An analytical model for membrane fouling evolution associated with gel layer growth during constant pressure stirred dead-end filtration

Kang Xiao, Yuexiao Shen, Xia Huang

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


Stirred dead-end filtration (SDEF) has been widely used for fundamental studies on membrane fouling caused by soluble and colloidal matter during microfiltration and ultrafiltration. Quantitative description of the SDEF fouling process which usually involves gel layer formation, however, has rarely been reported. In this study, an analytical model was derived based on theories of cake filtration and concentration polarization, to quantify the gel-associated fouling evolution process during constant pressure SDEF. The model formulates the relationship between filtration resistance (R) and specific permeate volume (V) as: V=C1+C2R+C3exp(-C4/R)+V0(C2dR/dV-1), where C1-C4 and V0 are constants. The model enables rigorous definition of characteristic points on the R vs. V curve to divide the fouling evolution process into the initial fouling stage, the gel layer growth stage and the gel layer mature stage. The model also gives a simplified piecewise expression: V=C1+C2R for the gel layer growth stage and V=C1+C2R+C3exp(-C4/R)-V0 for the mature stage. A two-step fitting approach was proposed for the simplified expression to evaluate the C1-C4 parameters. These parameters were found useful in determining the characteristic points of fouling evolution and further, in quantifying foulant and fouling layer properties including: hydrodynamic diameter and diffusion coefficient of foulant, mass transfer coefficient and boundary layer thickness of concentration polarization, and specific resistance and gel point concentration of gel layer. This model in combination with constant pressure SDEF experiments can serve as a tool for quantitative characterization of fouling propensity and foulant properties, and may thus assist in detailed analysis of fouling mechanisms.

Original languageEnglish
Pages (from-to)139-149
Number of pages11
JournalJournal of Membrane Science
StatePublished - Jan 5 2013


  • Fouling evolution
  • Gel layer
  • Membrane filtration
  • Modeling
  • Stirred dead-end filtration


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