Kinetic Model for the Simultaneous Processes of Flocculation and Coalescence in Emulsion Systems

We consider an emulsion system in which the two interrelated processes of flocculation and coalescence take place simultaneously. The flocculation is described in terms of von Smoluchowski's theory, whereas the coalescence is related to the rupture of the liquid films between the drops. Since the latter process takes place in aggregates, we adopt for it a kinetic scheme which formally resembles that of parallel chemical reactions. A set of differential equations governing the overall kinetics is formulated and solved for several particular cases. The rate constants of flocculation and coalescence stand as model parameters. Solutions for the number of single drops vs time are obtained in the asymptotic regimes of fast and slow coalescence. In the case of linearly built aggregates we derive an explicit expression for the total number of drops in the system. For arbitrary aggregates the complete set of kinetic differential equations is solved numerically. The results are compared with those obtained by other authors through particular averaged models of flocculation and coalescence. The theory can be employed to investigate the role of different factors for the emulsion stability: the solubility of the surfactant, the adsorption and the Gibbs elasticity of the layer, the surface viscosity etc.