A numerical model of steady-state permeate flux during cross-flow ultrafiltration

Yonghun Lee, Mark M. Clark*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


The mass transport mechanisms during cross-flow ultrafiltration (UF) are mathematically expressed using the two-dimensional convective diffusion equation where the axial diffusion term is neglected for an axial Peclet number much greater than the transverse Peclet number. A numerical scheme is presented to solve the steady-state two-dimensional convective diffusion equation for the case of known uniform permeate flux. However, in the actual cross-flow UF process, the permeate flux along the axial direction is unknown and usually decreases with axial distance. Therefore, an iterative algorithm is developed to predict the steady-state permeate flux based on the assumption that the concentration at membrane surface cannot exceed a certain limiting value. Using the numerical model with an effective diffusion coefficient, which is considered to be the sum of molecular diffusion and shear-induced hydrodynamic diffusion coefficients, the effects of particle size, feed concentration, and axial velocity on the steady-state permeate flux were investigated.

Original languageEnglish (US)
Pages (from-to)241-251
Number of pages11
Issue number3
StatePublished - Jun 1997


  • Concentration polarization
  • Cross-flow ultrafiltration
  • Flux decline
  • Molecular diffusion
  • Shear-induced hydrodynamic diffusion

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)
  • Materials Science(all)
  • Water Science and Technology
  • Mechanical Engineering

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