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Behaviour of dispersed phases


Duration :
21 hours

ECTS Credits : 2.5

Semester : S9

Person(s) in charge :

Jean-Pierre Bellot, Professor,

Keywords : Behaviour of dispersed phases

Prerequisites : None




Industrial and household effluent treatment (liquid and gaseous) almost always operates in multiphase media, and separation efficiency is measured not only by the mass yield, but also by size and composition (examples: wastewater treatment by flotation, dust, radioactively contaminated effluents).

This course aims to teach students the fundamental knowledge needed to deal with this difficult subject, with an analysis that goes from the microscopic scale to the macroscopic scale. During practical work and tutorials, students will apply the knowledge they have acquired, in particular by taking examples from environmental issues and analysing them with computer software.


  • Shapes of particles and boundary conditions for flow
    Practical work:

    • Shape and trajectory of an isolated bubble according to its size

    • Flow regimes in a bubble column, estimation of exchange surfaces

  • Particle interactions – continuous phase
    Analysis of the forces acting on the motion of a particle.
    Description and expression of all the forces.
    Example of the behaviour of a particle in a vortex.

  • Modelling the discrete phase
    Lagrangien calculation of a particle’s trajectory in laminar, algorithm and numerical method
    Tutorial on Fluent: simulation of solid particle flow in a wind tunnel (vertical)

  • Modelling of the discrete phase in a turbulent regime
    Behaviour of a particle in a turbulent flow and Lagrangian calculation of the trajectory

  • Population balance (PB)
    General PB equation. A small revision of the distribution functions.
    Transport equation for growth without agglomeration

Tutorial: Size distribution of crystals in a continuous crystallizer
Population balance with agglomeration. (Smoluchowski equation)
Methods for solving PB equations (Hounslow, Ramakrishna, parents and daughter)
Description of agglomeration kernel, in a turbulent regime.

Tutorial: example of an application on computer – Treating dust
Explanation of the combination: Fluid mechanics – Population balance

Tutorial: example of an application on computer – Follow-up and end

Abilities : 


Description and operational vocabulary













Evaluation :

  • Written test
  • Continuous Control
  • Oral Report
  • Project
  • Written Report
  • Aucune étiquette