Coalescence of Drops During Gravitational Settling

Consider a slow motion of conducting, charged drops under the action of gravity in a quiescent liquid in the presence of a uniform external electric field. 

Sedimentation of drops occurs under the influence of gravitational and buoyancy forces. The net force acting on i-th drop is 

Consider first the case when the external electric field Eo is parallel to the direction of the gravity force, that is, to the vector g. Then the motion of drop S2 relative to drop Si can be considered as planar motion in a meridian plane D = const of spherical system of coordinates (r, 6, D) (see Fig. 11.2). In this case the system is axially-symmetric with respect to axis OiZ, and the angle between vector Eo and the line of centers of drops coincides with the angle 0 of spherical system of coordinates. The expressions for electric forces acting on two conducting charged drops have been obtained received in Section 12.3. The components of these forces along axes r and 9 for each drop are 

At the final stage of drops approach it is necessary to take into account molecular forces of attraction (11.100), which at small clearance between the drops are given by 

The type of dominating interaction forces between drops can vary, depending on particles size, difference in phase densities, external electric field strength, and drop charges. Thus, in case of approaching colloidal particles (I 1 pm), the basic role is played by forces of molecular and electrostatic interactions (due to charges). For coarse-disperse systems (R 1 pm) it is necessary to take into account all the forces involved. 

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