Capillary interaction of spherical particles adsorbed on the surface of an oil/water droplet stabilized by the particles: 3. Effective interfacial tension

Abstract A theoretical study is made of the effective (macroscopic) interfacial tension of a planar oil water interface covered at variable packing with a regular array of adsorbed, identical, spherical solid particles. This tension acts over areas large compared with the particle size. It is less than the corresponding conventional (microscopic) tension of the interface in the absence of the particles and reduces to the latter tension as the separation between the adsorbed particles is increased. A distinctive feature is that equilibrium partitioning does not occur between particles suspended in the continuous bulk phase and those adsorbed on the interface. This is due to the deep capillary energy well into which each particle is adsorbed at the oil water interface and to the settling under gravity of the particles in the bulk phase. If the separation of the particles adsorbed in a regular array on the interface becomes substantial, restructuring may occur to produce more compact clusters of particles interspersed with areas of the interface which are free of particles. The effective interfacial tension is associated with the individual clusters, each of which contains many particles. The meniscus tension of an oil water interface covered with hydrophobic particles has previously been measured experimentally and is identified with the effective interfacial tension. The effective tension of the surface of an oil water droplet covered by a layer of adsorbed particles differs from that of the planar interface by a term of order x · r 0 where x is the particle radius and r 0 is the droplet radius. In Part 2 (see S. Levine and B.D. Bowen, Colloids Surfaces, 65 (1992) 273) the relevance of the effective interfacial tension to the theory of capillary interaction between particles adsorbed on an emulsion droplet was discussed using a conical cell model.