Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fields

Journal of Fluid Mechanics

Volumn 663, Issue , 2010, Pages 358-384

  Afkhami, S ^a,b   Tyler, A J ^c   Renardy, Y ^b   Renardy, M ^b   St Pierre, T G ^c   Woodward, R C ^c   Riffle, J S ^b  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^c UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

drops; ferrofluid; magnetohydrodynamics; volume of fluid method

Indexed keywords

BIOCOMPATIBILITY; DEFORMATION; DROPS; HYDROPHOBICITY; MAGNETIC FLUIDS; MAGNETOHYDRODYNAMICS;

ANALYTICAL FORMULAS; APPLIED MAGNETIC FIELDS; HIGH MAGNETIC FIELDS; LOW MAGNETIC FIELDS; NUMERICAL FORMULATION; TIME DEPENDENT SIMULATION; UNIFORM MAGNETIC FIELDS; VOLUME OF FLUID METHOD;

DROP BREAKUP;

COMPUTER SIMULATION; DROPLET; HYDROPHOBICITY; MAGNETIC FIELD; MAGNETOHYDRODYNAMICS; NUMERICAL METHOD;

EID: 78649963246     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010003551     Document Type: Article

References (49)

1. Afkhami, S., Renardy, Y., Renardy, M., Riffle, J. S. & St. Pierre, T. G. 2008a Field-induced motion of ferrofluid droplets through immiscible viscous media. J. Fluid Mech. 610, 363-380.
2. Afkhami, S., Renardy, Y., Renardy, M., Riffle, J. S. & St. Pierre, T. G. 2008b Numerical modeling of ferrofluid droplets in magnetic fields. In Proceedings of XVth International Congress on Rheology. American Institute of Physics.
3. Arkhipenko, V. I., Barkov, Y. D. & Bashtovoi, V. G. 1978 Investigation of the form of a drop of a magnetizing liquid in a homogeneous magnetic field. Magnetohydrodynamics 14, 131-134.
4. Bacri, J. C. & Salin, D. 1982 Instability of ferrofluid magnetic drops under magnetic field. J. Phys. Lett. 43, 649-654.
5. Basaran, O. A. & Wohlhuter, F. K. 1992 Effect of nonlinear polarization on shapes and stability of pendant and sessile drops in an electric (magnetic) field. J. Fluid Mech. 244, 1-16.
6. Blums, E., Cebers, A. & Maiorov, M. M. 1997 Magnetic Fluids. De Gruyter.
7. Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100, 335-354.
8. Cebers, A. 1982 Role of surface interactions in stratification of magnetic fluids. Magneto-hydrodynamics 18, 345-350.
9. Cebers, A. 1985 Virial method of investigation of statics and dynamics of drops of magnetizable liquids. Magnetohydrodynamics 21, 19-26.
10. Cebers, A. 2002 The anisotropy of the surface tension at the magnetic-field-induced phase transformations. J. Magn. Magn. Mat. 252, 259-261.
11. Dames, P., Gleich, B., Flemmer, A., Hajek, K., Seidl, N., Wiekhorst, F., Eberbeck, D., Bittmann, I., Bergemann, C., Weyh, T., Trahms, L., Rosenecker, J. & Rudolph, C. 2007 Targeted delivery of magnetic aerosol droplets to the lung. Nature Nanotech. 2, 495-499.
12. Dodgson, N. & Sozou, C. 1987 The deformation of a liquid drop by an electric field. J. Appl. Math. Phys. (ZAMP) 38, 424-432.
13. Drozdova, V. I., Skrobotova, T. V. & Chekanov, V. V. 1979 Experimental study of the hydrostatics characterizing the interphase boundary in a ferrofluid. Magnetohydrodynamics 15, 12-14.
14. Feng, J. Q. & Scott, T. C. 1996 A computational analysis of electrohydrodynamics of a leaky dielectric drop in an electric field. J. Fluid Mech. 311, 289-326.
15. Garton, C. G. & Krasucki, Z. 1964 Bubbles in insulating liquids: stability in an electric field. Proc. R. Soc. Lond. A 280, 211-226.
16. Holligan, D. L., Gillies, B. T. & Dailey, J. P. 2003 Magnetic guidance of ferrofluidic nanoparticles in an in vitro model of intraocular retinal repair. Nanotechnology 14 (6), 661-666.
17. Korlie, M. S., Mukherjee, A., Nita, B. G., Stevens, J. G., Trubatch, A. D. & Yecko, P. 2008 Modeling bubbles and droplets in magnetic fluids. J. Phys.: Condens. Matter 20, 204143.
18. Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S. & Zanetti, G. 1994 Modelling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 113, 134-147.
19. Landau, L. D. & Lifshitz, E. M. 1984 Electrodynamics of Continuous Media. Pergamon.
20. Lavrova, O., Matthies, G., Mitkova, T., Polevikov, V. & Tobiska, L. 2006 Numerical treatment of free surface problems in ferrohydrodynamics. J. Phys.: Condens. Matter 18 (38), S2657-S2669.
21. Lavrova, O., Matthies, G., Polevikov, V. & Tobiska, L. 2004 Numerical modeling of the equilibrium shapes of a ferrofluid drop in an external magnetic field. Proc. Appl. Math. Mech. 4, 704-705.
22. Li, J. & Renardy, Y. 1999 Direct simulation of unsteady axisymmetric core-annular flow with high viscosity ratio. J. Fluid Mech. 391, 123-149.
23. Li, J., Renardy, Y. & Renardy, M. 2000 Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method. Phys. Fluids 12, 269-282.
24. Liggieri, L., Sanfeld, A. & Steinchen, A. 1994 Effects of magnetic and electric fields on surface tension of liquids. Physica A 206, 299-331.
25. Liu, X., Kaminski, M. D., Riffle, J. S., Chen, H., Torno, M., Finck, M. R., Taylor, L. & Rosengart, A. J. 2007 Preparation and characterization of biodegradable magnetic carriers by single emulsion-solvent evaporation. J. Magn. Magn. Mat. 311, 84-87.
26. Markov, K. Z. 1999 Stability and instability in viscous fluids. In Heterogeneous Media: Modelling and Simulation (ed. K. Z. Markov & L. Preziosi), chap. 1, pp. 1-162.
27. Birkḧauser. Martin, J. E., Venturini, E. L. & Huber, D. L. 2008 Giant magnetic susceptibility enhancement in field-structured nanocomposites. J. Magn. Magn. Mat. 320, 2221-2227.
28. Mefford, O. T. 2007 Physical properties of macromolecule-metal oxide nanoparticle complexes: magnetophoretic mobility, size, and interparticle potentials. PhD thesis, Department of Chemistry, Virginia Tech.
29. Mefford, O. T., Carroll, M. R. J., Vadala, M. L., Goff, J. D., Mejia-Ariza, R., Saunders, M., Woodward, R. C., St. Pierre, T. G., Davis, R. M. & Riffle, J. S. 2008a Size analysis of PDMS-magnetite nanoparticle complexes: experiment and theory. Chem. Mater. 20 (6), 2184-2191.
30. Mefford, O. T., Vadala, M. L., Carroll, M. R. J., Mejia-Ariza, R., Caba, B. L., St. Pierre, T. G., Woodward, R. C., Davis, R. M. & Riffle, J. S. 2008b Stability of polydimethylsiloxane-magnetite nanoparticles against flocculation: interparticle interactions of polydisperse materials. Langmuir 24 (9), 5060-5069.
31. Mefford, O. T., Woodward, R. C., Goff, J. D., Vadala, T. P., St. Pierre, T. G., Dailey, J. P. & Riffle, J. S. 2007 Field-induced motion of ferrofluids through immiscible viscous media: testbed for restorative treatment of retinal detachment. J. Magn. Magn. Mater. 311, 347-353.
32. Mendelev, V. S. & Ivanov, A. O. 2004 Ferrofluid aggregation in chains under the influence of a magnetic field. Phys. Rev. E 70, 051502-1-051502-10.
33. Mikkelsen, C. I. 2005 Magnetic separation and hydrodynamic interactions in microfluidic systems. PhD thesis, Technical University of Denmark.
34. Miksis, M. J. 1981 Shape of a drop in an electric field. Phys. Fluids 24 (11), 1967-1972.
35. Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. McGraw-Hill.
36. Rallison, J. M. 1980 Note on the time-dependent deformation of a viscous drop which is almost spherical. J. Fluid Mech. 98 (3), 625-633.
37. Rosensweig, R. E. 1985 Ferrohydrodynamics. Cambridge University Press.
38. Scardovelli, R. & Zaleski, S. 1999 Direct numerical simulation of free surface and interfacial flow. Annu. Rev. Fluid Mech. 31, 567-604.
39. Shahnazian, H. & Odenbach, S. 2007 Yield stress in ferrofluids? Intl J. Mod. Phys. B 21, 4806-4812.
40. Sherwood, J. D. 1991 The deformation of a fluid drop in an electric field: a slender-body analysis. J. Phys. A 24, 4047-4053.
41. Stone, H. A., Lister, J. R. & Brenner, M. P. 1999 Drops with conical ends in electric and magnetic fields. Proc. R. Soc. Lond. A 455, 329-347.
42. Taylor, G. I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280, 383-397.
43. Tyatyushkin, A. N. & Verlarde, M. G. 2001 On the interfacial deformation of a magnetic liquid drop under the simultaneous action of electric and magnetic fields. J. Colloid Intl Sci. 235, 46-58.
44. Tyler, A. J. 2008 Presentation: dynamic behaviour of magnetic fluid droplets in non-uniform magnetic fields.
45. Tyler, A. J., Woodward, R. C. & St. Pierre, T. G. 2010 Variation in the surface energy of a ferrofluid droplet in an applied magnetic field (in preparation).
46. Voltairas, P. A., Fotiadis, D. I. & Massalas, L. K. 2001 Elastic stability of silicone ferrofluid internal tamponade (SFIT) in retinal detachment surgery. J. Magn. Mag. Mat. 225, 248-255.
47. Voltairas, P. A., Fotiadis, D. I. & Michalis, L. K. 2002 Hydrodynamics of magnetic drug targeting. J. Biomech. 35, 813-821.
48. Wohlhuter, F. K. & Basaran, O. A. 1992 Shapes and stability of pendant and sessile dielectric drops in an electric field. J. Fluid Mech. 235, 481-510.
49. Woodward, R. C., Heeris, J., St. Pierre, T. G., Saunders, M., Gilbert, E. P., Rutnakornpituk, M., Zhang, Q. & Riffle, J. S. 2007 A comparison of methods for the measurement of the particle-size distribution of magnetic nanoparticles. J. Appl. Cryst. 40, S495-S500.