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Magnetoelastic pattern formation in field-responsive fluids

Pedro O. S. Livera* and José A. Miranda†

  • Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil

  • *pedro.oslivera@outlook.com
  • †jme@df.ufpe.br
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Phys. Rev. Fluids 5, 014006 – Published 31 January, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.014006

Abstract

We study the development of interfacial magnetoelastic patterns when an initially circular droplet of a field-activated fluid (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. Elasticity takes effect when the fluids are brought into contact and, due to a chemical reaction, the interface separating them becomes a gel-like elastic layer. By modeling the interface as an elastic membrane having a curvature-dependent bending rigidity, a perturbative mode-coupling theory is employed to investigate the weakly nonlinear dynamics of the system. In this context, we examine how the interface responds to the influence of magnetic, elastic, and yield stress forces. Our findings support the relevance of a curvature weakening effect, in the sense that magnetoelastic fingering structures tend to arise and protrude in regions of lower bending rigidity. We contrast the magnetoelastic patterns with the corresponding usual shapes of magnetic fluid interfaces without bending rigidity, but with surface tension.

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References (50)

  1. R. E. Rosensweig, Ferrohydrodynamics (Cambridge University Press, Cambridge, 1985).
  2. E. Blums, A. Cebers, and M. M. Maiorov, Magnetic Fluids (de Gruyter, New York, 1997).
  3. J. M. Ginder, Behavior of magnetorheological fluids, MRS Bull. 23, 26 (1998).
  4. G. Bossis, S. Lacis, A. Meunier, and O. Volkova, Magnetorheological fluids, J. Magn. Magn. Mater. 252, 224 (2002).
  5. S. Genç and P. P. Phulé, Rheological properties of magnetorheological fluids, Smart Mater. Struct. 11, 140 (2002).
  6. P. Coussot, Yield stress fluid flows: A review of experimental data, J. Non-Newtonian Fluid Mech. 211, 31 (2014).
  7. S. A. Lira and J. A. Miranda, Field-controlled adhesion in confined magnetorheological fluids, Phys. Rev. E 80, 046313 (2009).
  8. R. H. Ewoldt, P. Tourkine, G. H. McKinley, and A. E. Hosoi, Controllable adhesion using field-activated fluids, Phys. Fluids 23, 073104 (2011).
  9. See, for instance, D. Andelman and R. E. Rosensweig, Modulated phases: Review and recent results, J. Phys. Chem. B 113, 3785 (2009); J.-C. Bacri and F. Elias, in Morphogenesis-Origins of Patterns and Shapes, edited by P. Bourgine and A. Lesne (Springer, New York, 2011); I. Torres-Díaz and C. Rinaldi, Recent progress in ferrofluids research: Novel applications of magnetically controllable and tunable fluids, Soft Matter 10, 8584 (2014).
  10. J. White, J. Oakley, M. Anderson, and R. Bonazza, Experimental measurements of the nonlinear Rayleigh-Taylor instability using a magnetorheological fluid, Phys. Rev. E 81, 026303 (2010).
  11. P. G. Saffman and G. I. Taylor, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. R. Soc. London Ser. A 245, 312 (1958).
  12. For review articles on Hele-Shaw flows see D. Bensimon, L. P. Kadanoff, S. Liang, B. I. Shraiman, and C. Tang, Viscous flows in two dimensions, Rev. Mod. Phys. 58, 977 (1986); G. M. Homsy, Viscous fingering in porous media, Annu. Rev. Fluid Mech. 19, 271 (1987); K. V. McCloud and J. V. Maher, Experimental perturbations to Saffman-Taylor flow, Phys. Rep. 260, 139 (1995); J. Casademunt, Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges, Chaos 14, 809 (2004).
  13. A. O. Tsebers and M. M. Maiorov, Magnetostatic instabilities in plane layers of magnetizable liquids, Magnetohydrodynamics 16, 21 (1980).
  14. A. O. Tsebers, Dynamics of magnetostatic instabilities, Magnetohydrodynamics 17, 113 (1981).
  15. D. P. Jackson, R. E. Goldstein, and A. O. Cebers, Hydrodynamics of fingering instabilities in dipolar fluids, Phys. Rev. E 50, 298 (1994).
  16. J. Kent-Dobias and A. J. Bernoff, Energy-driven pattern formation in planar dipole-dipole systems in the presence of weak noise, Phys. Rev. E 91, 032919 (2015).
  17. R. M. Oliveira, J. A. Miranda, and E. S. G. Leandro, Ferrofluid patterns in a radial magnetic field: Linear stability, nonlinear dynamics, and exact solutions, Phys. Rev. E 77, 016304 (2008).
  18. S. A. Lira, J. A. Miranda, and R. M. Oliveira, Field-induced patterns in confined magnetorheological fluids, Phys. Rev. E 81, 046303 (2010).
  19. P. H. A. Anjos, S. A. Lira, and J. A. Miranda, Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes, Phys. Rev. Fluids 3, 044002 (2018).
  20. S. Elborai, D.-K. Kim, X. He, S.-H. Lee, S. Rhodes, and M. Zahn, Self-forming, quasi-two-dimensional, magnetic-fluid patterns with applied in-plane-rotating and dc-axial magnetic fields, J. Appl. Phys. 97, 10Q303 (2005).
  21. E. O. Dias and J. A. Miranda, Azimuthal field instability in a confined ferrofluid, Phys. Rev. E 91, 023020 (2015).
  22. E. O. Dias, S. A. Lira, and J. A. Miranda, Interfacial patterns in magnetorheological fluids: Azimuthal field-induced structures, Phys. Rev. E 92, 023003 (2015).
  23. C.-Y. Chen and T.-S. Lin, in Advances in Computational Fluid-Structure Interaction and Flow Simulation, edited by Y. Bazilevs and K. Takizawa (Springer Nature, Basel, 2016).
  24. T. Podgorski, M. C. Sostarecz, S. Zorman, and A. Belmonte, Fingering instabilities of a reactive micellar interface, Phys. Rev. E 76, 016202 (2007).
  25. J. Fernandez and G. M. Homsy, Viscous fingering with chemical reaction: Effect of in-situ production of surfactants, J. Fluid Mech. 480, 267 (2003).
  26. Y. Nagatsu, K. Matsuda, Y. Kato, and Y. Tada, Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions, J. Fluid Mech. 571, 475 (2007).
  27. Y. Nagatsu, C. Iguchi, K. Matsuda, Y. Kato, and Y. Tada, Miscible viscous fingering involving viscosity changes of the displacing fluid by chemical reactions, Phys. Fluids 22, 024101 (2010).
  28. Z. Niroobakhsh, M. Litman, and A. Belmonte, Flow instabilities due to the interfacial formation of surfactant–fatty acid material in a Hele-Shaw cell, Phys. Rev. E 96, 053102 (2017).
  29. F. Haudin, J. H. E. Cartwright, F. Brau, and A. De Wit, Spiral precipitation patterns in confined chemical gardens, Proc. Natl. Acad. Sci. USA 111, 17363 (2014).
  30. Y. Nagatsu, Y. Ishii, Y. Tada, and A. De Wit, Hydrodynamic Fingering Instability Induced by a Precipitation Reaction, Phys. Rev. Lett. 113, 024502 (2014).
  31. F. Haudin and A. De Wit, Patterns due to an interplay between viscous and precipitation-driven fingering, Phys. Fluids 27, 113101 (2015).
  32. F. Haudin, V. Brasiliense, J. H. Cartwright, F. Brau, and A. De Wit, Genericity of confined chemical garden patterns with regard to changes in the reactants, Phys. Chem. Chem. Phys. 17, 12804 (2015).
  33. Y. Nagatsu, A. Hayashi, M. Ban, Y. Kato, and Y. Tada, Spiral pattern in a radial displacement involving a reaction-producing gel, Phys. Rev. E 78, 026307 (2008).
  34. Y. Sumino, H. Kitahata, Y. Shinohara, N. L. Yamada, and H. Seto, Formation of a multiscale aggregate structure through spontaneous blebbing of an interface, Langmuir 28, 3378 (2012).
  35. A. He, J. S. Lowengrub, and A. Belmonte, Modeling an elastic fingering instability in a reactive Hele-Shaw flow, SIAM J. Appl. Math. 72, 842 (2012).
  36. G. D. Carvalho, J. A. Miranda, and H. Gadêlha, Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study, Phys. Rev. E 88, 053006 (2013).
  37. M. Zhao, A. Belmonte, S. Li, X. Li, and J. S. Lowengrub, Nonlinear simulations of elastic fingering in a Hele-Shaw cell, J. Comput. Appl. Math. 307, 394 (2016).
  38. P. H. A. Anjos, G. D. Carvalho, S. A. Lira, and J. A. Miranda, Wrinkling and folding patterns in a confined ferrofluid droplet with an elastic interface, Phys. Rev. E 99, 022608 (2019).
  39. J. A. Miranda and M. Widom, Radial fingering in a Hele-Shaw cell: A weakly nonlinear analysis, Physica D 120, 315 (1998).
  40. L. Gordillo and E. Knobloch, Fluid-supported elastic sheet under compression: Multifold solutions, Phys. Rev. E 99, 043001 (2019).
  41. T. P. Meyrath, Experiments with Bose-Einstein condensation in an optical box, Ph.D. thesis, The University of Texas at Austin, 2005.
  42. T. H. Bergeman, G. Erez, and H. J. Metcalf, Magnetostatic trapping field for neutral atoms, Phys. Rev. A 35, 1535 (1987).
  43. J. G. E. Harris, R. A. Michniak, S. V. Nguyen, W. C. Campbell, D. Egorov, S. E. Maxwell, L. D. van Buuren, and J. M. Doyle, Deep superconducting magnetic traps for neutral atoms and molecules, Rev. Sci. Instrum. 75, 17 (2004).
  44. C.-Y. Chen, Y.-S. Yang, and J. A. Miranda, Miscible ferrofluid patterns in a radial magnetic field, Phys. Rev. E 80, 016314 (2009).
  45. C.-Y. Chen, W.-L. Wu, and J. A. Miranda, Magnetically induced spreading and pattern selection in thin ferrofluid drops, Phys. Rev. E 82, 056321 (2010).
  46. R. Aslam and W. Gonzáles-Viñas, Pattern formation in spin-coating of hybrid colloids in different magnetic field configurations, J. Phys. D 52, 344001 (2019).
  47. G. H. Covey and B. R. Stanmore, Use of the parallel-plate plastometer for the characterisation of viscous fluids with a yield stress, J. Non-Newtonian Fluid Mech. 8, 249 (1981).
  48. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 2000).
  49. Fluid-Structure Interactions in Low-Reynolds-Number Flows, edited by C. Duprat and H. Stone (RSC, Cambridge, 2016).
  50. E. Alvarez-Lacalle, E. Pauné, J. Casademunt, and J. Ortín, Systematic weakly nonlinear analysis of radial viscous fingering, Phys. Rev. E 68, 026308 (2003).

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Phys. Rev. Fluids 5, 014006– Published 31 January, 2020
  • Received 24 October 2019
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