Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 69, Issue 2, Pages 765-789Publisher
SPRINGER
DOI: 10.1007/s11538-006-9168-7
Keywords
biofilm; continuum model; mathematical modeling; multidimensional; multiple species
Categories
Funding
- NIGMS NIH HHS [R01GM067245-02] Funding Source: Medline
Ask authors/readers for more resources
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 new model 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available