On the structure of the velocity field under the free spheroidal surface of a viscous liquid drop oscillating in an electrostatic field |
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Authors: | A I Grigor’ev A R Paranin S O Shiryaeva |
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Institution: | 1.Demidov State University,Yaroslavl,Russia |
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Abstract: | An asymptotic analytical solution to an initial boundary-value problem considering (i) the time evolution of the capillary
oscillation amplitude as applied to a viscous spheroidal liquid drop placed in a uniform electrostatic field and (ii) the
liquid flow velocity field inside the drop is found. The problem is solved in an approximation that is linear in two small
parameters: the dimensionless oscillation amplitude and the dimensionless field-induced constant deformation of the equilibrium
(spherical) shape of the drop. Terms proportional to the product of the small parameters are retained. In this approximation,
interaction between oscillation modes is revealed. It is shown that the intensity of the eddy component of the oscillation-related
velocity field depends on the liquid viscosity and the external uniform electrostatic field strength. The intensity of the
eddy component decays rapidly with distance from the free surface. The depth to which the eddy flow (which is caused by periodical
flows on the free surface) penetrates into the drop is a nonmonotonic function of the polar angle and increases with dimensionless
viscosity and field strength. |
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