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Stability of combustion waves in a simplified gas-solid combustion model in porous media.

ABSTRACT: We study the stability of the combustion waves that occur in a simplified model for injection of air into a porous medium that initially contains some solid fuel. We determine the essential spectrum of the linearized system at a travelling wave. For certain waves, we are able to use a weight function to stabilize the essential spectrum. We perform a numerical computation of the Evans function to show that some of these waves have no unstable discrete spectrum. The system is partly parabolic, so the linearized operator is not sectorial, and the weight function decays at one end. We use an extension of a recent result about partly parabolic systems that are stabilized by such weight functions to show nonlinear stability.This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'.

SUBMITTER: Ozbag F

PROVIDER: S-EPMC5869607 | biostudies-literature | 2018 Apr

REPOSITORIES: biostudies-literature

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Stability of combustion waves in a simplified gas-solid combustion model in porous media.

Ozbag Fatih F Schecter Stephen S

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 20180401 2117

We study the stability of the combustion waves that occur in a simplified model for injection of air into a porous medium that initially contains some solid fuel. We determine the essential spectrum of the linearized system at a travelling wave. For certain waves, we are able to use a weight function to stabilize the essential spectrum. We perform a numerical computation of the Evans function to show that some of these waves have no unstable discrete spectrum. The system is partly parabolic, so ...[more]

PMID: 29507170

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Project description:ABSTRACT Porous media filters are used widely to remove bacteria from contaminated water, such as stormwater runoff. Biofilms that colonize filter media during normal function can significantly alter performance, but it is not clear how characteristics of individual populations colonizing porous media combine to affect bacterial retention. We assess how four bacterial strains isolated from stormwater and a laboratory strain, Pseudomonas aeruginosa PAO1, alter Escherichia coli retention in experimental sand columns under conditions of stormwater filtration relative to a clean-bed control. Our results demonstrate that these strains differentially affect E. coli retention, as was previously shown for a model colloid. To determine whether E. coli retention could be influenced by changes in relative abundance of strains within a microbial community, we selected two pairs of biofilm strains with the largest observed differences in E. coli retention and tested how changes in relative abundance of strain pairs in the biofilm affected E. coli retention. The results demonstrate that E. coli retention efficiency is influenced by the retention characteristics of the strains within biofilm microbial community, but individual strain characteristics influence retention in a manner that cannot be determined from changes in their relative abundance alone. This study demonstrates that changes in the relative abundance of specific members of a biofilm community can significantly alter filter performance, but these changes are not a simple function of strain-specific retention and the relative abundance. Our results suggest that the microbial community composition of biofilms should be considered when evaluating factors that influence filter performance. IMPORTANCE The retention efficiency of bacterial contaminants in biofilm-colonized biofilters is highly variable. Despite the increasing number of studies on the impact of biofilms in filters on bacterial retention, how individual bacterial strains within a biofilm community combine to influence bacterial retention is unknown. Here, we studied the retention of an E. coli K-12 strain, as a model bacterium, in columns colonized by four bacterial strains isolated from stormwater and P. aeruginosa, a model biofilm-forming strain. Simplified two-strain biofilm communities composed of combinations of the strains were used to determine how relative abundance of biofilm strains affects filter performance. Our results provide insight into how biofilm microbial composition influences bacterial retention in filters and whether it is possible to predict bacterial retention efficiency in biofilm-colonized filters from the relative abundance of individual members and the retention characteristics of cultured isolates.

Dataset Information

Stability of combustion waves in a simplified gas-solid combustion model in porous media.

Publications

Stability of combustion waves in a simplified gas-solid combustion model in porous media.

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