Mathematical multi-scale model of water purification

TL;DR

This paper develops a multi-scale mathematical model of water purification, linking microscopic lattice dynamics to macroscopic mass transfer, and analyzes how process efficiency depends on model parameters.

Contribution

It introduces a novel multi-scale modeling approach for water treatment, combining microscopic lattice random walks with macroscopic upscaling techniques.

Findings

Derived effective macroscopic equations for water purification

Analyzed the influence of microscopic parameters on macroscopic efficiency

Provided insights into dynamic and stationary purification regimes

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.