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Homogenisation problems in reactive decontamination

Part of: Partial differential equations

Published online by Cambridge University Press:  30 September 2019

E. LUCKINS ,
C. J. W. BREWARD Open the ORCID record for C. J. W. BREWARD [Opens in a new window] ,
I. M. GRIFFITHS Open the ORCID record for I. M. GRIFFITHS [Opens in a new window]  and
Z. WILMOTT
E. LUCKINS
Affiliation:
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford, OX2 6GG, UK email:ellen.luckins@maths.ox.ac.uk; breward@maths.ox.ac.uk; ian.griffiths@maths.ox.ac.uk; zachary.wilmott@maths.ox.ac.uk
C. J. W. BREWARD
Affiliation:
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford, OX2 6GG, UK email:ellen.luckins@maths.ox.ac.uk; breward@maths.ox.ac.uk; ian.griffiths@maths.ox.ac.uk; zachary.wilmott@maths.ox.ac.uk
I. M. GRIFFITHS
Affiliation:
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford, OX2 6GG, UK email:ellen.luckins@maths.ox.ac.uk; breward@maths.ox.ac.uk; ian.griffiths@maths.ox.ac.uk; zachary.wilmott@maths.ox.ac.uk
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Abstract

The decontamination of hazardous chemical agents from porous media is an important and critical part of the clean-up operation following a chemical weapon attack. Decontamination is often achieved through the application of a cleanser, which reacts on contact with an agent to neutralise it. While it is relatively straightforward to write down a model that describes the interplay of the agent and cleanser on the scale of the pores in the porous medium, it is computationally expensive to solve such a model over realistic spill sizes.

In this paper, we consider the homogenisation of a pore-scale model for the interplay between agent and cleanser, with the aim of generating simplified models that can be solved more easily on the spill scale but accurately capture the microscale structure and chemical activity. We consider two situations: one in which the agent completely fills local porespaces and one in which it does not. In the case when the agent does not completely fill the porespace, we use established homogenisation techniques to systematically derive a reaction–diffusion model for the macroscale concentration of cleanser. However, in the case where the agent completely fills the porespace, the homogenisation procedure is more in-depth and involves a two-timescale approach coupled with a spatial boundary layer. The resulting homogenised model closely resembles the microscale model with the effect of the porous material being incorporated into the parameters. The two models cater for two different spill scenarios and provide the foundation for further study of reactive decontamination.

Keywords

Homogenisationequations in media with periodic structurediffusion and convectionreaction effects in flowsinterface problems

MSC classification

Primary: 35B27: Homogenization; equations in media with periodic structure
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 5 , October 2020 , pp. 782 - 805
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Copyright
© Cambridge University Press 2019

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