Abstract
The paper considers the principles of constructing a mathematical model of water treatment based on the use of a biologically active layer, the bacteria of which absorb harmful impurities contained in water. A system of equations is presented on the basis of which a model of water purification is constructed in the simplest element, which is a rod covered with a biofilm. The system of equations is a system that includes a parabolic equation in a three-dimensional domain and a hyperbolic equation on a part of the surface of this domain, connected to each other through a boundary condition and a potential in an equation of hyperbolic type. Next, an asymptotic analysis of this system is carried out, which allows us to reduce the model of an individual element to the solution of a simple ordinary differential equation. On this basis, a model of the entire water treatment device is proposed.
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