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Interaction of a pair of ferrofluid drops in a rotating magnetic field

Published online by Cambridge University Press:  03 May 2018

Mingfeng Qiu
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
Shahriar Afkhami
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
Ching-Yao Chen
Affiliation:
Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 300, ROC
James J. Feng*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada
*
Email address for correspondence: james.feng@ubc.ca

Abstract

We use two-dimensional numerical simulation to study the interaction between a pair of ferrofluid drops suspended in a rotating uniform magnetic field. Numerical results show four distinct regimes over the range of parameters tested: independent spin, planetary motion, drop locking and direct coalescence. These are in qualitative agreement with experiments, and the transition between them can be understood from the competition between magnetophoretic forces and viscous drag. We further analyse in detail the planetary motion, i.e. the revolution of the drops around each other while each spins in phase with the external magnetic field. For drops, as opposed to solid microspheres, the interaction is dominated by viscous sweeping, a form of hydrodynamic interaction. Magnetic dipole–dipole interaction via mutual induction only plays a secondary role. This insight helps us explain novel features of the planetary revolution of the ferrofluid drops that cannot be explained by a dipole model, including the increase of the angular velocity of planetary motion with the rotational rate of the external field, and the attainment of a limit separation between the drops that is independent of the initial separation.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

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Qiu et al. supplementary movie 1

Experimental observation of the planetary motion of two ferrofluid drops in a rotation magnetic field, under conditions listed in the caption to figure 1 in the main article.

Download Qiu et al. supplementary movie 1(Video)
Video 2 MB

Qiu et al. supplementary movie 2

Numerical simulation of the planetary motion of two ferrofluid drops in a rotation magnetic field, under conditions listed in the caption to figure 6 in the main article.

Download Qiu et al. supplementary movie 2(Video)
Video 898 KB

Qiu et al. supplementary movie 3

Numerical simulation of the drop locking regime under conditions listed in the caption to figure 15 in the main article.

Download Qiu et al. supplementary movie 3(Video)
Video 107 KB

Qiu et al. supplementary movie 4

Experimental observation of drop locking, corresponding to the snapshots of figure 16 in the main article.

Download Qiu et al. supplementary movie 4(Video)
Video 3 MB
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