Predictions of the particle size distribution changes in emulsions and suspensions by digital computation

Abstract

The fundamental Smoluchowski flocculation rate equations including the effects of polydispersity and particle-particle potential energy barrier have been solved for any initial particle size distribution. The procedure for the numerical solution of the set of nonlinear differential equations involved the combined use of the Runge-Kutta and the Hamming methods by the IBM 360 computer. It was assumed that the only rate process is the passage of the particles over the primary electrical barrier to flocculation of suspensions (or coalescence of emulsion droplets). The input data were the surface potential, dielectric constant, temperature, Debye-Huckel kappa, viscosity, Hamaker constant, and the initial particle size distribution. The output included the time changes in the particle size distribution, the polydispersity and interaction barrier effects on the rate and the time dependency of the mean polydispersity and interaction barrier of the dispersed system. The changes in the particle size distribution have also been studied by means of a similarity transformation which leads to a self-preserving spectrum. When the electrical barrier was small, any given initial distribution became more polydispersed with time and the total number of particles decreased more rapidly than second order with respect to time owing to the preferential flocculation of Müller. When the electrical barrier was appreciable, the distribution narrowed with time. These results were consistent with the particle size effects on the interaction potential. The predictions can now be directly used to compare experimental Coulter counter data with theory. The general method of numerical analysis can be easily adapted to cases involving other forces of repulsion between suspension and emulsion particles such as steric (or entropic) repulsion.