Diffusion effect on passive solute transport inside an infinite two-dimensional array of vortices

Abstract

Abstract The transport process of solute in a two-dimensional liquid flow is studied. The infinite plane is “covered” by square cells with periodic conditions at its boundaries. The flow is provided by a periodic external force. If the amplitude of the external force reaches a certain critical value, then the flow in each cell contains a pair of vortices. The analysis of the transport of a passive solute in such a flow is investigated in terms of a special flow. In the framework of this approach the transport process is described by mapping functions that determine the coordinates of the particle at the end of the unit cell and the time of passage of the cell as a function of the coordinates at the entrance to the cell. These functions are obtained numerically by the random walk method taking diffusion into account. Using the special flow approach the distribution of an initially uniform distributed ensemble of passive particles with time is calculated for the passage of a long array of the unit cells. It is shown that for tiny values of diffusivity the transport slowing down some particles regarding the ensemble is observed. The speed-up of some particles regarding the ensemble is observed for moderate values of diffusivity and for high diffusivity we obtain the standard diffusion.