Ostwald ripening controlled by diffusion of a sparingly soluble component

TL;DR

This paper extends classical Ostwald ripening theory to include the effects of sparingly soluble additives, showing diffusion control, distribution patterns, and transition behaviors at different concentrations.

Contribution

It introduces an improved ripening rate equation accounting for component differences and non-ideality, and describes the transition from classic to bimodal particle distributions.

Findings

Ripening rate follows the classical cubic law at high additive concentrations.

Particle size distribution remains similar to LSW theory under certain conditions.

Transition from LSW pattern to bimodal distribution occurs at low additive concentrations, characterized by the lock-in parameter.

Abstract

Additives of sparingly soluble components are known to slow down or completely inhibit Ostwald ripening in dispersed systems. In this paper, our earlier model of stabilization against Ostwald ripening is revisited and extended. In a quasi-steady-state mode, the process is shown to be controlled by the diffusion of the less soluble component, and the whole machinery of the classical Lifshits-Slezov-Wagner (LSW) theory can be leveraged almost without any change. The particle size distribution is predicted to follow the same distribution function pattern as in the classic LSW theory. The rate of ripening follows the classic cubic law. To extend our earlier result, an improved extrapolatory equation for the ripening rate is derived, that covers the whole formulation range, accounts for the difference in molar volumes of the components and for the solution non-ideality. The behavior described above is observed over the range of high concentrations of the poorly soluble component, with the cutoff determined by the lock-in number described in the previous paper of this series. When the concentration of the additive is low, the kinetics no longer follows the LSW pattern; instead, the particle size distribution becomes bimodal, with the fraction of 'fines' enriched by the poorly soluble component and the fraction of the large particles to ripen as if no additive were present. The lock-in parameter L1 can be used to characterize for the transition from one mode to another. In the end, some practical stabilization approaches for emulsions are discussed.