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

Pablo B. Sáez; Bruce E. Rittmann

doi:10.1016/0043-1354(90)90040-D

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

Pablo B. Sáez, Bruce E. Rittmann

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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 S_min^* is critical to the evaluation. Deep solutions are accurate when S_S^*/S_min^* in large enough, but fully penetrated solutions rarely are accurate. First-order and zero-order solutions are accurate when S_S^* is less than about 3 × 10^-3 and greater than about 10², respectively, Most of the expected range of S_min^* values is accurately represented only by the full solution, unless S_S^*/S_min^* 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)
Pages (from-to)	1181-1185
Number of pages	5
Journal	Water Research
Volume	24
Issue number	10
DOIs	https://doi.org/10.1016/0043-1354(90)90040-D
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

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10.1016/0043-1354(90)90040-D

Cite this

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title = "Error analysis of limiting-case solutions to the steady-state-biofilm model",

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.",

keywords = "biofilms, kinetics, limited cases, steady state",

author = "S{\'a}ez, {Pablo B.} and Rittmann, {Bruce E.}",

note = "Funding Information: Acknowledgements--This work was supported by funds granted by Chemical Waste Management Inc., of Riverdale, Ill. and from grant ECE-83-51841 from the U.S. National Science Foundation.",

year = "1990",

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doi = "10.1016/0043-1354(90)90040-D",

language = "English (US)",

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pages = "1181--1185",

journal = "Water Research",

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T1 - Error analysis of limiting-case solutions to the steady-state-biofilm model

AU - Sáez, Pablo B.

AU - Rittmann, Bruce E.

N1 - Funding Information: Acknowledgements--This work was supported by funds granted by Chemical Waste Management Inc., of Riverdale, Ill. and from grant ECE-83-51841 from the U.S. National Science Foundation.

PY - 1990/10

Y1 - 1990/10

N2 - 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.

AB - 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.

KW - biofilms

KW - kinetics

KW - limited cases

KW - steady state

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

Abstract

Keywords

ASJC Scopus subject areas

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