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Differential analysis of capillary breakup rheometry for Newtonian liquids

Published online by Cambridge University Press:  08 September 2016

Louise L. McCarroll ,
Michael J. Solomon  and
William W. Schultz
Louise L. McCarroll
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Michael J. Solomon
Affiliation:
Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
William W. Schultz*
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: schultz@umich.edu
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Abstract

We present a Newtonian, one-dimensional, differential analysis for capillary breakup rheometry (CBR) to determine the surface tension to viscosity ratio $\unicode[STIX]{x1D6FC}$. Our local differential analysis does not require specific assumptions for the axial force to preclude its measurement. Our analysis indicates that measuring gradients in filament curvature is necessary to accurately determine $\unicode[STIX]{x1D6FC}$ when axial force is not measured. CBR experiments were performed on five silicone oils ($0.35~\text{Pa}~\text{s}<\unicode[STIX]{x1D707}<10~\text{ Pa}~\text{s}$), three sample volumes, and three strains to evaluate the operating range of the differential analysis and compare its performance to that of a standard integral method from literature. We investigate the role of filament asymmetry, caused mainly by gravity, on the performance of the differential method for the range of conditions studied. Experimental and analytical details for resolving gradients of curvature are also given.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Liquid bridges Non-Newtonian Flows: Rheology
Type
Papers
Information
Journal of Fluid Mechanics , Volume 804 , 10 October 2016 , pp. 116 - 129
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Copyright
© 2016 Cambridge University Press 

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