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Magnetic field driven micro-convection in the Hele-Shaw cell: the Brinkman model and its comparison with experiment

Published online by Cambridge University Press:  04 June 2015

G. Kitenbergs ,
A. Tatulcenkovs ,
K. Ērglis ,
O. Petrichenko ,
R. Perzynski  and
A. Cēbers
G. Kitenbergs
Affiliation:
MMML Lab, Faculty of Physics and Mathematics, University of Latvia, Riga, LV-1002, Latvia Sorbonne Universités, UPMC Univ. Paris 06, UMR 8234, PHENIX, Paris, F-75005, France CNRS, UMR 8234, PHENIX, Paris, F-75005, France
A. Tatulcenkovs
Affiliation:
Department of Theoretical Physics, University of Latvia, Riga, LV-1002, Latvia
K. Ērglis
Affiliation:
MMML Lab, Faculty of Physics and Mathematics, University of Latvia, Riga, LV-1002, Latvia
O. Petrichenko
Affiliation:
MMML Lab, Faculty of Physics and Mathematics, University of Latvia, Riga, LV-1002, Latvia
R. Perzynski
Affiliation:
Sorbonne Universités, UPMC Univ. Paris 06, UMR 8234, PHENIX, Paris, F-75005, France CNRS, UMR 8234, PHENIX, Paris, F-75005, France
A. Cēbers*
Affiliation:
Department of Theoretical Physics, University of Latvia, Riga, LV-1002, Latvia
*
†Email address for correspondence: aceb@tok.sal.lv
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Abstract

The micro-convection caused by the ponderomotive forces of the self-magnetic field in a magnetic fluid is studied here both numerically and experimentally. The theoretical approach based on the general Brinkman model substantially improves the description with respect to the previously proposed Darcy model. The predictions of both models are here compared to finely controlled experiments. The Brinkman model, in contrast to the Darcy model, allows us to describe the formation of mushrooms on the plumes of the micro-convective flow and the width of the fingers. In the Brinkman approach, excellent quantitative agreement is also obtained for the finger velocity dynamics and the velocity maximal values as a function of the magnetic Rayleigh number. The diffusion coefficient of particles of the water-based magnetic colloid determined by the threshold field strength value of the micro-convection is significantly larger than the diffusion coefficient of individual particles. This result is confirmed by independent measurements of the diffusion coefficient at the smearing of the diffusion front.

JFM classification

Complex Fluids: Colloids Low-Reynolds-number flows: Hele-Shaw flows MHD and Electrohydrodynamics: Magnetic fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 774 , 10 July 2015 , pp. 170 - 191
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Copyright
© 2015 Cambridge University Press 

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Numerical simulation result of the Brinkman model

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Kitenbergs et al. supplementary movie

Numerical simulation result of the Darcy model

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Kitenbergs et al. supplementary movie

Experimental observation

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