Interaction of Two Conducting Drops in a Uniform External Electric Field

Interaction of Two Conducting Drops in a Uniform External Electric Field 

Potential of an Electric Held in the Space Around Drops 

Consider two conducting spherical particles with radii R and Rz, carrying charges qi and qz and placed in a uniform external electric field of strength Eo (Fig. 12.1). The angle between the center line of the particles and vector Eq is denoted by ft The space between the particles is occupied by a quiescent homogeneous isotropic dielectric with dielectric permittivity e the particles do not move relative to this dielectric medium. There are no free charges outside of the spheres, and the potential of the electric field in this area satisfies the Laplace equation  

We now formulate the boundary conditions. Far from the particles, the strength of the electric field tends towards that of the external field  

Since the system of coordinates is chosen such that the vector Eq is in the plane xOz, it is evident that does not depend on y and is equal to  

---

Interaction of Two Conducting Drops in a Uniform External Electric Field Here, is the Euler psi-function [5]. 

Let us find the collision frequency of conducting uncharged spherical drops in a turbulent fiow of a dielectric liquid in the presence of a uniform external electric field. Just as before, we assume a developed fiow, with drop sizes smaller than the inner scale of turbulence. We assume the drops to be undeformed, which is possible if the external electric field strength Eo does not exceed the critical value and the size of drops is sufficiently small. Under these conditions, the factor of mutual diffusion of drops of two types 1 and 2 with regard to hydrodynamic interaction is given by (13.86), while h and are given by the expressions (13.85) that apply to drops with a completely retarded surface. We must also take into account molecular and electric interaction forces acting on the drops. 

---