Modeling of flux decline during crossflow ultrafiltration of colloidal suspensions

Yonghun Lee, Mark M. Clark*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


Mass transfer during crossflow ultrafiltration is mathematically expressed using the two-dimensional convective-diffusion equation. Numerical simulations showed that mass transfer in crossflow filtration quickly reaches a steady-state for constant boundary conditions. Hence, the unsteady nature of the permeate flux decline must be caused by changes in the hydraulic boundary condition at the membrane surface due to cake formation during filtration. A step-wise pseudo steady-state model was developed to predict the flux decline due to concentration polarization during crossflow ultrafiltration. An iterative algorithm was employed to predict the amount of flux decline for each finite time interval until the true steady-state permeate flux is established. For model verification, crossflow filtration of monodisperse polystyrene latex suspensions ranging from 0.064 to 2.16μm in diameter was studied under constant transmembrane pressure mode. Besides the crossflow filtration tests, dead-end filtration tests were also carried out to independently determine a model parameter, the specific cake resistance. Another model parameter, the effective diffusion coefficient, is defined as the sum of molecular and shear-induced hydrodynamic diffusion coefficients. The step-wise pseudo steady-state model predictions are in good agreement with experimental results of flux decline during crossflow ultrafiltration of colloidal suspensions. Experimental variations in particle size, feed concentration, and crossflow velocity were also effectively modeled. Copyright (C) 1998 Elsevier Science B.V.

Original languageEnglish (US)
Pages (from-to)181-202
Number of pages22
JournalJournal of Membrane Science
Issue number2
StatePublished - Oct 28 1998


  • Concentration polarization
  • Diffusion
  • Flux decline
  • Specific cake resistance
  • Ultrafiltration

ASJC Scopus subject areas

  • Biochemistry
  • Materials Science(all)
  • Physical and Theoretical Chemistry
  • Filtration and Separation


Dive into the research topics of 'Modeling of flux decline during crossflow ultrafiltration of colloidal suspensions'. Together they form a unique fingerprint.

Cite this