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      https://www.ias.ac.in/article/fulltext/pram/084/01/0009-0021

    • Keywords

       

      Population balance; aggregation; breakage; auxiliary equation method; Laplace transform.

    • Abstract

       

      This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary equation via auxiliary equation method (AEM). Travelling wave solutions of the complementary equation of a nonlinear PBE with appropriately chosen parameters is taken to be analogous to the description of the dynamic behaviour of the particulate processes. For an initial proof-of-concept, a general case when the number of particles varies with respect to time is chosen. Three cases, i.e. (1) balanced aggregation and breakage, (2) when aggregation can dominate and (3) breakage can dominate, are selected and solved for their corresponding analytical solutions. The results are then compared with the available analytical solution, based on Laplace transform obtained from literature. In this communication, it is shown that the solution approach proposed via AEM is flexible and therefore more efficient than the analytical approach used in the literature.

    • Author Affiliations

       

      Zehra Pinar1 2 Abhishek Dutta3 Guido Bény3 Turgut Öziş1

      1. Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-İzmir, Turkey
      2. Department of Mathematics, Faculty of Arts and Science, Namık Kemal University, 59030 Merkez-Tekirdağ, Turkey
      3. Faculteit Industriële Ingenieurswetenschappen, KU Leuven, Campus Groep T Leuven, Andreas Vesaliusstraat 13, B-3000 Leuven, Belgium
    • Dates

       
  • Pramana – Journal of Physics | News

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