Theoretical Framework for Multiple-Polymorph Particle Precipitation in Highly Supersaturated Systems

An overarching mathematical framework is proposed to describe entire mineral particle precipitation processes, including multiple polymorphic forms and ranges of temperatures. While existing models portray individual physical phenomena, the presented approach incorporates a diverse set of the physical phenomena simultaneously within a single mathematical description. The liquid and solid phase dynamics interact through coupling an aqueous ionic equilibrium-chemistry model with a set of population balance equations and a mixing model. Including the particle physical phenomena, nucleation, growth, dissolution, and aggregation together within a single framework allows for the exploration of nonintuitive and nontrivial coupling effects. To validate the proposed framework, the CaCO 3 system and results described within Ogino, T.; Suzuki, T.; Sawada, K. Geochim. Cosmochim. Acta 1987, 51, 2757–2767 were utilized. The proposed framework captures general trends and timescales, even while being constructed of relatively basic physical models with approximations and known uncertainties. Interpolymorph coupling effects, which were found to be important in the validation system’s evolution, and dynamics within each polymorph’s particle size distribution are captured by the framework.