Effects of randomly inhomogeneous diffusion barrier on impurity transport in a double-porous medium

Impurity transport regimes and concentration asymptotics in statistically homogeneous sharply contrast medium are analyzed in the case when the impurity source is surrounded by a barrier consisting of a low-permeable matrix and rare linear defects ("punctures") that provide a rapid exit of the impurity out of the barrier to the main medium. The behavior of transport regimes depends on which of the time intervals the current time falls. The intervals are determined by characteristic times of the problem, determined by the properties of both the primary medium and the barrier. At relatively short times, the presence of a barrier leads to a significant slowdown in transport. At sufficiently large times, the transport regimes coincide with those that are realized in the problem without a barrier. The action of the barrier leads to the appearance of precursors in the concentration distribution, as well as to the modification of concentration asymptotics, in comparison with the problem without a barrier. In particular, due to the presence of the barrier, an additional asymptotic stage appears. Graphical abstract:

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