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Effect of nonlinear polarization on shapes and stability of pendant and sessile drops in an electric (magnetic) field. (English) Zbl 0780.76030

In presence of an applied electric or magnetic field, supported and free drops of dielectric or magnetic liquids elongate in the direction of the applied field. For certain values of the ratio of the permeability of the drop to that of the surrounding fluid, drop deformation is experimentally seen to show hysteresis [J. C. Bacri and D. Salin, J. Phys. Lett. 43, 649 ff. (1983); and ibid. 44, No. 11, 415-420 (1983)]. Most of theoretical calculations, based on linearly polarizable media, had been unable to demonstrate the occurrence of hysteresis. The major goal of the present paper is to predict under which conditions supported drops can exhibit hysteresis in deformation under the influence of an applied field. The authors introduce for the polarization a nonlinear equation of the Langevin form. Nonlinear effects in the polarization had been included previously only in one occasion [C. Boudouvis, A. Puchalla and L. E. Scriven, Chem. Engn. Commun. 67, 129ff. (1988)] in conditions where only a monotonically increasing deformation curve resulted. In the present paper, it is demonstrated that at high values of the field strength, nonlinearly polarizable supported drops whose contact lines are fixed or whose contact angles are prescribed, display hysteresis in drop deformation over a wide range of values of Langevin parameters, in good agreement with experiments. The electric fields inside nonlinearly polarizable drops turn out to be very nonuniform, in contrast with those inside linearly polarizable drops.
Reviewer: D.Jou (Ballaterra)

MSC:

76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E30 Nonlinear effects in hydrodynamic stability
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[2] Bacri, J. Phys. Lett. 44 pp L649– (1983)
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