Lagrangian-recurrence tracking: a novel approach for description of mixing in liquid and particle-liquid flows

Chiya Savari, Hamzah Sheikh, Mostafa Barigou*

*Corresponding author for this work

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Experimental data obtained via a Lagrangian positron emission particle tracking technique have been used to drive a new methodology for the evaluation of mixing in mechanically agitated vessels. The long-term three-dimensional trajectories of multiphase flow components have been analyzed based on the recurrence theorem to quantify local and global mixing using the Shannon entropy of the probability distribution of recurrence structures as a measure of mixedness. The potential of this new data-driven method has been demonstrated by considering single-phase and particle–liquid systems in a vessel agitated by different impellers over a wide range of experimental conditions. Detailed pointwise maps of local mixedness have been constructed for different flow regimes, and indices of global mixedness have also been derived. The entropy mixing maps for single-phase water show that a Rushton disk turbine achieves better global as well as local mixing than an up-pumping or down-pumping pitch-blade turbine. The results for particle–liquid flows show that, for a given impeller design, different suspensions in the just-suspended regime display the same degree of mixedness regardless of the particle size or concentration. The state of suspension mixing improves significantly as impeller speed increases above the just-suspended speed, but a plateau is reached at high speeds and it becomes thenceforth difficult to improve mixing further. This study has shown that the new methodology driven by Lagrangian flow trajectory data has potential for the design and analysis of multiphase flow systems.

Original languageEnglish
Pages (from-to)18501-18512
Number of pages12
JournalIndustrial & Engineering Chemistry Research
Issue number50
Early online date9 Dec 2021
Publication statusPublished - 22 Dec 2021

Bibliographical note

Funding Information:
This work was supported by EPSRC Programme grant EP/R045046/1: Probing Multiscale Complex Multiphase Flows with Positrons for Engineering and Biomedical Applications (PI: M.B., University of Birmingham).

Publisher Copyright:
© 2021 American Chemical Society.


  • General Chemistry
  • Industrial and Manufacturing Engineering
  • General Chemical Engineering

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Chemistry(all)
  • Industrial and Manufacturing Engineering


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