Center for Biofilm Engineering

Abstract:  

"A Multidimensional Multispecies Continuum Model for Heterogeneous Biofilm Development”" 

We propose a multidimensional continuum model for heterogeneous
growth of biofilm systems with multiple species and multiple substrates. The new
model provides a deterministic framework for the study of the interactions between
several species and their effects on biofilm heterogeneity. It consists of a
system of partial differential equations derived on the basis of conservation laws
and reaction kinetics. The derivation and key assumptions are presented. The assumptions
used are a combination of those used in the established one dimensional
model, due to Wanner and Gujer, and for the viscous fluid model, of Dockery and
Klapper. The work of Wanner and Gujer in particular has been extensively used
through the years, and thus this newmodel is an extension to several spatial dimensions
of an already proven working model. The model equations are solved using
numerical techniques, for purposes of simulation and verification. The new model
is applied to two different biofilm systems in several spatial dimensions, one of
which is equivalent to a system originally studied by Wanner and Gujer. Dimensionless
formulations for these two systems are given, and numerical simulation
results with varying initial conditions are presented.
 

Alpkvist E, Klapper I, " “A Multidimensional Multispecies Continuum Model for Heterogeneous Biofilm Development”," Bull Math Biol 2007; 69 (2): 765-789 Abstract 07-018