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Motion and shape of a viscoelastic drop falling through a viscous fluid

Published online by Cambridge University Press:  29 December 2003

MICHAEL C. SOSTARECZ  and
ANDREW BELMONTE
MICHAEL C. SOSTARECZ
Affiliation:
The W. G. Pritchard Laboratories, Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
ANDREW BELMONTE
Affiliation:
The W. G. Pritchard Laboratories, Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
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Abstract

The steady shape of a drop of dilute polymer solution falling through a quiescent viscous Newtonian fluid is considered. Experimentally, we find that an immiscible drop of 0.16% xanthan gum in 80:20 glycerol/water falling through 9.8 P polydimethylsiloxane oil may exhibit a stable dimple at its trailing edge. At higher volumes the dimple extends far into the interior of the drop, and pinches off via a Rayleigh-type instability, injecting oil droplets into the polymer drop. At even larger volumes, a toroidal shape develops. We show that the dimpled shape can be reproduced mathematically with axisymmetric solutions for Stokes flow past a non-Newtonian drop, using the constitutive equation for a Simple Fluid of Order Three.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 497 , 25 December 2003 , pp. 235 - 252
Copyright
© 2003 Cambridge University Press

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