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Instability of the miscible magnetic/non-magnetic fluid interface

Published online by Cambridge University Press:  03 March 2021

Mikhail S. Krakov*
Affiliation:
Belarusian National Technical University, 4 Nezavisimosti Ave., Minsk220013, Belarus
Arthur R. Zakinyan
Affiliation:
North-Caucasus Federal University, 1 Pushkin Street, Stavropol355017, Russia
Anastasia A. Zakinyan
Affiliation:
North-Caucasus Federal University, 1 Pushkin Street, Stavropol355017, Russia
*
Email address for correspondence: [email protected]

Abstract

The behaviour of the diffusion front of a magnetic fluid in contact with a miscible non-magnetic fluid in a normal magnetic field is studied. It was found that the magnetic field is a cause of the diffusion front bending and its movement accompanied by intense advective flows. These flows lead to the fast growth of the wavy shape of the diffusion front and formation of the peaks. This phenomenon is studied both numerically and experimentally. The reasons for the instability of the diffusion front in a magnetic field are discussed. The influence of the parameters of the problem (Schmidt number, magnetic Rayleigh number, magnetic field, the thickness of the layer, diffusion front width, etc.) on the instability parameters is studied both numerically and experimentally. It is shown that the studied instability differs from Rosensweig's instability.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Bacri, J.C., Salin, D. & Massart, R. 1982 Study of the deformation of ferrofluid droplets in a magnetic field. J. Phys. Lett. 43, 179184.CrossRefGoogle Scholar
Bashtovoi, V.G. 1978 Instability of a stationary thin layer of a magnetizable liquid. J. Appl. Mech. Tech. Phys. 19, 6569.CrossRefGoogle Scholar
Bashtovoi, V.G., Krakov, M.S. & Reks, A.G. 1985 Instability of a flat layer of magnetic liquid for supercritical magnetic fields. Magnetohydrodynamics 21 (1), 1924.Google Scholar
Berkovsky, B.M., Medvedev, V.F. & Krakov, M.S. 1993 Magnetic Fluids: Engineering Applications. Oxford University Press.Google Scholar
Bratsun, D., Kostarev, K., Mizev, A. & Mosheva, E. 2015 Concentration-dependent diffusion instability in reactive miscible fluids. Phys. Rev. E 92, 011003(R).CrossRefGoogle ScholarPubMed
Cai, G., Xue, L., Zhang, H. & Lin, J. 2017 A review on micromixers. Micromachines 8, 274300.CrossRefGoogle ScholarPubMed
Cao, Q., Han, X. & Li, L. 2012 Numerical analysis of magnetic nanoparticle transport in microfluidic systems under the influence of permanent magnets. J. Phys. D: Appl. Phys. 45, 465001.CrossRefGoogle Scholar
Cao, Q., Han, X. & Li, L. 2015 An active microfluidic mixer utilizing a hybrid gradient magnetic field. Intl J. Appl. Electromag. Mech. 47, 583592.CrossRefGoogle Scholar
Cebers, A. 1997 Stability of diffusion fronts of magnetic particles in porous media (Hele-Shaw cell) under the action of external magnetic field. Magnetohydrodynamics 33, 6774.Google Scholar
Cebers, A. & Igonin, M. 2002 Convective instability of magnetic colloid and forced Rayleigh scattering experiment. Magnetohydrodynamics 38, 265270.Google Scholar
Cowley, M.D. & Rosensweig, R.E. 1967 The interfacial stability of a ferromagnetic fluid. J. Fluid Mech. 30, 671688.CrossRefGoogle Scholar
Dikansky, Y.I., Zakinyan, A.R. & Mkrtchyan, L.S. 2010 Instability of a thin layer of a magnetic fluid in a perpendicular magnetic field. Tech. Phys. 55, 12701274.CrossRefGoogle Scholar
Eckert, K., Acker, M. & Shi, Y. 2004 Chemical pattern formation driven by a neutralization reaction. I. Mechanism and basic features. Phys. Fluids 16, 385399.CrossRefGoogle Scholar
Erglis, K., Tatulcenkov, A., Kitenbergs, G., Petrichenko, O., Ergin, F.G., Watz, B.B. & Cebers, A. 2013 Magnetic field driven micro-convection in the Hele-Shaw cell. J. Fluid Mech. 714, 612633.CrossRefGoogle Scholar
Hurle, D.T.J. & Jakeman, E. 1971 Soret-driven thermosolutal convection. J. Fluid Mech. 47 (4), 667687.CrossRefGoogle Scholar
Islam, A., Sharif, M.A.R. & Carlson, E.C. 2013 Density driven (including geothermal effect) natural convection of carbon dioxide in brine saturated porous media in the content of geological sequestration. In 2013 Proceedings of the Thirty-Eighth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, February 11–13, SGP-TR-198. Available at: https://pangea.stanford.edu/ERE/pdf/IGAstandard/SGW/2013/Islam.pdfGoogle Scholar
Ivanov, A.S. 2019 Experimental verification of anomalous surface tension temperature dependence at the interface between coexisting liquid-gas phases in magnetic and Stockmayer fluids. Phys. Fluids 31, 052001.CrossRefGoogle Scholar
Kitenbergs, G., Tatulcenkovs, A., Erglis, K., Petrichenko, O., Perzynski, R. & Cebers, A. 2015 Magnetic field driven micro-convection in the Hele-Shaw cell: the Brinkman model and its comparison with experiment. J. Fluid Mech. 774, 170191.CrossRefGoogle Scholar
Kitenbergs, G., Tatulcenkovs, A., Pukina, L. & Cebers, A. 2018 Gravity effects on mixing with magnetic micro-convection in microfluidics. Eur. Phys. J. E 41, 138148.CrossRefGoogle ScholarPubMed
Korteweg, D.J. 1901 Sur la forme que prennent les équations du mouvements des fluides si l'on tient compte des forces capillaires causées par des variations de densité considérables mais connues et sur la théorie de la capillarité dans l'hypothèse d'une variation continue de la densité. Arch. Néerl. Sci. Exact. Nat. 6, 124.Google Scholar
Patankar, S. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere Series on Computational Methods in Mechanics and Thermal Science. Taylor & Francis.Google Scholar
Schechter, R.S., Prigogine, I. & Hamm, J.R. 1972 Thermal diffusion and convective stability. Phys. Fluids 15 (3), 379386.CrossRefGoogle Scholar
Turner, J.S. 1985 Multicomponent convection. Annu. Rev. Fluid Mech. 17, 1144.CrossRefGoogle Scholar
Vand, V. 1948 Viscosity of solutions and suspensions. I. Theory. J. Phys. Colloid Chem. 52, 277299.CrossRefGoogle Scholar
Vislovich, A.N. 1990 Phenomenological equation of static magnetization of magnetic fluids. Magnetohydrodynamics 26, 178183.Google Scholar
Zakinyan, A., Mkrtchyan, L. & Dikansky, Y. 2016 Experimental investigation of surface instability of a thin layer of a magnetic fluid. Eur. J. Mech. (B/Fluids) 56, 172177.CrossRefGoogle Scholar
Zeldovich, Y.B. 1949 About surface tension of a boundary between two miscible fluids. Zhurnal Phizicheskoi Khimii (J. Phys. Chem.) 23, 931935 (in Russian).Google Scholar
Zhu, G.P. & Nguyen, N.T. 2012 Rapid magnetofluidic mixing in a uniform magnetic field. Lab on a Chip 12, 47724780.CrossRefGoogle Scholar

Krakov et al. supplementary movie 1

Animation of the diffusion front instability

Download Krakov et al. supplementary movie 1(Video)
Video 45.1 MB

Krakov et al. supplementary movie 2

Diffusion front instability in the experiment.

Download Krakov et al. supplementary movie 2(Video)
Video 1.3 MB