Towards establishing a combined rate law of nucleation and crystal growth – The case study of gypsum precipitation

The main obstacle in the formulation of a quantitative rate-model for mineral precipitation is the absence of a rigorous method for coupling nucleation and growth processes. In order to link both processes, we conducted a series of batch experiments in which gypsum nucleation was followed by crystal growth. Experiments were carried out using various stirring methods in several batch vessels made of different materials. In the experiments, the initial degree of supersaturation of the solution with respect to gypsum (Ω_gyp) was set between 1.58 and 1.82. Under these conditions, heterogeneous nucleation is the dominant nucleation mode. Based on changes in SO₄²⁻ concentration with time, the induction time of gypsum nucleation and the following rate of crystal growth were calculated for each experiment. The induction time (6–104 h) was found to be a function of the vessel material, while the rates of crystal growth, which varied over three orders of magnitude, were strongly affected by the stirring speed and its mode (i.e. rocking, shaking, magnetic stirrer, and magnetic impeller). The SO₄²⁻ concentration data were then used to formulate a forward model that couples the simple rate laws for nucleation and crystal growth of gypsum into a single kinetic model. Accordingly, the obtained rate law is based on classical nucleation theory and heterogeneous crystal growth.