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Electrohydrodynamic rotation of drops at large electric Reynolds numbers

  • Ehud Yariv (a1) and Itzchak Frankel (a2)

When subject to sufficiently strong electric fields, particles and drops suspended in a weakly conducting liquid exhibit spontaneous rotary motion. This so-called Quincke rotation is a fascinating example of nonlinear symmetry-breaking phenomena. To illuminate the rotation of liquid drops we here analyse the asymptotic limit of large electric Reynolds numbers, $\mathit{Re}\gg 1$ , within the framework of a two-dimensional Taylor–Melcher electrohydrodynamic model. A non-trivial dominant balance in this singular limit results in both the fluid velocity and surface-charge density scaling as $\mathit{Re}^{-1/2}$ . The flow is governed by a self-contained nonlinear boundary-value problem that does not admit a continuous fore–aft symmetric solution, thus necessitating drop rotation. Furthermore, thermodynamic arguments reveal that a fore–aft asymmetric solution exists only when charge relaxation within the suspending liquid is faster than that in the drop. The flow problem possesses both mirror-image (with respect to the direction of the external field) and flow-reversal symmetries; it is transformed into a universal one, independent of the ratios of electric conductivities and dielectric permittivities in the respective drop phase and suspending liquid phase. The rescaled angular velocity is found to depend weakly upon the viscosity ratio. The corresponding numerical solutions of the exact equations indeed collapse at large $\mathit{Re}$ upon the asymptotically calculated universal solution.

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Bricard, A., Caussin, J.-B., Desreumaux, N., Dauchot, O. & Bartolo, D. 2013 Emergence of macroscopic directed motion in populations of motile colloids. Nature 503 (7474), 9598.
Cēbers, A. 2004 Bistability and negative viscosity for a suspension of insulating particles in an electric field. Phys. Rev. Lett. 92 (3), 034501.
Das, D. & Saintillan, D. 2013 Electrohydrodynamic interaction of spherical particles under Quincke rotation. Phy. Rev. E 87 (4), 043014.
Feng, J. Q. 2002 A 2D electrohydrodynamic model for electrorotation of fluid drops. J. Colloid Interface Sci. 246 (1), 112121.
Ha, J.-W. & Yang, S.-M. 2000 Electrohydrodynamics and electrorotation of a drop with fluid less conductive than that of the ambient fluid. Phys. Fluids 12 (4), 764772.
He, H., Salipante, P. F. & Vlahovska, P. M. 2013 Electrorotation of a viscous droplet in a uniform direct current electric field. Phys. Fluids 25 (3), 032106.
Jones, T. B. 1984 Quincke rotation of spheres. IEEE Trans. Ind. Applics. 4, 845849.
Krause, S. & Chandratreya, P. 1998 Electrorotation of deformable fluid droplets. J. Colloid Interface Sci. 206 (1), 1018.
Lanauze, J. A., Walker, L. M. & Khair, A. S. 2015 Nonlinear electrohydrodynamics of slightly deformed oblate drops. J. Fluid Mech. 774, 245266.
Leal, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press.
Lemaire, E. & Lobry, L. 2002 Chaotic behavior in electro-rotation. Physica A 314 (1), 663671.
Lemaire, E., Lobry, L., Pannacci, N. & Peters, F. 2008 Viscosity of an electro-rheological suspension with internal rotations. J. Rheol. 52 (3), 769783.
Lobry, L. & Lemaire, E. 1999 Viscosity decrease induced by a DC electric field in a suspension. J. Electrostat. 47 (1), 6169.
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1 (1), 111146.
Pannacci, N., Lemaire, E. & Lobry, L. 2007a Rheology and structure of a suspension of particles subjected to Quincke rotation. Rheol. Acta 46 (7), 899904.
Pannacci, N., Lobry, L. & Lemaire, E. 2007b How insulating particles increase the conductivity of a suspension. Phys. Rev. Lett. 99 (9), 094503.
Peters, F., Lobry, L. & Lemaire, E. 2005 Experimental observation of Lorenz chaos in the Quincke rotor dynamics. Chaos 15 (1), 013102.
Quincke, G. 1896 Ueber Rotationen im constanten electrischen Felde. Ann. Phys. Chem. 59, 417486.
Salipante, P. F. & Vlahovska, P. M. 2010 Electrohydrodynamics of drops in strong uniform dc electric fields. Phys. Fluids 22, 112110.
Salipante, P. F. & Vlahovska, P. M. 2013 Electrohydrodynamic rotations of a viscous droplet. Phys. Rev. E 88 (4), 043003.
Taylor, G. 1966 Studies in electrohydrodynamics. I. The circulation produced in a drop by electrical field. Proc. R. Soc. Lond. A 291 (1425), 159166.
Yariv, E. 2006 ‘Force-free’ electrophoresis? Phys. Fluids 18, 031702.
Yeo, K., Lushi, E. & Vlahovska, P. M. 2015 Collective dynamics in a binary mixture of hydrodynamically coupled microrotors. Phys. Rev. Lett. 114 (18), 188301.
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Journal of Fluid Mechanics
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