Applied Mathematics Seminars: Decontamination of Neat Agents: A Study Group Story
10 March 2017 14:00 in CM219
Following a spill of a hazardous chemical, it is important to remove the contaminating agent as quickly and completely as possible. This is often achieved by applying a cleanser, such as bleach, that will react with the agent to produce less harmful products. In many cases, a variety of different cleansers could be applied to deal with the same agent, and these different cleansers may react with the agent by different mechanisms to form different reaction products. This then leads to the central question: what properties of a cleanser (and, by association, what properties of the reaction mechanisms and reaction products) will promote fast and effective removal of an agent? This is, in essence, a problem that was presented at ESGI100 in Oxford in 2014, and has been the source of ongoing research by myself and others who participated in the study group.
In many cases of concern, contaminating agents are oily substances, while the cleansers that are effective against them are water-based. This means that the agent and cleanser are immiscible and the decontamination reaction takes place at the interface between the two phases. Since contaminating agents are often neat, this creates a moving boundary problem where the interface between the cleanser phase and the agent phase moves as the agent is consumed. In this talk, I will present and analyse a 1D mathematical model of decontamination that accounts for the moving boundary between the phases. This model includes a partition coefficient in order to represent the fact that the reaction product can be soluble in both phases, and leads to an unusual variety of Stefan problem. I will present work in which we use asymptotic and numerical methods to analyse the speed of the reaction and the movement of the interface, and we find that the time taken to total removal of the agent depends strongly on the concentration of the cleanser and on the partition coefficient, and less strongly on the reaction rate constant.
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