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Near-contact thermocapillary motion of two non-conducting drops

Published online by Cambridge University Press:  26 April 2006

Michael Loewenberg  and
Robert H. Davis
Michael Loewenberg
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

The axisymmetric, thermocapillary-driven motion of a pair of non-conducting, spherical drops in near contact is analysed for conditions of small Reynolds and Marangoni numbers. The pairwise motion and an associated contact force are computed by considering touching drops in point contact. Relative motion for nearly touching drops results from the contact force balanced by a lubrication resistance. A new, analytical solution is obtained for the axisymmetric temperature field around an unequal pair of non-conducting, tangent spheres embedded in an ambient temperature gradient. Numerical results for the pairwise migration velocity, contact force, and the relative and individual drop velocities are presented for all size ratios and a wide range of viscosity ratios, and asymptotic formulae are derived for small size ratios. For nearly equisized drops, the ratio of the relative velocity for two drops in near contact to that for widely separated drops is similar for thermocapillary-driven and gravity-driven motion. For small and moderate size ratios, however, this ratio is much larger for thermocapillary-driven relative motion than for gravity-driven relative motion, indicating that the former represents a more efficient coalescence mechanism. An explanation for this finding is provided in terms of the thermocapillary motion of the interface of the larger drop aiding the withdrawal of continuous phase from between the two drops.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 107 - 131
Copyright
© 1993 Cambridge University Press

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