A reduced-order model of concentration polarization in reverse osmosis systems with feed spacers

Jacob Johnston, Sarah M. Dischinger, Mostafa Nassr, Ji Yeon Lee, Pedram Bigdelou, Benny D. Freeman, Kristofer L. Gleason, Denis Martinand, Daniel J. Miller, Sergi Molins, Nicolas Spycher, William T. Stringfellow, Nils Tilton

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


Feed spacers in reverse osmosis systems generate complex fluid flows that limit computational fluid dynamics (CFD) simulations to small length and time scales. That limits our ability to simulate mineral scaling and other membrane fouling phenomena, which occur over longer length and time scales. Thus motivated, we develop a reduced model that replaces the CFD simulation of the velocity field with an analytical model that mimics spacers. This focuses the remaining numerical effort on simulating the advection–diffusion equation governing solute transport. We motivate and validate the model with CFD simulations and bench-scale experiments of spacer filaments in three different arrangements, including cases of unsteady vortex shedding. We show that the model produces a roughly 10,000-fold speedup compared to CFD, and accurately reproduces CFD predictions of not only the average and maximum concentrations, but also the local concentration distribution along the membrane. We also demonstrate the model for simulating a feed channel with a length-to-height ratio of 200. The model provides a simple testbed for exploratory studies of multispecies transport, precipitation, and membrane fouling phenomena for which simulating spacers is often prohibitive.

Original languageEnglish
Article number121508
Number of pages15
JournalJournal of Membrane Science
Publication statusPublished - 5 Jun 2023
Externally publishedYes


  • Computational fluid dynamics
  • Concentration polarization
  • Feed spacers
  • Reduced model
  • Reverse osmosis

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