# The mathematics of chemical decontamination

by Ellen Luckins

Following a chemical weapons attack, it is crucial for public safety that any hazardous chemical agent remaining in the environment is properly removed. In particular, if the hazardous agent has seeped into porous building materials such as plasterboard, brick, or concrete, it cannot simply be wiped away. Defra and DSTL are UK Government agencies with responsibility for the remediation in such scenarios. To decontaminate a porous material, a cleanser solution is typically applied to the surface, and allowed to react in, neutralising the agent in a chemical reaction. It is crucial that all agent is reacted away, but practitioners would also like to complete the clean-up in as short a time as possible, and with minimal wasted cleanser, but there are few parameters that practitioners can control to achieve this: only the type and strength of the applied cleanser solution.

Oxford mathematicians Ellen Luckins, Chris Breward, Ian Griffiths, and Colin Please are investigating the dynamics of this decontamination procedure using mathematical modelling. Since the two reacting chemicals are immiscible (the agent is typically an oily liquid while cleansers are often aqueous) the chemical reaction occurs at the agent-cleanser interfaces within the pores of the porous material. The decontamination dynamics are therefore closely related to the distribution of the two fluids in the porespace.

Homogenised, or averaged, models for the decontamination (which carefully account for the pore-scale processes while remaining tractable over large spill-scale domains) have been developed for two different porescale distributions of agent [1], and are illustrated in the figure. We have quantified the dependence of the decontamination time on parameters including spill depth, chemical reaction rate, and the strength of the applied cleanser solution. The decontamination time may differ by orders of magnitude between the two pore-scale agent/cleanser distributions. If the process is limited by the reaction rate then decontamination is faster in the case where pores contain both cleanser and agent, since there is greater surface area for the reaction. Conversely for reaction rates or deep spills, limited by chemical transport, the porous medium initially saturated with agent is decontaminated faster. For both models, we have shown that a faster chemical reaction rate results in less cleanser wasted as well as faster decontamination. However, while a stronger applied cleanser speeds up the decontamination, it also results in a larger quantity of unreacted cleanser that is wasted in the process [2]. Decontamination practitioners must therefore decide how to prioritise between speed and chemical waste in each scenario.

Figure 1. Illustration of different possible distributions of hazardous agent (green) and cleanser (white) chemicals within the porespace.

Additional recent work with Yibin Geng and Alissa Kamilova [3] has explored the effect of chemical contraction or expansion due to the reaction: expansion was shown to slow the decontamination, as the chemicals have to diffuse against the flow of material to reach the reaction front. Two current masters projects, sponsored by Defra/DSTL and supervised by Ellen Luckins and Yixuan Sun, are ongoing: Harvey Turner is investigating how best to apply cleanser in order to minimise wasted cleanser while retaining fast agent clean-up, and Aoibheann Murray is studying how to accurately detect whether agent is lurking unseen within porous building materials.

[2] EK Luckins, CJW Breward, IM Griffiths, CP Please. The effect of pore-scale contaminant distribution on the reactive decontamination of porous media. EJAM (accepted 2023)

[3] Y Geng, AA Kamilova, EK Luckins. Fluid-flow effects in the reactive decontamination of porous materials driven by chemical swelling or contraction. J.Eng.Math. (accepted 2023)