Mathematical modelling of chemical decontamination by cleanser solution and contamination of porous media contamination and decontamination models

When a hazardous chemical soaks into a porous material such as a concrete floor, it can be difficult to remove. One approach is chemical decontamination, where a cleanser is added to react with and neutralise the contaminating agent. The goal of this thesis is to investigate the reaction dynamics and the factors that affect contamination and efficacy of the decontamination procedure. This thesis has two parts: the decontamination of a saturated medium and the contamination of an unsaturated medium.

In the first half of the thesis, we consider a one-dimensional model, previously presented by Dalwadi et al. (2017), for the decontamination of saturated porous medium. The cleanser and agent are assumed to be immiscible, and so the neutralising reaction takes place at the sharp interface that forms between them. Reaction products formed at the interface may dissolve in one or both liquids. We first consider the scenario where products dissolve entirely in the cleanser solution, and apply different numerical techniques commonly used for solving Stefan problems to determine the most suitable method for future work in this field. We then study the scenario where product can dissolve in either phase, previously considered by Dalwadi et al. (2017), going beyond their limitation that the depth of the porous medium must be large compared to the length scale over which concentrations vary inside the medium. By investigating other parameter regimes, we highlight how different parameters in the model impact clean-up times and, hence, make suggestions on how to improve decontamination procedures.

In the second half of this thesis, we consider the step prior to decontamination, in which the agent infiltrates a porous medium. We consider a one-dimensional model of infiltration described by the Richards equation, a leading-order approximation of the Buckingham–Darcy equation, where the viscosity of the penetrating fluid is large relative to the viscosity of air in the medium. Using a combination of perturbation methods and scientific computing, we study the dynamics of contamination. We compare results from the Richards with numerical results obtained using the Buckingham–Darcy equation for small but non-zero values of the viscosity ratio. Despite the popularity of the Richards equation, we find that it is in fact a poor approximation of certain infiltration systems and investigate why using perturbation methods.