ERROR ANALYSIS OF LIMITING-CASE SOLUTIONS TO THE STEADY-STATE-BIOFILM MODEL

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. © 1990.