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

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 shape-sensitive kernels.