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Deformation and breakup of a viscoelastic drop in a Newtonian matrix under steady shear

Published online by Cambridge University Press:  25 July 2007

NISHITH AGGARWAL  and
KAUSIK SARKAR
NISHITH AGGARWAL
Affiliation:
University of Delaware, Newark, USA
KAUSIK SARKAR
Affiliation:
University of Delaware, Newark, USA
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Abstract

The deformation of a viscoelastic drop suspended in a Newtonian fluid subjected to a steady shear is investigated using a front-tracking finite-difference method. The viscoelasticity is modelled using the Oldroyd-B constitutive equation. The drop response with increasing relaxation time λ and varying polymeric to the total drop viscosity ratio β is studied and explained by examining the elastic and viscous stresses at the interface. Steady-state drop deformation was seen to decrease from its Newtonian value with increasing viscoelasticity. A slight non-monotonicity in steady-state deformation with increasing Deborah number is observed at high Capillary numbers. Transient drop deformation displays an overshoot before settling down to a lower value of deformation. The overshoot increases with increasing β. The drop shows slightly decreased alignment with the flow with increasing viscoelasticity. A simple ordinary differential equation model is developed to explain the various behaviours and the scalings observed numerically. The critical Capillary number for drop breakup is observed to increase with Deborah number owing to the inhibitive effects of viscoelasticity, the increase being linear for small Deborah number.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 584 , 10 August 2007 , pp. 1 - 21
Copyright
Copyright © Cambridge University Press 2007

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