A finite element model for concentration polarization and osmotic effects in a membrane channel

Nicolás Carro, David Mora, Jesus Vellojin*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this article, we study a mathematical model that represents the concentration polarization and osmosis effects in a reverse osmosis cross-flow channel with dense membranes at some of its boundaries. The fluid is modeled using the Navier–Stokes equations and the solution-diffusion is used to impose the momentum balance on the membrane. The scheme consist of a conforming finite element method with the velocity–pressure formulation for the Navier–Stokes equations, together with a primal scheme for the convection–diffusion equations. The Nitsche's method is used to impose the permeability condition across the membrane. Several numerical experiments are performed to show the robustness of the method. The resulting model accurately replicates the analytical models and predicts similar results to previous works. It is found that the submerged configuration has the highest permeate production, but also has the greatest pressure loss of all three configurations studied.

Original languageEnglish
JournalInternational Journal for Numerical Methods in Fluids
Volume96
Issue number5
Pages (from-to)601-625
ISSN0271-2091
DOIs
Publication statusPublished - 2024

Keywords

  • Finite elements
  • Navier–Stokes equations
  • Nitsche's method
  • Reverse osmosis

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