Modelling of Transportation Process in Plane Flows with Stagnation Points

Abstract

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.