Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T13:43:41.840Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetic micro-droplet in rotating field: numerical simulation and comparison with experiment

Published online by Cambridge University Press:  22 May 2017

J. Erdmanis ,
G. Kitenbergs Open the ORCID record for G. Kitenbergs [Opens in a new window] ,
R. Perzynski  and
A. Cēbers Open the ORCID record for A. Cēbers [Opens in a new window]
J. Erdmanis
Affiliation:
MMML Lab, Faculty of Physics and Mathematics, University of Latvia, Riga, LV-1002, Latvia
G. Kitenbergs
Affiliation:
MMML Lab, Faculty of Physics and Mathematics, University of Latvia, Riga, LV-1002, Latvia
R. Perzynski
Affiliation:
Sorbonne Universités, UPMC Univ. Paris 06, CNRS, UMR 8234, PHENIX, Paris, F-75005, France
A. Cēbers*
Affiliation:
MMML Lab, Faculty of Physics and Mathematics, University of Latvia, Riga, LV-1002, Latvia Chair of Theoretical Physics, University of Latvia, Riga, LV-1002, Latvia
*
†Email address for correspondence: aceb@tok.sal.lv
Get access Rights & Permissions [Opens in a new window]

Abstract

Magnetic droplets obtained by induced phase separation in a magnetic colloid show a large variety of shapes when exposed to an external field. However, the description of the shapes is often limited. Here, we formulate an algorithm based on three-dimensional boundary-integral equations for strongly magnetic droplets in a high-frequency rotating magnetic field, allowing us to find their figures of equilibrium in three dimensions. The algorithm is justified by a series of comparisons with known analytical results. We compare the calculated equilibrium shapes with experimental observations and find a good agreement. The main features of these observations are the oblate–prolate transition, the flattening of prolate shapes with the increase of magnetic field strength and the formation of starfish-like equilibrium shapes. We show both numerically and in experiments that the magnetic droplet behaviour may be described with a triaxial ellipsoid approximation. Directions for further research are mentioned, including the dipolar interaction contribution to the surface tension of the magnetic droplets, accounting for the large viscosity contrast between the magnetic droplet and the surrounding fluid.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Drops and Bubbles: Drops MHD and Electrohydrodynamics: Magnetic fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , pp. 266 - 295
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Afkami, S., Tyler, A. J., Renardy, Y., Renardy, M., Pierre, T. G. St., Woodward, R. C. & Riffle, J. S. 2010 Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fields. J. Fluid Mech. 663, 358–384.Google Scholar
Arhipenko, V. I., Barkov, Yu. D. & Bashtovoi, V. G. 1978 Shape of a drop of magnetized fluid in a homogeneous magnetic field. Magnetohydrodynamics 14, 373–376.Google Scholar
Bacri, J. C., Cebers, A. & Perzynski, R. 1994 Behavior of a magnetic fluid microdrop in a rotating magnetic field. Phys. Rev. Lett. 72, 2705–2708.Google Scholar
Bacri, J. C. & Salin, D. 1982 Instability of ferrofluid magnetic drops under magnetic field. J. Phys. 43, L771–L777.Google Scholar
Bacri, J.-C. & Salin, D. 1983 Dynamics of the shape transition of a magnetic ferrofluid drop. J. Phys. Lett. 44, L415–L420.Google Scholar
Bashtovoi, V. G., Pogirnitskaya, S. G. & Reks, A. 1987 Determination of the shape of a free drop of magnetic fluid in a uniform magnetic field. Magnetohydrodynamics 23, 248–251.Google Scholar
Baygents, J. C., Rivette, N. J. & Stone, H. A. 1998 Electrohydrodynamic deformation and interaction of drop pairs. J. Fluid Mech. 368, 359–375.Google Scholar
Beleggia, M., Graef, M. De & Millev, Y. T. 2006 The equivalent ellipsoid of a magnetized body. J. Phys. D: Appl. Phys. 39, 891–899.Google Scholar
Blums, E., Cebers, A. & Maiorov, M. M. 1997 Magnetic Liquids. W. de G. Gruyter.Google Scholar
Brochu, T. & Bridson, R. 2009 Robust topological operations for dynamic explicit surfaces. SIAM J. Sci. Comput. 31 (4), 2472–2493.Google Scholar
Cebers, A 1985 Virial method of investigation of statics and dynamics of drops of magnetizable liquids. Magnetohydrodynamics 21, 19–26.Google Scholar
Cebers, A. & Lacis, S. 1995 Magnetic fluid free surface instabilities in high-frequency rotating magnetic fields. Braz. J. Phys. 25, 101–111.Google Scholar
Cebers, A. & Zemitis, A. 1983 Numerical simulation of mhd instability in the free surface of a gripped drop of magnetic liquid. Part I. Magnetohydrodynamics 19, 360–368.Google Scholar
Cristini, V., Bławzdziewicz, J. & Loewenberg, M. 2001 An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence. J. Comput. Phys. 168 (2), 445–463.Google Scholar
Dikansky, Y., Cebers, A. & Shatsky, V. P. 1990 Magnetic emulsion properties in electric and magnetic fields. 1. statics. Magnetohydrodynamics 26 (1), 25–30.Google Scholar
Douezan, S., Guevorkian, K., Naouar, R., Dufour, S., Cuvelier, D. & Brochard-Wyart, Fr. 2011 Spreading dynamics and wetting transition of cellular aggregates. Proc. Natl Acad. Sci. USA 18, 7315–7320.Google Scholar
Erdmanis, J.2016 MDrop: Julia code for simulations of magnetic liquid droplet. Available at: doi:10.5281/zenodo.168177.Google Scholar
Frasca, G., Du, V., Bacri, J. C., Gazeau, F., Gay, C. & Wilhelm, C. 2014 Magnetically shaped cell aggregates: from granular to contractile materials. Soft Matt. 10, 5045–5054.Google Scholar
Janiaud, E., Elias, F., Bacri, J.-C., Cabuil, V. & Perzynski, R. 2000 Spinning ferrofluid microscopic droplets. Magnetohydrodynamics 36, 300–311.Google Scholar
Jin, S., Lewis, R. R. & West, D. 2005 A comparison of algorithms for vertex normal computation. Vis. Comput. 21 (1–2), 71–82.Google Scholar
Keaveny, E. E. & Shelley, M. J. 2011 Applying a second-kind boundary integral equation for surface tractions in stokes flow. J. Comput. Phys. 230, 2141–2159.Google Scholar
Kitenbergs, Guntars2015 Hydrodynamic instabilities in microfluidic magnetic fluid flows. PhD thesis, University of Pierre and Marie Curie, University of Latvia.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1960 Electrodynamics of Continuous Media. Pergamon.Google Scholar
Massart, R. 1981 Preparation of aqueous magnetic liquids in alkaline and acidic media. IEEE Trans. Magn. 17 (2), 1247–1248.Google Scholar
Morozov, K. I., Engel, A. & Lebedev, A. V. 2002 Shape transformations in rotating ferrofluid drops. Europhys. Lett. 58, 229–235.Google Scholar
Morozov, K. I. & Lebedev, A. V. 2000 Bifurcations of the shape of a magnetic fluid droplet in a rotating magnetic field. J. Expl Theor. Phys. 91, 1029–1032.Google Scholar
Persson, P. O. & Strang, G. 2004 A simple mesh generator in MATLAB. SIAM Rev. 46 (2), 329–345.CrossRefGoogle Scholar
Pozrikidis, C. 2003 Practical Guide to Boundary Element Methods with Software Library BEMLIB. Chapman and Hall.Google Scholar
Pozrikidis, C. 2000 Theoretical and computational aspects of the self-induced motion of three-dimensional vortex sheets. J. Fluid Mech. 425, 335–366.Google Scholar
Pozrikidis, C. 2001 Interfacial dynamics for stokes flow. J. Comput. Phys. 169 (2), 250–301.Google Scholar
Rosensweig, R. E. 1985 Ferrohydrodynamics. Cambridge University Press.Google Scholar
Rowghanian, P., Meinhart, C. D. & Camps, O. 2016 Dynamics of ferrofluid drop deformations under spatially uniform magnetic fields. J. Fluid Mech. 802, 245–262.Google Scholar
Sandre, O., Browaeys, J., Perzynski, R., Bacri, J. C., Cabuil, V. & Rosensweig, R. E. 1999 Assembly of microscopic highly magnetic droplets: magnetic alignment versus viscous drag. Phys. Rev. E 59, 1736–1746.Google Scholar
Seeman, R., Brinkman, M., Pfohl, Th. & Herminghaus, S. 2012 Droplet based microfluidics. Rep. Prog. Phys. 75, 016601.Google Scholar
Taylor, G. I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280, 383–397.Google Scholar
Timonen, J. V. I., Latikka, M., Leibler, L., Ras, R. H. A. & Ikkala, O. 2013 Switchable static and dynamic self-assembly of magnetic droplets on superhydrophobic surfaces. Science 341 (6143), 253–257.Google Scholar
Zakinyan, A. & Dikansky, Yu. 2011 Drops deformation and magnetic permeability of a ferrofluid emulsion. Colloids Surf. A 380 (13), 314–318.Google Scholar
Zinchenko, A., Rother, M. A. & Davis, R. H. 1997 A novel boundary-integral algorithm for viscous interaction of deformable drops. Phys. Fluids 9 (6), 1493–1511.Google Scholar
Zinchenko, A., Rother, M. A. & Davis, R. H. 1999 Cusping, capture, and breakup of interacting drops by a curvatureless boundary-integral algorithm. J. Fluid Mech. 391, 249–292.Google Scholar