Particle shape manipulation and optimization in cooling crystallization involving multiple crystal morphological forms

Abstract

A population balance model for predicting the dynamic evolution of crystal shape distribution is further developed to simulate crystallization processes in which multiple crystal morphological forms co-exist and transitions between them can take place. The new model is applied to derive the optimal temperature and supersaturation profiles leading to the desired crystal shape distribution in cooling crystallization. Since tracking an optimum temperature or supersaturation trajectory can be easily implemented by manipulating the coolant flowrate in the reactor jacket, the proposed methodology provides a feasible closed-loop mechanism for crystal shape tailoring and control. The methodology is demonstrated by applying it to a case study of seeded cooling crystallization of potash alum. V

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

“…The shape evolutions of a potash alum crystal demonstrate that the initial 26 faces remain at the end of the simulation, but the shape and size in every face direction are changed. The value of (a 1 -1) 2 + (a 2 -1) 2 approaches zero as the operating condition follows the optimal supersaturation profile [111] which indicates that its morphology does grow to approach the desired morphology. This study demonstrated that the model can be used to derive optimal supersaturation and temperature profiles for a given objective function related to particle shape, hence providing a closed-loop methodology for crystal shape tailoring, which can be easily implemented via a standard feedback or cascade control system using jacket cooling water.…”

“…(3) can be further simplified as (4) It is worth to note that Equations (1-4) can be applied to any crystal systems with the x being crystal internal coordinates and/or other crystal properties. The morphology transformations can be accounted for by varying the number of internal coordinates according to the transformations [111]. Recent studies by Singh et al [112] developed a morphology domain concept which covers all kind of morphologies of a compound, and incorporated it into a MPBM model for automatically detect and model the morphology transformations.…”

“…An alternative approach, high resolution finite volume method, was proposed [90,129,132] to provide high accuracy while avoiding the numerical diffusion (that is, smearing) and numerical dispersion (that is, nonphysical oscillations) associated with other finite difference and finite volume methods. This method has been shown to be a promising method and applied to various crystallisation systems [90,105,111,129,130] and further developed for effectively reducing the computation time using either an adaptive mesh technique [130] through redistributing the mesh by moving the spatial grid points iteratively and obtaining the corresponding numerical solution at the new grid points by solving a linear advection equation or a coordinate transformation technique [131] which utilizes a coordinate transformation technique to convert a size-dependent growth rate process into a size-independent growth rate problem with a larger time step to be allowed.…”

“…Therefore, a three-dimensional MPBM, the corresponding three parameters, x, y, z, as shown in Figure 4, can be formed to simulate the morphological evolution of potash alum crystals. This complex inorganic hydrate compound, potash alum, was specially chosen in several PB studies [94][95][96]111], which displays no extensive attrition and without observed significant particle/particle agglomeration. By solving the morphological PB equation for a time interval of t, the growth of individual faces, {111}, {100} and{110}, can be obtained, and, hence, used to calculate the new locations of the corresponding crystal faces, with respect to their previous locations.…”

“…Symmetric polytopes can be used for geometric description of crystal morphology with Miller indices. The following symmetric polytope can be used to describe the crystal shape of potash alum [111]: Protein crystals have significant benefits in the delivery of biopharmaceuticals. Although many different experimental techniques have been employed to investigate protein crystallisation, the majority has focused on fundamental investigations at the molecular and single crystal levels.…”