Monopole capillary force

In a different setup, the presence of an external electric field E perpendicular to the undistorted flat interface polarizes the particles, which repel each other laterally due to the electrostatic interaction. However, the vertical pull on the particles by both gravity and the external electric field generates a capillary monopole and therefore a lateral capillary attraction. The equilibrium separation between the particles can be varied with the controllable field E, since sizable capillary forces already appear for not too large values of the electric field [37] this has been demonstrated in recent experiments [17,43]. 

In reference [ 11 ], it was proposed that the capillary force was of the monopole form (Equation 2.31) due to the vertical electtic force on the particle leading to a monopole 0. We have seen, however, that the relevant amplitude of the monopole force is actually io = + Po = 0. This was noted in... 

The first term with m = 0 in the right-hand side of Equation 4.167a accounts for the contribution of the capillary charges (or capillary monopoles ). Analytical expressions for the force and energy of interaction between two capillary multipoles of arbitrary order have been derived [324]. 

The simplest situation is the interaction between particles with a permanent capillary monopole. By Equation 2.10, it means that the particles are under the action of an external vertical force the best-known example is the buoyancy force due to gravity. The potential of mean force between two particles under the action of vertical buoyancy forces and respectively, is asymptotically (i.e.,... 

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