A moment projection method for population balance dynamics with a shrinkage term

Authors: Shaohua Wu, Edward K. Y. Yapp, Jethro Akroyd, Sebastian Mosbach, Rong Xu, Wenming Yang, and Markus Kraft

  • A moment projection method for solving particle population balance equations is developed.
  • A Blumstein-Wheeler algorithm is adopted in this method to track the number of the smallest particles.
  • This method is tested for modelling particle shrinkage process and showed high accuracy.
  • The method developed has the advantages of ease of implementation and numerical robustness.

abstractA new method of moments for solving the population balance equation is developed and presented. The moment projection method (MPM) is numerically simple and easy to implement and attempts to address the challenge of particle shrinkage due to processes such as oxidation, evaporation or dilution. It directly solves the moment transport equation for the moments and tracks the number of the smallest particles using the algorithm by Blumstein and Wheeler [Phys. Rev. B, 8:1764–1776, 1973]. The performance of the new method is measured against the method of moments (MOM) and the hybrid method of moments (HMOM). The results suggest that MPM performs much better than MOM and HMOM where shrinkage is dominant. The new method predicts mean quantities which are almost as accurate as a high-precision stochastic method calculated using the established direct simulation algorithm (DSA).

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Keywords: oxidation, method of moments, shrinkage, dilution, population balance equation

Associated Projects: Numerics and Particle Processes