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Magnetic field driven micro-convection in the Hele-Shaw cell

Published online by Cambridge University Press:  02 January 2013

K. Ērglis ,
A. Tatulcenkov ,
G. Kitenbergs ,
O. Petrichenko ,
F. G. Ergin ,
B. B. Watz  and
A. Cēbers
K. Ērglis
Affiliation:
Department of Theoretical Physics, University of Latvia, Riga, Zellu 8, LV-1002, Latvia
A. Tatulcenkov
Affiliation:
Department of Theoretical Physics, University of Latvia, Riga, Zellu 8, LV-1002, Latvia
G. Kitenbergs
Affiliation:
Department of Theoretical Physics, University of Latvia, Riga, Zellu 8, LV-1002, Latvia
O. Petrichenko
Affiliation:
Department of Theoretical Physics, University of Latvia, Riga, Zellu 8, LV-1002, Latvia
F. G. Ergin
Affiliation:
Dantec Dynamics A/S, Tonsbakken 16-18, Skovlunde, 2740, Denmark
B. B. Watz
Affiliation:
Dantec Dynamics A/S, Tonsbakken 16-18, Skovlunde, 2740, Denmark
A. Cēbers*
Affiliation:
Department of Theoretical Physics, University of Latvia, Riga, Zellu 8, LV-1002, Latvia
*
†Email address for correspondence: [email protected]
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Abstract

Micro-convection caused by ponderomotive forces of the self-magnetic field of a magnetic fluid in the Hele-Shaw cell under the action of a vertical homogeneous magnetic field is studied both experimentally and numerically. It is shown that a non-potential magnetic force at magnetic Rayleigh numbers greater than the critical value causes fingering at the interface between the miscible magnetic and non-magnetic fluids. The threshold value of the magnetic Rayleigh number depends on the smearing of the interface between fluids. Fingering with its subsequent decay due to diffusion of particles significantly increases the mixing at the interface. Velocity and vorticity fields at fingering are determined by particle image velocimetry measurements and qualitatively correspond well to the results of numerical simulations of the micro-convection in the Hele-Shaw cell carried out in the Darcy approximation, which account for ponderomotive forces of the self-magnetic field of the magnetic fluid. Gravity plays an important role at the initial stage of the fingering observed in the experiments.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows MHD and Electrohydrodynamics: MHD and Electrohydrodynamics MHD and Electrohydrodynamics: Magnetic fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 714 , 10 January 2013 , pp. 612 - 633
Copyright
©2013 Cambridge University Press

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References

Cabral, B. & Leedom, L. 1993 Imaging vector fields using line integral convolution. Proc. ACM 93, 263–270.Google Scholar
Cebers, A. 1981 Dynamics of magnetostatic instabilities. Magnetohydrodynamics 17, 113–121.Google Scholar
Cebers, A. 1997 Stability of diffusion fronts of magnetic particles in porous media under the action of external magnetic field. Magnetohydrodynamics 33, 48–55.Google Scholar
Cebers, A. & Maiorov, M. M. 1980 Magnetostatic instabilities in plane layers of magnetizable fluids. Magnetohydrodynamics 16, 21–27.Google Scholar
Chen, C.-Y. 2003 Numerical simulations of fingering instabilities in miscible magnetic fluids in a Hele-Shaw cell and the effect of Korteweg stress. Phys. Fluids 15, 1086–1089.Google Scholar
Chen, C.-Y. & Wen, C.-Y. 2002 Numerical simulations of miscible magnetic flows in a Hele-Shaw cell. Radial flows. J. Magnetism Magnetic Mater. 252, 296–298.Google Scholar
Derec, C., Boltenhagen, P., Neveu, S. & Bacri, J.-C. 2008 Magnetic instability between miscible fluids in a Hele-Shaw cell. Magnetohydrodynamics 44, 135–142.Google Scholar
Ergin, F. G., Watz, B. B., Erglis, K. & Cebers, A. 2010 Poor-contrast particle image processing in micro scale mixing. Proceedings of the ASME 10th BiennialConference on Engineering Systems Design and Analysis, pp. 1–5. ASME.Google Scholar
Goyal, N. & Meiburg, E. 2006 Miscible displacements in Hele-Shaw cells: two-dimensional base states and their linear stability. J. Fluid Mech. 558, 329–355.Google Scholar
Igonin, M. 2004 Hydrodynamic instabilities of miscible and immiscible magnetic fluids in a Hele-Shaw cell. PhD thesis, D. Diderot University Paris 7.Google Scholar
Igonin, M. & Cebers, A. 2003 Labyrinthine instability of miscible magnetic fluids. Phys. Fluids 15, 1734–1744.Google Scholar
Jackson, D. P., Goldstein, R. E. & Cebers, A. O. 1994 Hydrodynamics of fingering instabilities in dipolar fluids. Phys. Rev. E 50, 298–307.Google Scholar
Maiorov, M. & Cebers, A. 1983 Magnetic microconvection on the diffusion front of ferroparticles. Magnetohydrodynamics 19, 376–380.Google Scholar
Mezulis, A. & Blums, E. 2005 Experimental investigations of the microconvective instability in optically induced gratings. Magnetohydrodynamics 41, 341–348.Google Scholar
Rosensweig, R. E. 1985 Ferrohydrodynamics. Cambridge University Press.Google Scholar
Samarskij, A. A. & Gulin, A. V. 1989 Numerical Methods. Nauka.Google Scholar
Tan, C. T. & Homsy, G. M. 1988 Simulation of nonlinear viscous fingering in miscible displacement. Phys. Fluids 31, 1330–1338.Google Scholar
Wen, C.-Y., Chen, Ching-Yao & Kuan, D.-C. 2007 Experimental studies of labyrinthine instabilities of miscible ferrofluids in a Hele-Shaw cell. Phys. Fluids 19, 084101.Google Scholar
Zimmerman, W. B. & Homsy, G. M. 1992 Viscous fingering in miscible displacements: unification of effects of viscosity contrast, anisotropic dispersion, and velocity dependence of dispersion on nonlinear finger propagation. Phys. Fluids 4 (11), 2348–2359.Google Scholar