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Magnetic torque-induced suppression of van-der-Waals-driven thin liquid film rupture

Published online by Cambridge University Press:  26 January 2017

E. Kirkinis*
Affiliation:
Department of Physics, University of Washington, Seattle, WA 98195, USA
*
Email address for correspondence: kirkinis@uw.edu

Abstract

An ultra-thin film of a carrier liquid containing nanosize ferromagnetic particles sitting on a solid substrate and surrounded by an ambient gas phase can be acted upon, apart from viscous and capillary forces, by attractive van der Waals forces which may promote instability leading to film rupture and substrate dewetting. In this article we show that the collective rotation of the particles on the liquid–gas interface, due to a magnetic torque, competes against the instability induced by the van der Waals forces that tend to deepen depressions of the liquid. The competition between the two effects (forcing and instability) leads to the generation of a permanent nonlinear interfacial viscous–capillary wave. Thus, film rupture and substrate dewetting are both averted. This is a general effect that may also be employed to suppress other types of instabilities such as the Rayleigh–Taylor and thermocapillary instabilities. This effect has yet to be observed in experiment.

Type
Papers
Copyright
© 2017 Cambridge University Press 

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References

Andreev, A. V., Son, D. T. & Spivak, B. 2010 Hydrodynamics of liquids of chiral molecules and suspensions containing chiral particles. Phys. Rev. Lett. 104 (19), 198301.Google Scholar
Chaves, A. & Rinaldi, C. 2014 Interfacial stress balances in structured continua and free surface flows in ferrofluids. Phys. Fluids 26 (4), 042101.Google Scholar
Chaves, A., Zahn, M. & Rinaldi, C. 2008 Spin-up flow of ferrofluids: asymptotic theory and experimental measurements. Phys. Fluids 20 (5), 053102.Google Scholar
Condiff, D. W. & Dahler, J. S. 1964 Fluid mechanical aspects of antisymmetric stress. Phys. Fluids 7 (6), 842854.Google Scholar
Dahler, J. S. & Scriven, L. E. 1961 Angular momentum of continua. Nature 192, 3637.Google Scholar
Davis, M. J., Gratton, M. B. & Davis, S. H. 2010 Suppressing van der Waals driven rupture through shear. J. Fluid Mech. 661, 522539.Google Scholar
Davis, S. H. 1987 Thermocapillary instabilities. Annu. Rev. Fluid Mech. 19 (1), 403435.CrossRefGoogle Scholar
Davis, S. H. 2002 Interfacial fluid dynamics. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research (ed. Batchelor, G. K., Moffatt, H. K. & Worster, M. G.), pp. 151. Cambridge University Press.Google Scholar
Dussan V, E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77 (04), 665684.Google Scholar
Dzyaloshinskii, I. E., Lifshitz, E. M. & Pitaevskii, L. P. 1960 van der Waals forces in liquid films. Sov. Phys. JETP 37 (1), 161170.Google Scholar
Dzyaloshinskii, I. E., Lifshitz, E. M. & Pitaevskii, L. P. 1961 The general theory of van der Waals forces. Adv. Phys. 10 (38), 165209.Google Scholar
Erneux, T. & Davis, S. H. 1993 Nonlinear rupture of free films. Phys. Fluids A 5 (5), 11171122.Google Scholar
Kirkinis, E., Andreev, A. V. & Spivak, B. 2012 Electromagnetic propulsion and separation by chirality of nanoparticles in liquids. Phys. Rev. E 85, 016321.Google Scholar
Kirkinis, E. & Davis, S. H. 2013 Hydrodynamic theory of liquid slippage on a solid substrate near a moving contact line. Phys. Rev. Lett. 110, 234503.Google Scholar
Kirkinis, E. & Davis, S. H. 2014 Moffatt vortices induced by the motion of a contact line. J. Fluid Mech. 746, R3.CrossRefGoogle Scholar
Kirkinis, E. & Davis, S. H. 2015 Stabilization mechanisms in the evolution of thin liquid-films. Proc. R. Soc. Lond. A 471, 20150651.Google Scholar
O’Malley, R. E. Jr & Kirkinis, E. 2009 Examples illustrating the use of renormalization techniques for singularly perturbed differential equations. Stud. Appl. Maths 122 (2), 105122.Google Scholar
O’Malley, R. E. Jr. & Kirkinis, E. 2010 A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Maths 124 (4), 383410.Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 931980.Google Scholar
Rinaldi, C.2002 Continuum modeling of polarizable systems. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Rinaldi, C. & Zahn, M. 2002 Effects of spin viscosity on ferrofluid flow profiles in alternating and rotating magnetic fields. Phys. Fluids 14 (8), 28472870.Google Scholar
Shliomis, M. I. 1974 Magnetic fluids. Sov. Phys. Uspekhi 17 (2), 153169.Google Scholar
Shliomis, M. I. 2002 Ferrohydrodynamics: retrospective and issues. In Ferrofluids (ed. Odenbach, S.), pp. 85111. Springer.Google Scholar
Stewart, P. S. & Davis, S. H. 2013 Self-similar coalescence of clean foams. J. Fluid Mech. 722, 645664.Google Scholar
Torres-Díaz, I. & Rinaldi, C. 2014 Recent progress in ferrofluids research: novel applications of magnetically controllable and tunable fluids. Soft Matt. 10 (43), 85848602.Google Scholar
Williams, M. B. & Davis, S. H. 1982 Nonlinear theory of film rupture. J. Colloid Interface Sci. 90 (1), 220228.Google Scholar
Zahn, M. & Greer, D. R. 1995 Ferrohydrodynamic pumping in spatially uniform sinusoidally time-varying magnetic fields. J. Magn. Magn. Mater. 149 (1), 165173.Google Scholar