Agglomeration of Needle-like Crystals in Suspension. II. Modeling

Abstract

A population balance model for the agglomeration of nonspherical particles in a well-mixed batch reactor is presented. In the model, two separate distributions are used: one for primary particles, which are described by multiple characteristic sizes, and one for agglomerates, which are characterized only by their volume. The two coupled population balance equations describing the evolution of both particle populations over time are solved in parallel together with the material balance. The output of the model for varying operating conditions and using different agglomeration kernelsincluding two simple, shape-sensitive functionsis assessed and finally compared to experimental results for needle-like crystals reported in the first part of this series. It is found that the qualitative trends for three important characteristics, the average needle length, the average width, and the total agglomeration degree, are well-described by all kernels. However, the average aspect ratio of primary particles, as well as the particle size and shape distribution of primary particles in general, are described better with the shapesensitive kernels.

Particle design via spherical agglomeration: A critical review of controlling parameters, rate processes and modelling

“…There is an opportunity to further improve modelling in this area by using the experimental understanding of the combined nucleation, growth, and agglomeration rate processes. Peña et al [87] extended the work of Ochsenbein et al [86] by using a coupled PBM to track the total crystals, un-agglomerated crystals and agglomerates of a spherical agglomeration process that exhibited nucleation, growth, and agglomeration. In their work, the coupled PBM was used in an optimisation framework to achieve a target primary crystal mean size for bioavailability, and a target…”

Disorientation angle distribution of primary particles in potash alum aggregates

“…These aspects have typically been simplified by considering a point or linear contact between spherical particles, as reviewed by Hounslow et al [4]. Shape information has so far been included in the aggregation modeling through a shape-sensitive aggregation kernel [5] or by adopting a Monte Carlo approach and a hierarchical aggregate representation [6,7].…”

Simulations of crystal aggregation and growth: Towards correct crystal area

“…In classical aggregation models, particles are described by one size dimension, such as length or volume, leading to a one‐dimensional (1D) population balance equation (see reference [] for a recent review). Such an aggregation model can furthermore be coupled to a 2D, or more classically, 1D model of particle growth. These classical (here called “simple”) aggregation models assume that particles have a constant shape factor.…”