Impurity transport in fractal media in the presence of a degrading diffusion barrier

Abstract

We have analyzed the transport regimes and the asymptotic forms of the impurity concentration in a randomly inhomogeneous fractal medium in the case when an impurity source is surrounded by a weakly permeable degrading barrier. The systematization of transport regimes depends on the relation between the time t 0 of emergence of impurity from the barrier and time t * corresponding to the beginning of degradation. For t 0 < t *, degradation processes are immaterial. In the opposite situation, when t 0 > t *, the results on time intervals t < t * can be formally reduced to the problem with a stationary barrier. The characteristics of regimes with t * < t < t 0 depend on the scenario of barrier degradation. For an exponentially fast scenario, the interval t * < t < t 0 is very narrow, and the transport regime occurring over time intervals t < t * passes almost jumpwise to the regime of the problem without a barrier. In the slow power-law scenario, the transport over long time interval t * < t < t 0 occurs in a new regime, which is faster as compared to the problem with a stationary barrier, but slower than in the problem without a barrier. The asymptotic form of the concentration at large distances from the source over time intervals t < t 0 has two steps, while for t > t 0, it has only one step. The more remote step for t < t 0 and the single step for t > t 0 coincide with the asymptotic form in the problem without a barrier.