How to Measure Diffusion Coefficients in Biofilms: A Critical Analysis

Effective diffusion coefficients are often required for kinetic descriptions of biofilms. Many previous studies have measured diffusion coefficients for specific molecule-biofilm combinations. As a result, many biofilm researchers today rely on literature values of diffusion coefficients for their own biofilm system. However, the reported diffusion coefficients in literature fall within a wide range, even for the same molecule. One potential cause of this range is the accuracy of the methods used to measure diffusion coefficients. The objective of this study was to determine the precision (similarity between repeated experiments) and bias (difference between measured and true diffusion coefficient) of six common methods. The six selected methods were based on determining mass balances and on microelectrode measurements. The precision and bias were quantified based on mathematical models of the six methods, with oxygen diffusion in granular sludge as a case study. The precision was assessed by a Monte Carlo uncertainty analysis, which considers the propagation of uncertainty in the input experimental parameters. The bias was determined for six potential sources of error: solute sorption, biomass deactivation, a concentration boundary layer, granule roughness, granule shape, and granule size distribution. From the Monte Carlo analysis, it followed that the precision of the methods ranged from 4-77% relative standard deviation. The microelectrode methods were more accurate than the mass balance methods. The bias due to the combined effect of the six errors was an underestimation of the diffusion coefficient by 74%. This shows that current methods are unable to accurately determine diffusion coefficients. We do not propose improvements to the current methods, but instead discuss why inaccurate diffusion coefficients are sufficient for accurate engineering of biofilm processes.