Interaction between like-charged particles at a liquid interface: Electrostatic repulsion vs. electrocapillary attraction

Abstract

The electric field of charged particles, which are adsorbed at a liquid interface, induces interfacial deformations (capillary menisci). The overlap of such deformations gives rise to electrocapillary force of interaction between the particles. Our goal is to quantify this interaction on the basis of a force approach, which is different from the approaches (mostly based on energy calculations) used by other authors. The fact that the electric field of adsorbed particles has a dipolar asymptotics (due to the image-charge effect) is utilized to derive an analytical expression for the meniscus profile. The comparison of the calculated profile with experimental data indicates that the results based on the dipolar approximation agree excellently with the data, except some small deviations near the contact line. The effect of the interfacial deformation on the electrostatic pressure is also taken into account. The two-particle electrocapillary problem is solved in bipolar coordinates without using the superposition approximation. It turns out that for uniform distribution of the surface charges, the electrocapillary attraction is weaker than the electrostatic repulsion at interparticle distances at which the dipolar approximation is applicable, so that the net force is repulsive. This result is in agreement with the conclusions of other authors obtained by using different theoretical approaches and with available experimental data. The analytical expressions for the electrocapillary and electrodipping forces derived in the present article provide a simple and convenient way for estimation of these forces.