Reaction dynamics and early-time behaviour of chemical decontamination

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 paper is to investigate the reaction dynamics and the factors that affect the efficacy of the decontamination procedure. We consider a one-dimensional porous medium initially saturated with an oil-based agent. An aqueous cleanser is applied at the surface, so the two chemicals are immiscible and a boundary forms between them. A neutralising reaction takes place at this boundary in which cleanser and agent are consumed and reaction products are created. This is a Stefan problem, and the boundary between the cleanser and agent moves as the reaction proceeds. Reaction products formed at the interface may dissolve in one or both liquids. This may temporarily prevent cleanser and/or agent from reaching the reaction site, so diffusion of the chemical species, in particular the diffusion of product from the interface, plays a key role. The scenario described above was considered previously by Dalwadi et al. (2017, Mathematical modelling of chemical agent removal by reaction with an immiscible cleanser. SIAM J. Appl. Math., 77, 1937–1961) in the limit where the depth of the porous medium is large compared to the length scale over which concentrations vary inside the medium. Here, we present results that are valid for any ratio between these length scales and an analysis of agent removal times for various dimensionless parameter regimes. We also highlight the emergence of a boundary layer associated with diffusion in the oil phase for early times, where the thickness of the boundary layer is directly proportional to the square root of the time variable.