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Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fields

Published online by Cambridge University Press:  08 September 2010

S. AFKHAMI ,
A. J. TYLER ,
Y. RENARDY ,
M. RENARDY ,
T. G. St. PIERRE ,
R. C. WOODWARD  and
J. S. RIFFLE
S. AFKHAMI
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
A. J. TYLER
Affiliation:
School of Physics, M013, The University of Western Australia, Crawley, WA 6009, Australia
Y. RENARDY*
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
M. RENARDY
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
T. G. St. PIERRE
Affiliation:
School of Physics, M013, The University of Western Australia, Crawley, WA 6009, Australia
R. C. WOODWARD
Affiliation:
School of Physics, M013, The University of Western Australia, Crawley, WA 6009, Australia
J. S. RIFFLE
Affiliation:
Department of Chemistry and the Macromolecules and Interfaces Institute, Virginia Tech, Blacksburg, VA 24061, USA
*
†Email address for correspondence: [email protected]
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Abstract

The effect of applied magnetic fields on the deformation of a biocompatible hydrophobic ferrofluid drop suspended in a viscous medium is investigated numerically and compared with experimental data. A numerical formulation for the time-dependent simulation of magnetohydrodynamics of two immiscible non-conducting fluids is used with a volume-of-fluid scheme for fully deformable interfaces. Analytical formulae for ellipsoidal drops and near-spheroidal drops are reviewed and developed for code validation. At low magnetic fields, both the experimental and numerical results follow the asymptotic small deformation theory. The value of interfacial tension is deduced from an optimal fit of a numerically simulated shape with the experimentally obtained drop shape, and appears to be a constant for low applied magnetic fields. At high magnetic fields, on the other hand, experimental measurements deviate from numerical results if a constant interfacial tension is implemented. The difference can be represented as a dependence of apparent interfacial tension on the magnetic field. This idea is investigated computationally by varying the interfacial tension as a function of the applied magnetic field and by comparing the drop shapes with experimental data until a perfect match is found. This estimation method provides a consistent correlation for the variation in interfacial tension at high magnetic fields. A conclusion section provides a discussion of physical effects which may influence the microstructure and contribute to the reported observations.

JFM classification

Drops and Bubbles: Drops
Type
Papers
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 358 - 384
Copyright
Copyright © Cambridge University Press 2010

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