Micellar effects on Ostwald ripening in emulsions: Transition from cubic to quadratic particle size growth

Abstract

Ostwald ripening in O/W emulsions in presence of solubilizing micelles is theoretically studied. At small average sizes, the kinetics is predicted to follow the classical Lifshits-Slezov-Wagner cubic law, with the rate proportional to the molecular solubility of the oil in water, as if no micelles were present. At larger particle sizes the kinetics transitions to the Wagner's quadratic law. The crossover point for the kinetics depends on the dynamics of the oil solubilizate-micelle exchange; it is set by the value of the oil atmosphere distribution parameter, kappa, which, somewhat like Debye length, is proportional to the square root of the micellar concentration. It should be noted that in the range when 1/kappa is close to the particle average radius, the ripening kinetics still nearly follows the cubic law, with only moderate deviations; in this case, the micellar effects are experimentally seen not as the deviations from the linearity, but as an apparent increase in the cubic rate. The increase is predicted to be larger in case of nonionic micelles of ethylene oxide type compared to ionic ones.