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 CaCO3 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.

This study presents the results of computational fluid dynamics simulations of a multiphase, reacting, turbulent mixing layer in an idealized geometry. The purpose is to compare large-eddy simulation (LES) to one-dimensional turbulence (ODT) and examine the trends of the flow under differing mixing conditions. Aqueous streams are mixed together to precipitate polymorphs of calcium carbonate. The polymorphs of calcium carbonate are tracked numerically using population balance equations (PBE). Each PBE contains all of the relevant physical models to track the particle evolution including nucleation, growth, and aggregation. A simple subgrid mixing model that is convenient for use with PBEs was implemented in the LES code. The higher spatial resolution achievable with ODT allowed an investigation on the effect of resolution on the mixing-model error. The Reynolds number of the flow is varied and is shown to cause a decrease in average particle sizes with higher mixing rates. V C 2015 American Institute of Chemical Engineers AIChE J, 61: [3185][3186][3187][3188][3189][3190][3191][3192][3193][3194][3195][3196][3197] 2015