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Mathematical Modeling.

Botond Szilágyi1

  • 1Budapest University of Technology and Economics, Budapest, Hungary. szilagyi.botond@vbk.bme.hu.

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|March 13, 2026
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Summary
This summary is machine-generated.

Solution crystallization is vital for pharmaceutical biomolecule separation and purification. Mathematical modeling and control strategies enhance understanding, design, and optimization of these green, scalable industrial processes.

Keywords:
Biomolecular crystallizationCrystallization process designMetastable intermediate phaseNucleation and growth kineticsParticle size distributionPopulation balance modelingProcess analytical technologySolubity modeling

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Area of Science:

  • Biochemistry and Pharmaceutical Engineering
  • Chemical Engineering and Process Control

Background:

  • Solution crystallization is crucial for biomolecule separation, purification, and particle formation in pharmaceuticals.
  • It offers a green and scalable industrial method, though macromolecule crystallization can be challenging.
  • Key thermodynamic conditions (solvent, precipitant, concentration, pH, temperature) must be optimized.

Purpose of the Study:

  • To provide an overview of crystallization process engineering, focusing on mathematical modeling and control.
  • To bridge the understanding of biomolecular crystallization with established inorganic crystallization theories.
  • To detail methods for process understanding, design, optimization, and control at an industrial scale.

Main Methods:

  • Mathematical modeling and simulation for process analysis and optimization.
  • Development of control solutions for industrial crystallizers.
  • Leveraging established crystallization theories for biomolecular systems.

Main Results:

  • Demonstrated the applicability of mathematical modeling for understanding, analyzing, and optimizing crystallization processes.
  • Presented control strategies for effective realization of desired products in crystallizers.
  • Highlighted the correspondence between biomolecular and inorganic small-molecule crystal growth mechanisms.

Conclusions:

  • Mathematical modeling and control are essential tools for advancing industrial-scale biomolecule crystallization.
  • Biomolecular crystallization behavior largely aligns with inorganic crystallization principles.
  • This work provides a framework for optimizing pharmaceutical crystallization processes.