A 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 non-intuitive and non-trivial coupling effects. To validate the proposed framework, the CaCO3 system and results described within Ogino T., Suzuki, T., and Sawada K., 1987 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. 1 Overview and Scope Historically, the investigation of mineral kinetics has primarily focused on isolated phenomena such as specific particle growth mechanisms or nucleation-rates at particular sets of conditions. Our approach provides a synchronous description of particle size distributions, aqueousphase ionic equilibrium-chemistry, and physical processes that simultaneously effect both phases through a single, overarching theoretical framework. Physical properties captured within the framework include the solution’s supersaturation states, polymorphic abundances, mixing extents and growth, dissolution, nucleation, and aggregation rates. Such comprehensive understanding is necessary due to the nonobvious and pervasive coupling between individual phenomena. Seeking to capture particlesize distribution (PSDs) based physical phenomena such as Ostwald ripening, similar to Steefel and van Cappellen 1 and Noguera et al. 2 , the quadrature method of moments (QMOM) is implemented as a computationally efficient mathematical method to achieve this goal. The work presented directly addresses the coupling between multiple processes including: aqueous-phase ionic equilibrium-chemistry, simultaneous presence of multiple polymorphs, nucleation rate of each polymorph, interfacial tension that depends on temperature and nanoscale effects on physical properties, and time-