Design formulae for reactive barrier membranes

Modeling reveals three regimes for the time varying flux. For early times most reactive sites are still present, and an initial flux plateau is observed. For intermediate times, a moving reaction front is found to travel across the film coupled with an increasing flux of the mobile species. Finally, for long times when most reactive sites are consumed, the transient flux approaches its steady value. Analytic design equations characterizing the flux in these three regimes are developed based on perturbation theory and matched asymptotic expansions. They agree closely with the exact numerical solutions. Algebraic formulae for the kill time, time lag and speed of the reaction front also correspond to the full numerical solutions.