Simple model for the instabilities in the aggregation of silica sols in a sol-gel process

A simple kinetic model based on the Prigogine's Brusselator model was used to explain some unstable non-linear oscillations found in the particle size profile of sols in a sol-gel process. These oscillations were explained, in some previous papers, by using the stability criterion from the non-linear irreversible thermodynamics; it is the excess entropy production that characterizes the stability of a system and the occurrence of new structures. In the solgel reaction considered here, one of the steps is auto-catalytic; this fact produces local gradients in the concentration of one of the chemical components, forming a wide variety of new unstable structures. With this model we obtained a relationship for the reaction constants that determines the unstable character of the reaction, and the dependence of the frequency of oscillations on the reactant concentrations. The dependence of the oscillation frequency on water and ethanol concentrations obtained from the experimental data, were well explained by using this model.