast, several kinds of relative trajectories exist for a pair of drops in simple shear flow, including open trajectories, collision trajectories, and closed and semi-closed trajectories, in the absence of interdroplet forces. When the ratio of small to large drop diameters is smaller than a critical value, which increases with increasing drop viscosity, all of the relative trajectories that start with the two drops far apart remain open (no collisions), unless in the presence of attractive forces. Attractive van der Walls forces are shown to increase the collision rates.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 265 , 25 April 1994 , pp. 161 - 188
Copyright
© 1994 Cambridge University Press

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