Particles are encountered in a wide range of engineering applications and processing industries. Examples include coagulation, flocculation, dispersion, emulsification, and minerals separation by froth flotation. Generally in these applications, particle size is small, and their overall behavior is determined by forces associated with the surface properties rather than those related to mass or volume. The surface properties of a particle in a liquid medium are the result of a complex interaction between molecules, atoms, and ions on the particle surface and the surrounding liquid. If a number of particles are present, interactions also take place between particles at short separation distances, and it is this interaction which is of most interest as it can determine the overall stability or instability of dispersion and suspension systems. As a consequence of the influence that particle-particle interactions have on engineering applications and processes, it is important to have a clear understanding of the forces and the interaction energies that dominate at close separation distances. It is customarily assumed that the overall particle-particle interaction can be quantified by a net surface force that is the sum of a number of independent forces. The most often considered force components are those due to the electrodynamic or van der Waals interactions, the electrostatic double-layer (EDL) interaction, and other non-DLVO interactions. Calculation of the force-energy due to the EDL interaction between particles has not been an easy task due to the highly nonlinear governing equations. A number of approximate and exact numerical computational theories have been successfully developed for the calculation. This article provides a critical review of simple yet accurate approximate expressions for forces and energies associated with the EDL interaction between spherical surfaces, which are convenient for use in engineering applications. This article is organized as follows: In Electrostatic Double-Layer Interaction, the basic equations used in the determination of the EDL interaction between surfaces are formulated. The Derjaguin Approximation and the Deby-Hückel Linearization provides a review of the relevant approximate expressions obtained in the limit of low surface potentials. Approximations for the EDL interaction at moderate and high surface potentials are described in Approximations at Moderate and High Surface Potentials. These approximations for the EDL interaction are obtained for large (micron-size) particles. In Improvements on the Derjaguin Approximation, approximations for submicron-size particles are briefly reviewed and compared with the exact numerical results. Finally, Summary includes a summary of the review and the recommended approximate expressions for calculating the EDL interaction between spherical particles.
Encyclopedia of Surface and Colloid Science p. 630-641