A Model of Water Treatment by Nanoparticles in a Channel with Adjustable Width under a Magnetic Field

Abstract

The process of water treatment by nanoparticles is one of the most considerable subjects in the cross-field of hydrodynamics, chemistry, and mathematics. This paper is dedicated to the case of the flows that appear when squeezing and stretching a channel with mixing of water, nanoparticles, and contaminants. It is assumed that fluid is homogeneous at the starting moment, the parameters of the nanoparticles and contaminants are known, and there is a constant non-homogeneous magnetic field applied to the system. The flow starts moving when the walls of the channel shift to each other. Exact and numerical solutions of the system of ordinary differential equations are used to obtain the results. The article gives an answer to the question about stability of the flow and proposes the technique to evaluate the essential characteristics of the system to achieve the treatment process efficiency. The main result is that the considered system shows excellent properties concerning purification of water on the selected part of the squeezing stage. This effect does not appear without a magnetic field. The mentioned properties are: decreasing of nanoparticle concentration to zero inside of the unsteady layer under magnetic field close to 1 T and this effect stays until the channel become about 10% of initial width as a result of the squeezing.