Error analysis of limiting-case solutions to the steady-state-biofilm model

Pablo B. Sáez, Bruce E. Rittmann

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Simple analytical solutions for the limiting cases of deep, fully penetrated, first-order and zero-order biofilms are evaluated for accuracy by comparison with the full solution of the steady-statebiofilm model. The fundamental dimensionless parameter Smin* is critical to the evaluation. Deep solutions are accurate when SS*/Smin* in large enough, but fully penetrated solutions rarely are accurate. First-order and zero-order solutions are accurate when SS* is less than about 3 × 10-3 and greater than about 102, respectively, Most of the expected range of Smin* values is accurately represented only by the full solution, unless SS*/Smin* is significantly greater than 1.0. This analysis emphasizes that the limiting-case solutions have restrictive ranges of applicability for steady-state biofilms.

Original languageEnglish (US)
Pages (from-to)1181-1185
Number of pages5
JournalWater Research
Issue number10
StatePublished - Oct 1990
Externally publishedYes


  • biofilms
  • kinetics
  • limited cases
  • steady state

ASJC Scopus subject areas

  • Water Science and Technology
  • Ecological Modeling
  • Pollution
  • Waste Management and Disposal
  • Environmental Engineering
  • Civil and Structural Engineering


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