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 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 10 2, 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.