Mathematical multi-scale model of water purification

Abstract

In this work, we consider a mathematical model of the water treatment process and determine the effective characteristics of this model. At the microscopic length scale, we describe our model in terms of a lattice random walk in a high-contrast periodic medium with absorption. Applying then the upscaling procedure, we obtain the macroscopic model for total mass evolution. We discuss both the dynamic and the stationary regimes and show how the efficiency of the purification process depends on the characteristics of the macroscopic model.