TY - JOUR

T1 - Field-induced motion of ferrofluid droplets through immiscible viscous media

AU - Afkhami, S.

AU - Renardy, Y.

AU - Renardy, M.

AU - Riffle, J. S.

AU - St Perre, T.

N1 - Funding Information:
This research is supported by NSF-DMS 0405810, NCSA TG-CTS060013N and NSF-ARC Materials World Network for the Study of Macromolecular Ferrofluids (DMR-0602932 -LX0668968). We thank O. T. Mefford for discussions and data, and the referee who provided extensive comments for improvement.

PY - 2008/9

Y1 - 2008/9

N2 - 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.

AB - 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.

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U2 - 10.1017/S0022112008002589

DO - 10.1017/S0022112008002589

M3 - Article

AN - SCOPUS:54749151884

SN - 0022-1120

VL - 610

SP - 363

EP - 380

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -