State-of-the-art review on various mathematical approaches towards solving population balanced equations in pharmaceutical crystallization process

Abstract

Crystallization is an important process, which possesses an undeniable role in many chemical industries. In recent years, significant endeavors have been made to increase the efficiency of this process via designing novel crystallizers. Development of numerical models and their efficient solutions is known as an important approach to justify the behavior of contributed mechanism in crystallization process. The emergence of various complexities towards the modeling of crystallization process is due to the existence of disparate mechanisms such as crystal birth, growth, and death processes. The prominent purpose of this study is to review various employed models to justify crystal birth, death, and growth in the crystallization process. Additionally, various numerical approaches like method of moments (MOM), discretized sizing technique (DST) and method of weighted residuals (MOWR) are presented in this review paper and their advantages and disadvantages to solve PBE are discussed in detail. At the end, future perspectives towards increasing the efficiency of various employed approaches foe solving population balance equation (PBE) in the crystallization process are presented, which can be of great interest for expert readers as well as non-expert investigators to be more acquainted with the undeniable role of mathematical modeling approaches in the crystallization process.

Keywords

• Crystallization process
• Mathematical modelling
• Agglomeration
• Crystal growth