Interparticle interactions in concentrate water-oil emulsions.
The present investigation is based on the description of electrostatic interaction in concentrated disperse systems proposed 45 years ago by Albers and Overbeek. Starting from their model, we developed a stability theory of concentrated Brownian W/O emulsions in which nondeformed droplets undergo electrostatic and Van der Waals interactions. While the droplets in dilute emulsion may be described by pair interaction, in dense emulsions, every droplet is closely surrounded by other droplets, and when two of them come together, not only the energy of their pair interaction, but also their interaction with surrounding droplets change. Unlike in dilute emulsion, for which the reference energy of the pair is the energy at infinity (taken equal to zero), in concentrate emulsion, the reference energy is not zero but is the energy of interaction with averaged ensemble of nearest droplets. The larger the volume fraction, the higher the reference energy and, thus, the lower the energy barrier between two coagulating droplets, which enhances the coagulation. In dense packing of drops, the energy of interaction and the reference energy coincide, therefore, the height of energy barrier vanishes. In contrast with dense emulsion, at medium volume fraction, when two coagulating droplets interact only with a few nearest neighbors, our analysis shows that the energy barrier may also increase, which extends thus the domain of stability. Because in W/O emulsion, the thickness of the electric double layer is of the same order or larger than the size of droplets, the electrostatic energy was calculated with a correction factor beta that accounts for the deviation of double layers from sphericity. A more complete van der Waals interaction with account of screening of interaction by electrolyte has been used. Both factors promote the decrease of energy barrier between coagulating droplets and enhance the coagulation. Our model introduces two critical volume fractions. The first one, phi(c1), is the volume fraction depending on the characteristics of system (size of drops, thickness of double layer, surface potential, dielectric permittivity of medium) that limits the validity of the pair interaction model. The second one, phi(c2), is a volume fraction that limits the applicability of the simplified model of interaction of three or more double layers. By comparing the energies of barrier height and of Brownian motion, a critical volume fraction phi(c3) is defined, which determines the starting point of rapid coagulation. Finally, the influence of drop interaction on gravitational coagulation is also briefly presented. It is shown that the probability of coagulation between fixed in space and sedimenting droplets is larger than with only Brownian coagulation. Unlike at free sedimentation of two identical drops, the gravitation cannot accelerate their aggregation. The surface potential, which leads to the equilibration of surface forces, gravitational and Archimedes forces for a given volume fraction, is then obtained.