A simultaneous determination of nucleation and growth rates from batch spontaneous precipitation

Abstract

A review of the literature shows that many methods for determining the nucleation and growth rates from batch precipitation experiments are inaccurate. Therefore, a new method has been developed to derive these two rates based on the simultaneous measurement of the supersaturation and the crystal size distribution during a batch spontaneous precipitation. All experimental data are used without any previous numerical treatment and the differential kinetic equations are replaced by integral ones to avoid numeric derivation. The kinetic parameters of the two postulated laws of nucleation and crystal growth rates in kinetic equations are separately determined by non-linear optimization. This method was applied to barium sulphate precipitation. Experiments were performed in a 20 l stirred reactor. Effects of reagent adding order and stirring speed were noticed. The influence of initial supersaturation was determined. The nucleation rate was found to obey an exponential law with a primary heterogeneous dominating process. The linear rate of crystal growth follows a 2.1 power law and the process seems to be limited by a surface integration step. The kinetic results were compared to those previously reported.