Forces acting on dielectric colloidal spheres at a water/nonpolar-fluid interface in an external electric field. 1. Uncharged particles

Abstract

Here, we calculate the electric forces acting on uncharged dielectric colloidal particles, which are attached to the interface between a nonpolar fluid (air, oil) and water, in the presence of an applied uniform external electric field directed normal to the interface. The uncharged particle becomes a source of dipolar electric field because it is polarized by the external field. Our goal is to calculate the normal (electrodipping) force acting on each separate particle, and the force of interaction between two identical particles. An exact analytical solution is obtained by solving the Laplace equation in toroidal coordinates and by separating the variables using the Mehler–Fock integral transform. The results show that the dependence of the normal force on particle contact angle is non-monotonic, with a maximum and a minimum. This force can be directed upward or downward depending on the particle contact angle and dielectric constant. An analytical asymptotic expression is derived for the force of interaction between two floating particles in external field. The magnitude of the latter force depends strongly on the particle contact angle α. At a certain value of α, the leading dipolar term becomes zero, and the interaction force is determined by the short-range octupolar term. Then, the attractive lateral capillary forces and van der Waals forces can overcome the electrostatic repulsion and can induce two-dimensional coagulation of the particles at the interface. The effects of the external electric field could find applications for control of the distances between particles in non-densely packed interfacial colloid crystals used in lithographic masks for the production of antireflective coatings, microlens arrays, etc. The case of charged particles in external field is considered in the second part of this study.