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Invasion moving boundary problem for a biofilm reactor model

Published online by Cambridge University Press:  05 April 2018

B. D'ACUNTO ,
L. FRUNZO ,
V. LUONGO  and
M. R. MATTEI
B. D'ACUNTO
Affiliation:
Department of Mathematics and Applications, University of Naples “Federico II”, Complesso Monte Sant'Angelo, 80124 Naples, Italy emails: dacunto@unina.it, luigi.frunzo@unina.it, vincenzo.luongo@unina.it, mariarosaria.mattei@unina.it
L. FRUNZO
Affiliation:
Department of Mathematics and Applications, University of Naples “Federico II”, Complesso Monte Sant'Angelo, 80124 Naples, Italy emails: dacunto@unina.it, luigi.frunzo@unina.it, vincenzo.luongo@unina.it, mariarosaria.mattei@unina.it
V. LUONGO
Affiliation:
Department of Mathematics and Applications, University of Naples “Federico II”, Complesso Monte Sant'Angelo, 80124 Naples, Italy emails: dacunto@unina.it, luigi.frunzo@unina.it, vincenzo.luongo@unina.it, mariarosaria.mattei@unina.it
M. R. MATTEI
Affiliation:
Department of Mathematics and Applications, University of Naples “Federico II”, Complesso Monte Sant'Angelo, 80124 Naples, Italy emails: dacunto@unina.it, luigi.frunzo@unina.it, vincenzo.luongo@unina.it, mariarosaria.mattei@unina.it
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Abstract

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The work presents the analysis of the free boundary value problem related to the one-dimensional invasion model of new species in biofilm reactors. In the framework of continuum approach to mathematical modelling of biofilm growth, the problem consists of a system of non-linear hyperbolic partial differential equations governing the microbial species growth and a system of semi-linear elliptic partial differential equations describing the substrate trends. The model is completed with a system of elliptic partial differential equations governing the diffusion and reaction of planktonic cells, which are able to switch their mode of growth from planktonic to sessile when specific environmental conditions are found. Two systems of non-linear differential equations for the substrate and planktonic cells mass balance within the bulk liquid are also considered. The free boundary evolution is governed by a differential equation that accounts for detachment. The qualitative analysis is performed and a uniqueness and existence result is presented. Furthermore, two special models of biological and engineering interest are discussed numerically. The invasion of Anammox bacteria in a constituted biofilm inhabiting the deammonification units of the wastewater treatment plants is simulated. Numerical simulations are run to evaluate the influence of the colonization process on biofilm structure and activity.

Keywords

Invasion modelbiofilm reactorhyperbolic free boundary value problemnumerical simulationsAnammox process
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Special Issue 6: Biofilms , December 2018 , pp. 1079 - 1109
Copyright
Copyright © Cambridge University Press 2018 

References

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