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Mathematical Modeling of Different Breakage PBE Kernels Using Monte Carlo Simulation Results

In: Optimization of Pharmaceutical Processes

Author

Listed:
  • Ashok Das

    (Indian Institute of Technology Kharagpur)

  • Jitendra Kumar

    (Indian Institute of Technology Kharagpur)

Abstract

This chapter discusses the development of some breakage PBE kernels. Three different types of breakage processes are considered, namely linear breakage, nonlinear collisional breakage, and sonofragmentation of rectangular shaped crystals. Mathematical models of monovariate linear breakage selection function and nonlinear collisional breakage kernel are presented, which are dependent on particle volume and process time simultaneously. Furthermore, a bivariate breakage PBE is considered for a particular set of sonofragmentation experiments on δ-form of pyrazinamide (rectangular shaped) crystals. Consequently, the corresponding bivariate breakage selection function and breakage distribution function were discussed to predict the experimental results. The developed bivariate breakage selection function takes care of the time dependence in particle selections along with the size dependence. For the verification of the presented models, the Monte Carlo (MC) method is used. For the first two processes, MC merely acts as the replication tool to produce experimental results. However, for the sonofragmentation process, the MC technique was used to understand the breakage behavior accurately.

Suggested Citation

  • Ashok Das & Jitendra Kumar, 2022. "Mathematical Modeling of Different Breakage PBE Kernels Using Monte Carlo Simulation Results," Springer Optimization and Its Applications, in: Antonios Fytopoulos & Rohit Ramachandran & Panos M. Pardalos (ed.), Optimization of Pharmaceutical Processes, pages 79-101, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-90924-6_4
    DOI: 10.1007/978-3-030-90924-6_4
    as

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