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Linear shape oscillations and polymeric time scales of viscoelastic drops

Published online by Cambridge University Press:  25 September 2013

Günter Brenn  and
Stephan Teichtmeister
Günter Brenn*
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Graz University of Technology, Inffeldgasse 25/F, 8010 Graz, Austria
Stephan Teichtmeister
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Graz University of Technology, Inffeldgasse 25/F, 8010 Graz, Austria
*
†Email address for correspondence: brenn@fluidmech.tu-graz.ac.at
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Abstract

We study small-amplitude axisymmetric shape oscillations of viscoelastic drops in a gas. The Jeffreys model is used as the rheological constitutive equation of the liquid, which represents a liquid with a frequency-dependent dynamic viscosity. The analysis of the time-dependent deformations caused by the oscillations yields the characteristic equation for the complex frequency, which describes the oscillation frequency and damping rate dependence on the viscous liquid behaviour and the stress relaxation and deformation retardation time scales ${\lambda }_{1} $ and ${\lambda }_{2} $ involved in the viscoelastic material law. The aim of this study is to quantify the influences of the two time scales on the oscillation behaviour of the drop and to propose an experimental method to determine one of the time scales by measuring damped oscillations of a drop. A proof-of-concept experiment is presented to show the potential and limitations of the method. Results show that values of ${\lambda }_{2} / {\lambda }_{1} $ from these measurements are orders of magnitude smaller than typical values used in simulations of viscoelastic flows.

JFM classification

Waves/Free-surface Flows: Capillary waves Drops and Bubbles: Drops Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 733 , 25 October 2013 , pp. 504 - 527
Copyright
©2013 Cambridge University Press 

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