Abstract
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 language | English (US) |
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Pages (from-to) | 1181-1185 |
Number of pages | 5 |
Journal | Water Research |
Volume | 24 |
Issue number | 10 |
DOIs | |
State | Published - Oct 1990 |
Externally published | Yes |
Keywords
- 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