Biomedical Implications of the Porosity of Microbial Biofilms - Porous Media: Applications in Biological Systems and Biotechnology - page 138

Stewart (1998) distinguishes between two parameters that are both
referred to as effective diffusion coecients. Following the terminology of
Libicki and colleagues (Libicki et al. 1988), D e denotes the effective diffusion
coecient and D e denotes the effective diffusive permeability. Both parame-
ters are defined by Fick's first law, but with different definitions of the solute
concentration in the concentration gradient.
The mass transport in biofilms is affected by the biofilm structure and its
composition. A quantitative understanding on how biofilm structure is linked
to mass transport is essential for understanding the biofilm behavior. Two
main approaches can be used to correlate biofilm structure to mass transport.
One approach is to explicitly describe the complex three-dimensional struc-
ture of the different biofilm components where the three-dimensional structure
can be obtained from direct imaging of biofilms (Staudt et al. 2003) or from
mathematical modeling (van Loosdrecht et al. 2002). These approaches require
detailed information of the three-dimensional structure and the specific dif-
fusion coecients throughout the various parts of the biofilm system, that
is, cell clusters and local different types of extracellular polymeric substances
(EPS). Such specific microscopic diffusion coecients are, however, dicult to
measure experimentally. Therefore, in most three-dimensional mathematical
models usually a diffusion coecient uniform throughout the entire biofilm
was assumed. Another approach was to correlate the overall biofilm diffu-
sion to the biofilm structure based on macroscale parameters, such as overall
biofilm density and porosity. A disadvantage of the latter approach is that the
spatial resolution of the three-dimensional biofilm structure is lost. It carries,
however, the advantage that established methods for measuring parameters
describing the overall biofilm structure and the overall diffusion coecients
become available.
Biofilms are mainly composed of water, and the macroscale diffusion coef-
ficient for the biofilm ( D F ) is often related to the diffusion coecient in pure
water ( D W )as

D F = f D D W (4.1)

where f D is the relative diffusivity (Hinson and Kocher 1996). Values for f D
reported in the literature range from 0.1 to 1.0 depending on the charac-
teristics of the biofilm and of the solute (Hinson and Kocher 1996; Stewart
1998). Three main approaches have been used to quantify f D experimen-
tally: (1) The two-chamber method, where a biofilm on a membrane is placed
between two chambers and the rate of diffusion through it is quantified by
bulk-phase measurements in the two chambers (Matson and Characklis 1976);
(2) microelectrode measurements, where f D is determined from the change
in the concentration gradient measured above and inside the biofilm matrix
(Cronenberg and van den Heuvel 1991); and (3) quantification of the overall
substrate removal and assuming a substrate conversion rate inside the biofilm
(Yano et al. 1961). These three methods have been applied to a large variety of