We study transport of passive tracers by plane laminar flows with stagnation points. This setup serves as a simple model of transport in porous media. Close to stagnation points, the flow velocity is much lower than on the average. Many experimental data disclose that transport through porous media is slower than predictions of the standard advection-diffusion model. Commonly, in descriptions of flows through porous media the heterogeneity of flow is disregarded, and some average velocity is adopted. To model regular arrays of flow patterns with stagnation points, we employ the construction of special flow: a combination of mapping and a sort of ceiling function with singularity. We show that, depending on the type of stagnation points, many experimentally established effects can be reproduced. This includes the linear sorption, usually described by the standard MIM model, as well as subdiffusion, described by the fractional MIM model. We also show that slow molecular diffusion does not eliminate the effects of the transport slowdown.

中文翻译：

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具有驻点的平面流中的运输过程建模

我们研究了具有停滞点的平面层流对被动示踪剂的传输。此设置可用作多孔介质中的简单传输模型。接近停滞点时，流速远低于平均水平。许多实验数据表明，通过多孔介质的传输比标准对流扩散模型的预测要慢。通常，在描述通过多孔介质的流动时，不考虑流动的非均质性，而采用一些平均速度。为了对具有停滞点的流动模式的规则阵列进行建模，我们采用了特殊流动的构造：映射和一种具有奇异性的天花板函数的组合。我们表明，根据停滞点的类型，可以重现许多实验确定的效果。这包括线性吸附，通常由标准 MIM 模型描述，以及由分数 MIM 模型描述的亚扩散。我们还表明，缓慢的分子扩散并不能消除运输减速的影响。