Abstract
In this paper, we present a numerical and experimental study of the laminar flow that results from the interaction of vortices driven electromagnetically in a thin layer of an electrolyte. The fluid motion is generated by a Lorentz force due to a uniform D.C. current and a non-uniform magnetic field produced by different symmetric arrays of small permanent magnets placed on the perimeter of a circle. Depending on the number of magnets and the intensity of the electric current, we find that steady or unsteady vortex flow patterns may arise. We developed a quasi-two-dimensional numerical model that accounts for the effect of the boundary layer adhered to the bottom wall. Once the velocity field is obtained, we perform a Lagrangian tracking that shows a good qualitative comparison with the experimental flow visualization. From numerical and experimental results, a map of stability that defines regions of steady and unsteady flow, according to the electric current intensity and magnet arrays, is built. We find that the larger the number of magnets, the less intense the applied current required to transit from steady to unsteady flow patterns.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aref H (2007) J Math Phys 48:065401
Aref H (2009) Phys Fluids 21:094101
Clercx HJH, Van Heijst GJF, Zoeteweij (2003) Phys Rev E 67:066303
Dirksen T (2012) Masters thesis, Technical University of Denmark
Durán-Matute M, Kamp LPJ, Clercx HJH, van Heijst GJF (2010) Phys Rev E 82:026314
Figueroa A, Cuevas S, Ramos E (2011) Phys Fluids 23:013601
Figueroa A, Demiaux F, Cuevas S, Ramos E (2009) J Fluid Mech 641:245–261
Figueroa A, Meunier P, Cuevas S, Villermaux E, Ramos E (2014) Phys Fluids 26:013601
Helmholtz HV (1858) J für die reine und angewandte Mathematik 55:25–55
Kelvin L (1867) Proc R Soc Edinb VI:94–105
Lara CG (2013) Theoretical and experimental study of electromagnetic stirring in shallow fluid flows. MSc Thesis, National Autonomous University of Mexico (in Spanish)
McCaig M (1977) Wiley
Meunier P, Leweke T (2005) J Fluid Mech 533:125–159
Ottino JM (1990) Annu Rev Fluid Mech 22:207–253
Rossi L, Lardeau S (2011) J Turbul 12:1–31
Rossi L, Vassilicos JC, Hardalupas Y (2006) Phys Rev Lett 97(14):144501
Satijn MP, Cense AW, Verzicco R, Clercx HJH, Van Heijist GJF (2001) Phys Fluids 13(7):1932–1945
Sommeria J (1988) J Fluid Mech 189:553–569
Versteeg HK, Malalasekera W (1995) Longman Scientific & Technical
Acknowledgments
Financial support from CONACYT, Mexico, through Project 131399 is gratefully acknowledged. C.G. Lara and A. Figueroa thank, respectively, a grant and a posdoctoral fellowship from CONACYT.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Lara, C.G., Figueroa, A., Cuevas, S. (2015). Steady and Unsteady Vortex Flow Generated by Electromagnetic Forcing. In: Klapp, J., Ruíz Chavarría, G., Medina Ovando, A., López Villa, A., Sigalotti, L. (eds) Selected Topics of Computational and Experimental Fluid Mechanics. Environmental Science and Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-11487-3_32
Download citation
DOI: https://doi.org/10.1007/978-3-319-11487-3_32
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11486-6
Online ISBN: 978-3-319-11487-3
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)