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Field-induced motion of ferrofluid droplets through immiscible viscous media

Published online by Cambridge University Press:  08 August 2008

S. AFKHAMI ,
Y. RENARDY ,
M. RENARDY ,
J. S. RIFFLE  and
T. St PIERRE
S. AFKHAMI
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA
Y. RENARDY
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA
M. RENARDY
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA
J. S. RIFFLE
Affiliation:
Department of Chemistry, Virginia Tech, Blacksburg, VA 24061-0212, USA
T. St PIERRE
Affiliation:
School of Physics, M013, The University of Western Australia, Crawley, WA 6009, Australia
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Abstract

The motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field is investigated numerically in an axisymmetric geometry. Initially, the drop is spherical and placed at a distance away from the magnet. The governing equations are the Maxwell equations for a non-conducting flow, momentum equation and incompressibility. A numerical algorithm is derived to model the interface between a magnetized fluid and a non-magnetic fluid via a volume-of-fluid framework. A continuum-surface-force formulation is used to model the interfacial tension force as a body force, and the placement of the liquids is tracked by a volume fraction function. Three cases are studied. First, where inertia is dominant, the magnetic Laplace number is varied while the Laplace number is fixed. Secondly, where inertial effects are negligible, the Laplace number is varied while the magnetic Laplace number is fixed. In the third case, the magnetic Bond number and inertial effects are both small, and the magnetic force is of the order of the viscous drag force. The time taken by the droplet to travel through the medium and the deformations in the drop are investigated and compared with a previous experimental study and accompanying simpler model. The transit times are found to compare more favourably than with the simpler model.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 610 , 10 September 2008 , pp. 363 - 380
Copyright
Copyright © Cambridge University Press 2008

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