Abstract
The accelerations of sessile, viscous ferrofluid droplets across a flat, smooth hydrophobic substrate, due to surface deformations induced by a perpendicularly rotating magnetic field, are investigated with coupled finite element/boundary element computer simulations. For moderate field strengths, monotonically increasing relationships are found between acceleration and both magnetic field strength and inverse viscosity, with maxima at a rotation frequency approximately one-third that of the natural harmonic of the droplet. At higher field strengths a variety of more extreme droplet rolling, bounding and jumping behaviour in the opposite travel direction is observed for the same range of rotation speeds.
Similar content being viewed by others
References
Bormashenko E, Pogreb R, Bormashenko Y (2008) New investigations on ferrofluidics: ferrofluidic marbles and magnetic-field-driven drops on superhydrophobic surfaces. Langmuir 24:12119–22
García AA, Egatz-Gomez A, Lindsay SA (2007) Magnetic movement of biological fluid droplets. J Magn Magn Mater 311:238–243
Guo Z-G (2006) “Stick and slide” ferrofluidic droplets on superhydrophobic surfaces. Appl Phys Lett 89:081911
Hong X, Gao X, Jiang L (2007) Application of superhydrophobic surface with high adhesive force in no lost transport of superparamagnetic microdroplet. J Am Chem Soc 129:1478–9
Nguyen N-T, Yap Y-F, Liu J (2011) Numerical study of the formation process of ferrofluid droplets. Phys Fluids 23:10
Pelevina DA, Turkov VA, Kalmykov SA, Naletova VA (2015) The influence of a rotating magnetic field on the sample with magnetizable materials near the vessel bottom. Solid State Phenom 233:343–346. https://doi.org/10.4028/www.scientific.net/SSP.233-234.343
Pelevina DA, Turkov VA, Kalmykov SA, Naletova VA (2015) Motions of objects with magnetizable materials along a horizontal plane in a rotating magnetic field. J Magn Magn Mater 390
Persson PO, Strang G (2004) A simple mesh generator in MATLAB. SIAM Rev 46:329–345
Radcliffe AJ (2013) Non-conforming finite elements for axisymmetric charged droplet deformation dynamics and coulomb explosions. Int J Numer Methods Fluids 71:249–268. https://doi.org/10.1002/fld.3667
Radcliffe AJ (2016) Arbitrary Lagrangian-Eulerian simulations of highly electrically charged micro-droplet coulomb explosion deformation pathways. Int J Mod Simul Sci Comp 7:1650016-1-14. https://doi.org/10.1142/S1793962316500161
Radcliffe AJ (2021) Numerical study of ferro-droplet breakup initiation induced by a slowly rotating uniform magnetic field. Eng Rep. https://doi.org/10.1002/eng2.12316
Rayleigh L (1882) On the equilibrium of liquid conducting masses charged with electricity. Philos Mag 14:184–186
Rowghanian P, Meinhart CD, Campas O (2016) Dynamics of ferrofluid drop deformations under spatially uniform magnetic fields. J Fluid Mech 802:245–262
Schneider J, Egatz-Gomez A, Melle S (2008) Motion of viscous drops on superhydrophobic surfaces due to magnetic gradients. Colloids Surf A Physicochem Eng Aspects 323:19–27
Sterr V, Krauss R, Morozov KI, Rehberg I, Engel A, Richter R (2008) Rolling ferrofluid drop on the surface of a liquid. New J Phys 10:063029
Walkley MA, Gaskell PH, Jimack PK, Kelmanson MA, Summers JL (2005) Finite element simulation of three-dimensional free-surface flow problems. J Sci Comp 24:147–162
Woltermann M The Sphere Circumscribing a Tetrahedron, Web resource. http://www2.washjeff.edu/users/mwoltermann/Dorrie/70.pdf
Young T (1805) An essay on the cohesion of fluids. Philos Trans R Soc Lond 95:65–87
Zakinyan A, Nechaeva O, Dikansky Y (2012) Motion of a deformable drop of magnetic fluid on a solid surface in a rotating magnetic field. Exp Therm Fluid Sci 39:265–268
Zhao Y, Fang J, Wang H (2010) Magnetic liquid marbles: manipulation of liquid droplets using highly hydrophobic Fe3O4 nanoparticles. Adv Mater 22:707–10
Zhu GP, Nguyen NT, Ramanujan RV, Huang XY (2011) Nonlinear deformation of a ferrofluid droplet in a uniform magnetic field. Langmuir 27:14834–14841. https://doi.org/10.1021/la203931q
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Radcliffe, A.J. Droplet moonwalking. Engineering with Computers 38 (Suppl 4), 3099–3109 (2022). https://doi.org/10.1007/s00366-021-01434-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-021-01434-3