Capillary forces spherical charged particle

Kralchevsky et al. [14] also proved from the energy method that Eqn. (3.49) is valid for calculating the horizontal force between the two floating spherical particles. Since r is always positive, the sign of capillary charge Q. depends solely on y/.. If both particles have the same sign of y/., the lateral capillary force between the two floating spheres is attractive otherwise, the force is repulsive. 

The last configuration for Cheerios effect in this article is a spherical particle with capillary charge Q floating in vicinity of an infinite vertical wall. In order to find the horizontal capillary force between the wall and particle, one may consider a simple case where the contact angle at the wall is fixed at 0 = 90°, i.e., the boxmdary condition is... 

The possible relevance of this quadrupole-quadrupole force at colloidal length scales was advanced in references [9,46,47]. As emphasized in reference [9], the natural surface roughness in the nanometer scale of a micrometer-sized spherical particle could conceivably cause a force of this kind. It was also proposed as an explanation of the structures observed experimentally [47] in 2D colloids of nonspherical micrometer particles at a fluid interface. This motivated the theoretical investigation of the anisotropic capillary forces The main difficulty lies in the determination of the capillary charges in terms of given properties of the particles (e.g., wettability and shape). Different simplifications were applied the contact line is approximated by a circle [48-50] or by an expansion in small eccentricity [45] highly elongated shapes are dealt with numerically [51]. 

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