The Kinetics of Coagulation of an Emulsion

Abstract

Under s~iitable conditions, the coagulatio~i of GI<-S lates by s~~l p h u r i c acid has been foulid to eshibit second order rate characteristics, and to be represented by the equation, Cowhere Cis the co~ice~itratio~i of polymer a t time t , CG is the i~iitial co~icentration of polymer, and iH+)' is the concentratiori of H+ ion in escess of the critical concentration necessary to initiate coag~llatio~i. Coagulation is accompanied by desorption of soap fro111 the surface of the lates particles, and the variation of surface tension resulting from this follows the equation log y = -4 -B log t. where y is the surface tensiori and A and B are coristants. Appropriate adjustment of the temperature was found to stabilize the emulsion markedly in the presence of acid. . A mecha~iism for the coagolation process is considered.'The phenomenon of coagulation of colloidal systems is analogous in Inan>-respects to a chemical reaction, proceeding a t a definite rate dependent on temperature and concentration. Frequently, however, it is a diffusion-controlled process to which the standard kinetic methods based on equilibrium between reactants, activated complex, and products cannot be applied. I t is only when the probability of coalescence of the particles taking part in a collision is reduced, that is when the particles are 1elative1~-stable, that an equilibrium state can be postulated.Statistical treatment of the problem bl-S n~o l u c l~o~~s l~i and others ( I , 6, 15, 16) has yielded the relation to represent the number of particles n present a t time t in a monodispel-se system which a t time t = 0 consists of n o primary particles. In this expression, E is a numerical constant of value 0 < E < 1, which depends on the charge or other stabilizing factors of the particle, and k is equal to 47rDR, where D is the diffusion coefficient of the primary particle and R is the radius of its sphere of ,tttraction. R is defined as the distance to which two particles must approach for coalescence, which must be equal to a t least twice the radius of the primarJparticles. This equation has been found to be generally valid when E = 1 (9,19,21), that is, for uncharged particles, but has been found to be in poor agreement with experinlent in many cases where the charge on the particles has been only partially neutralized (slow coagulation) (3, 4, 7).With emulsions the particles are generally stabilized by emulsifiers adsorbed a t the interface between the internal phase and the external suspending