Electrostatic interactions between nanoparticles in confined spaces: Influence of confining wall roughness

Nanoparticles confined in capillaries is a commonly encountered system in a variety of micro and nano electromechanical devices. In this paper we study the influence of the confining geometry on the electrostatic-interaction forces between two nanoparticles. Predictions of electrostatic double layer interaction forces between two similarly charged smooth spherical colloidal particles inside a long "rough " capillary are presented. A simple numerical model of a rough surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The nonlinear Poisson-Boltzmann equation governing the electrical potential distribution in the electrolyte is solved using finite element technique. The interaction force between the spheres was affected significantly by the proximity of the rough capillary wall. The influence of surface undulations on the particle-particle interaction force was most pronounced when the particle radius was comparable to the wavelength of the surface undulations of the capillary. According to present simulations, it seems possible to utilize this oscillation of electrostatic force to move a particle through micro-channels for controlled delivery of fluids in devices like micro-arrays and labs-on-a-chip.