Reactions in porous media

Spill a nasty chemical onto a smooth surface, and a careful choice of cleaning materials are required to wipe it up properly.  Spill a nasty chemical onto a porous surface, such as untreated concrete, and the situation is significantly more difficult to deal with.  A cleansing agent must "chase" the contaminant into the porous material, and react there to neutralise it.   The success of this procedure is dependent on the correct choice of neutralising agent, and is difficult to study experimentally.  A mathematical modelling challenge on this topic was therefore proposed at the 100th European Study Group with Industry.

In 2015-2017, our modelling team developed a mathematical model for the neutralization reaction between a contaminant and a neutralizing agent inside porous medium.  We studied the effect of parameters such as chemical reaction rate and diffusion coefficients on the time taken to neutralize the contaminant.    We found that increasing the speed of chemical reaction has limited benefit, but that the efficiency with which neutralizing agent and neutral product are transported to and from the reaction front is pivotal.

In 2020-2024, Sarah Murphy completed a PhD on mathematical modelling of contamination and decontamination processes.  In her first publication, she improved existing models for decontamionation by accounting for finite size effects, and found that reaction dynamics can be significantly altered by the size of a spill.  Stay tuned for more forthcoming publications, in which Sarah delves into the contamination process, figuring out how to accurately track the amount of a chemical spill that has seeped into a floor, and how deep it has travelled.