The Conducting Drops in an Electric Field

If the system is unstable, that is, repulsive forces are not taken into account, then each collision of particles results in their coagulation. The presence of a stabilizer (electrolyte) in the liquid gives rise to additional forces due to the formation of electric double layers at particle surfaces. It means that coagulation will slow down. Therefore such coagulation is referred to as slow coagulation. 

The rate of coagulation is characterized by the stability factor W( which is equal to the ratio of the number of particle collisions without electrostatic repulsion and the number of collisions with the repulsion present [9)  

If both internal and external liquids happen to be ideal dielectrics and there are no free charges at the interface, or if liquid inside the drop is highly conductive and the external liquid is an isolator, the external electric field leads to the appearance of a force distributed over the surface of drop. This phenomenon is caused by the discontinuity of the electric field at the interface [55]. The force is perpendicular to the interface and is directed from the liquid with higher dielectric permittivity (or from the conducting liquid) toward the liquid with lower dielectric permittivity (or toward the isolator). For the equilibrium shape of a motionless drop in a quiescent liquid to be conserved, the condition of equality of the surface electric force and the surface tension force must be satisfied. As a result, at static conditions, the drop assumes the shape of an ellipsoid extended along the direction of the external electric field. 

Experiments whose outcomes are listed in [65] have shown only a qualitative agreement with the theory [64], while quantitative differences, in particular, in the extent of drop deformation, appeared to be significant. An attempt to take into account the higher-order terms in the asymptotic expansion was made in [66], but it did not eliminate the discrepancy with experimental results. It should be noted that performing a successful experiment is a difficult task because one has to impose a strict requirement that drops should remain motionless (no sedimentation or lifting), for which it is necessary to make sure that the drops are very small, and the densities of the internal and external liquids should not differ by a lot. 

A more general case is considered in [67], which studies the behavior of a drop suspended in a liquid, where the conductivities of both the drop and the liquid are finite. The equation of motion takes into account nonlinear inertial terms. 

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