The paper is devoted to the study of longitudinal solute transport through an array of vortices, bounded by rigid walls. Since the fluid velocity in such system is very heterogeneous, the transfer of solute particles has non-trivial properties. Some particles can flow into the vortex driving by diffusion. These particles do not move in a longitudinal direction. As a result, the observed transport process is similar to the transport with immobilisation. It allows dividing the full solute concentration to mobile and immobile by analogy to the MIM approach. Mobile solute transports with the mean flow in a longitudinal direction. The immobile solute is immobilized by the vortices. The solute transition between these two phases is provided by the diffusion and determines by the concentrations in both phases. The MIM approach is used very often for modelling the transport in porous media. Usually, the particle immobilisation in porous media is explained by the interaction of solute particles with a solid matrix of porous media. However, the flow through porous media is complex and vortices are formed by the interaction of flow with the solid matrix of media. We model the transport of initially heterogeneous distributed solute through the channel by the flow with vortices. The modelling is performed into the terms of special flow by the microscopic methods. The distribution of passage time is compared for the same distribution obtained by standard linear macroscopic MIM model. The comparison is performed by the solution of the inverse problem with minimization the difference between these two distributions. As a result, the parameters of the linear MIM model is defined and its dependence on the vortices structure and the molecular diffusivity is obtained.

该论文致力于研究通过一系列以刚性壁为界的涡流的纵向溶质传输。由于这种系统中的流体速度非常不均匀，因此溶质粒子的转移具有非平凡的性质。一些粒子可以通过扩散驱动流入涡流。这些粒子不会沿纵向移动。因此，观察到的运输过程类似于固定化运输。类似于 MIM 方法，它允许将完整的溶质浓度划分为可移动和不可移动。移动溶质以纵向平均流传输。固定的溶质被涡流固定。这两相之间的溶质转变由扩散提供，并由两相中的浓度决定。MIM 方法经常用于模拟多孔介质中的传输。通常，多孔介质中的颗粒固定是通过溶质颗粒与多孔介质固体基质的相互作用来解释的。然而，通过多孔介质的流动是复杂的，涡流是由流动与介质的固体基质相互作用形成的。我们模拟了最初异质分布的溶质通过带有涡流的流动通过通道的传输。采用微观方法对特殊流动项进行建模。将通过时间的分布与通过标准线性宏观 MIM 模型获得的相同分布进行比较。比较是通过解决反问题来执行的，同时最小化这两个分布之间的差异。因此，