Capillary interaction of spherical particles adsorbed on the surface of an oil/water droplet stabilized by the particles. Part II

Abstract

We develop a conical-cell model for determining the capillary interaction between identical spherical particles forming a monolayer adsorbed at variable packing on the surface of an oil-in-water (Pickering) emulsion droplet. Each adsorbed particle is assigned a cone-shaped section of the droplet volume. The vertex of the cone is located at the center of the droplet and the axis of the cone passes through the center of the adsorbed particle. A typical adsorbed particle is surrounded by an oil/water interfacial shell having circular symmetry about the axis of the cone. The shape of the oil/ water interface is obtained by solving the Young—Laplace equation. It is required that the volume of the dispersed phase in the droplet, which is contained in the cone, does not change on adsorption of the monolayer of particles. The interfacial energy assigned to a single adsorbed particle and its surrounding oil/water interface situated within its cone is determined. The capillary interaction is obtained by subtracting the corresponding interfacial energy when capillary interaction between the adsorbed particles is ignored. One method of obtaining interfacial energy without capillary interaction between the particles is based on the model of Menon, Nagarajan and Wasan, described in part I (S. Levine and B.D. Bowen, Colloids Surfaces, 59 (1991) 377). With this choice of interfacial energy without particle interactions, the capillary interaction is small and attractive. The leading term is identical with that obtained in Part I, by developing further the model of Menon, Nagarajan and Wasan. This term is proportional to the fourth power of the particle radius and diminishes as the inverse square of the separation between the particles. The use of the conical-cell model yields an additional term which is expressed in terms of the difference between the so-called effective (macroscopic) interfacial tension, due to the layer of adsorbed particles, and the conventional (microscopic) tension of the oil/water interface without particles. Although our result is consistent with the order of magnitude of the capillary interaction found with an earlier cylindrical-cell model, which was intended to apply to a very large droplet, the latter gave an incorrect capillary repulsion between the adsorbed particles.