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Stochastic modelling of membrane filtration.

A U Krupp1, I M Griffiths1, C P Please1

  • 1Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK.

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This study introduces an efficient model for particle filtration, simulating pore clogging and surface deposition. The model accurately predicts filtration behavior with diverse particle sizes and membrane structures, offering faster simulations.

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Area of Science:

  • Filtration science
  • Chemical engineering
  • Materials science

Background:

  • Membrane fouling is a critical issue in particle filtration, caused by pore clogging, pore entrance coverage, and surface deposition.
  • Existing models often address these fouling mechanisms individually, limiting comprehensive analysis.

Purpose of the Study:

  • To develop an efficient computational model for particle filtration that integrates various fouling mechanisms.
  • To accurately simulate the behavior of filters considering diverse particle sizes, membrane geometries, and pore interactions.

Main Methods:

  • A novel model based on a 'conductivity function' to describe individual pore blockage by arriving particles.
  • Incorporation of stochastic particle arrival times and pore-level interactions.
  • Formulation of the model as a system of ordinary differential equations.

Main Results:

  • The model accurately describes various filtration scenarios, including simultaneous multiple fouling mechanisms.
  • Successfully simulated the filtration of mixed particle sizes (small and large) through track-etched membranes.
  • Demonstrated effective particle separation using interconnected pore networks.

Conclusions:

  • The developed model provides an efficient and accurate method for simulating complex membrane fouling processes.
  • It enables the study of simultaneous fouling mechanisms and particle separation in interconnected pore networks.
  • The model's speed advantage over stochastic simulations makes it a valuable tool for future research and applications.