Abstract
A mathematical model of water softening in a mechanical filter based on the balance relations for the mass components of the thermodynamical system is constructed. The initial-boundary value problem of convective diffusion accompanied by a chemical reaction is formulated for one-dimensional case of spatial coordinates and reduced to the equivalent system of integro-differential equations. The solution of this system is constructed by the method of successive iterations by decomposing the functions of the mass concentrations of impurity in water solution and in the body skeleton into series around the solutions of the homogeneous linear initial-boundary value problem. Based on the expression for the impurity concentration in the aqueous solution the mass flows of impurity are obtained and investigated. The nonlinearity of steady-state regime, which is caused by the transfer of mass simultaneously by diffusion and convection mechanisms, is shown.
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