Affordable Access

Publisher Website

Numerical and Similarity Solutions for Reversible Population Balance Equations with Size-Dependent Rates

Authors
Journal
Journal of Colloid and Interface Science
0021-9797
Publisher
Elsevier
Publication Date
Volume
246
Issue
2
Identifiers
DOI: 10.1006/jcis.2001.8073
Keywords
  • Continuous Distribution Kinetics
  • Population Balance Equations
  • Particle Size Distributions
  • Similarity Solutions
  • Steady State Solutions
  • Fragmentation
  • Aggregation
Disciplines
  • Mathematics

Abstract

Abstract Population balance equations (PBEs) for reversible aggregation–fragmentation processes are important to particle agglomeration and dissolution, polymerization and degradation, liquid droplet coalescence and breakup, and floc coagulation and disintegration. Moment solutions provide convenient solutions to the PBEs, including steady state and similarity solutions, but may not be feasible for complex forms of size-dependent rate coefficients and stoichiometric kernels. Numeric solutions are thus necessary not only for applications, but also for the study of the mathematics of PBEs. Here we propose a numerical method to solve PBEs and compare the results to moment solutions. The numeric results are consistent with known steady state and asymptotic long-time similarity solutions and show how processes can be approximated by self-similar formulations.

There are no comments yet on this publication. Be the first to share your thoughts.