The
mechanistic modeling of mineral crystallization is essential
for the understanding and control of many natural and industrial processes.
In the past century, many mechanisms and models have been proposed
to explain observations in different crystallization stages. However,
most models only focus on a certain step or mechanism (e.g., nucleation,
aggregation) and lack a comprehensive view. Incorporating nucleation,
aggregation, and surface reaction together, this study developed an
analytical two-stage crystallization model to simulate the particle
size and number concentration versus time and correlate them with
the measured solution turbidity. Through measuring solution turbidity
in real time, this model can reproduce the crystallization process
by predicting the key parameters: nucleation rate, particle size,
number concentration, surface tension, induction time, and particle
linear growth rate. Most of these values for barite crystallization
match with literature data and our direct cryo-transmission electron
microscopy (cryo-TEM) measurements. Moreover, the established relationships
of these key parameters versus temperature and supersaturation enable
this model to predict barite crystallization kinetics based only on
the initial supersaturation and temperature. This study is a potential
starting point to more quantitatively and comprehensively analyze
and control mineral crystallization, important to various science
and engineering applications.