Stabilization of emulsions by fine particles II. capillary and van der Waals forces between particles

The effective surface tension (free energy per unit area) of a planar oil/water interface completely covered with a closely-packed monolayer of identical spherical particles is determined as a function of contact angle. The surface tension diminishes as contact angle increases from 0° to 90° or decreases from 180° to 90°. Preliminary experimental results show this general trend. A theoretical study is made of the capillary forces acting between the interfacial spherical particles which stabilize oil/water emulsion droplets. Applying a two-dimensional cell model, the oil/water meniscus immediately surrounding a given particle of a closely-packed monolayer structure is assumed to have circular symmetry. Changes in interfacial areas between the oil, water and solid occur when an isolated surface particle becomes a member of the monolayer structure. For the simplified model used here the accompanying energy change due to interfacial tension yields a repulsion between the surface particles for all contact angles. By applying the well-known Derjaguin method of determining the interaction of particles at close separation, the van der Waals attraction between adjacent spheres in the monolayer is calculated as a function of the contact angle. The magnitudes of the capillary and van der Waals energy per particle are smaller by three or four orders of magnitude than the depth of the energy well in which an isolated solid sphere is trapped at the oil/water interface.