Exact Effective Transport Dynamics under Spatially Random Adsorption

We report on effective transport under linear equilibrium adsorption, which is characterized by a spatially random retardation factor. We present a methodology to quantify explicitly the impact of spatial disorder on effective transport dynamics within a stochastic framework. An exact effective transport equation can be derived, which describes transport under linear kinetic adsorption characterized by a spectrum of adsorption times. The distribution of adsorption times is given explicitly in terms of the spatial disorder distribution. The derived effective transport equation is formally equivalent to a decoupled continuous time random walk. The explicit nature of the derived results allows for the first time a mapping of the static disorder distribution on the transition time distribution.