Attraction between particles at a liquid interface due to the interplay of gravity- and electric-field-induced interfacial deformations.

In a previous study, we established that the attraction between electrically charged particles attached to a water/tetradecane interface is stronger than predicted on the basis of the gravity-induced lateral capillary force. Here, our goal is to explain this effect. The investigated particles are hydrophobized glass spheres of radii between 240 and 320 microm. Their weight is large enough to deform the liquid interface. The interfacial deformation is considerably greater for charged particles because of the electrodipping force that pushes the particles toward the water phase. By independent experiments with particles placed between two electrodes, we confirmed the presence of electric charges at the particle/tetradecane interface. The theoretical analysis shows that if the distribution of these surface charges is isotropic, the meniscus produced by the particle electric field decays too fast with distance and cannot explain the experimental observations. However, if the surface-charge distribution is anisotropic, it induces a saddle-shaped deformation in the liquid interface around each particle. This deformation, which is equivalent to a capillary quadrupole, decays relatively slow. Its interference with the gravity-induced isotropic meniscus around the other particle gives rise to a long-range attractive capillary force, F approximately 1/L3 (L=interparticle distance). The obtained agreement between the experimental and theoretical curves, and the reasonable values of the parameters determined from the fits, indicate that the observed stronger attraction in the investigated system can be really explained as a hybrid interaction between gravity-induced "capillary charges" and electric-field-induced "capillary quadrupoles".