The Electrical Double Layer Force between Spherical Particles Which Are Partially Submerged in Water

We study the EDL force between two colloidal particles that are adsorbed to the surface of an electrolyte solution. The attachment of colloidal particles to a free surface of an electrolyte solution, which may interface with another liquid or vapor phase, is a well-known phenomenon that is employed in many scientific and industrial applications, the most well-known of which is the Pickering emulsion. In addition to capillary stresses, the particles will experience an electrical double layer (EDL) force when they are close to each other. The force originates from the overlap of the diffusive layers of ions that appear in the electrolyte solution next to the charged surfaces of the particles and the charged surface of the electrolyte solution, which is free of particles. Here, we elucidate the contribution of the free surface of the electrolyte solution to the EDL force between two spherical particles, which are half-submerged in the electrolyte solution. We solve the linearized Poisson-Boltzmann equation for the excess electrical potential near the particles and integrate over the resulting excess Maxwell and osmotic stresses on the particles. We further give corresponding Pa ' de approximations, thus enabling the use of simple formulas for the EDL force between interacting particles in cases similar to the ones in this study without the need to repeat the mathematical procedure employed here.