Mathematical Modeling of Chemical Agent Removal by Reaction with an Immiscible Cleanser

Abstract

When a hazardous chemical agent has soaked into a porous medium, such as concrete, it can be difficult to neutralize. One removal method is chemical decontamination, where a cleanser is applied to react with and neutralize the agent, forming less harmful reaction products. There are often several cleansers that could be used to neutralize the same agent, so it is important to identify the cleanser features associated with fast and effective decontamination. As many cleansers are aqueous solutions while many agents are immiscible with water, the decontamination reaction often takes place at the interface between two phases. In this paper, we develop and analyze a mathematical model of a decontamination reaction between a neat agent and an immiscible cleanser solution. We assume that the reaction product is soluble in both the cleanser phase and the agent phase. At the moving boundary between the two phases, we obtain coupling conditions from mass conservation arguments and the oil--water partition coefficient of the product. We analyze our model using both asymptotic and numerical methods, and we investigate how different features of a cleanser affect the time taken to remove the agent. Our results reveal the existence of two regimes characterized by different rate-limiting transport processes, and we identify the key parameters that control the removal time in each regime. In particular, we find that the oil--water partition coefficient of the reaction product is significantly more important in determining the removal time than the effective reaction rate.