Environmental Engineering Reference
In-Depth Information
In recent years, mathematical models have become powerful tools in the study of
bioilms. Such models focus on initiation, growth of bioilms and the degradation of
bioilms with antibiotics and antimicrobials [50]. Models of bacterial attachment on
polymer surfaces have recently gained a lot of prominence. Attachment of microbes
on the substratum depends on the physicochemical interactions between the microbe
and the substratum. A number of researchers have tried to understand the forces
responsible for adhesion using various theoretical models, such as the Derjaguin-
Landau-Verwey-Overbeek (DLVO) model, the thermodynamic approach and the
extended DLVO theory. The DLVO theory illustrates the total interaction between
a cell and a surface as a balance between two additive factors, because of attractive
van der Waals interactions and repulsive interactions from the overlap between the
electrical double layer of the cell and the substratum [51]. However, this theory does
not give details of the various molecular interactions involved during the contact
between the bacterial surface and polymers such as the substratum molecular groups,
molecules on the bacterial surfaces that affect cell surface distance and substratum
roughness [52].
Another approach is the thermodynamic theory that accounts for the various types of
attractive and repulsive interactions, and expresses them as free energy [53]. In this
approach, the surface free energy of the bacterial and substratum surfaces and the
surface free energy of the suspending solution are estimated to determine the Gibbs
adhesion energy. This model is an equilibrium model and not a kinetic model and is
used only on closed systems. Also it is not easy to obtain precise free energy values.
Thus, the models using thermodynamic theory have not been entirely able to predict
all the attachment behaviours and properties [52].
An extended DLVO theory [51, 54] was suggested in which the hydrophobic/
hydrophilic interactions were also included. The extended DLVO model has more
potential in the study of bacterial adhesion, but this has not been extensively used.
Although the physicochemical theory provides an explanation for several phenomena,
it still has not been able to completely predict the bioilm formation, development
and microbial adhesion. The main reason for the limitation of the use of this theory is
the complexity of the bacterial cell surface. Thus, calculations and predictions based
only on physicochemical models are impractical because the cell surface proteins,
polysaccharides, conditioning ilms on surfaces in attaching bacteria also inluence
the adhesion of cells [52].
Barton and co-workers [55] developed several mathematical models for growth
rates of bacteria on surfaces. They correlated the adsorption and desorption from
surfaces using various assumptions. The models relate growth rates and adsorption
rates and could be used in designing polymers that can resist bioilm formation.
The mathematical models show that the population of bacteria on a surface is a
