ION EXCHANGE ON A FIBROUS ION EXCHANGER IN A FLO-TYPE CAPACITIVE APPARATUS

The objective of this study is to elaborate the analytical theory of ion exchange in the field of solving the boundary value problems of non steady state mass transfer in solids with a canonical form taking into account a change in the concentration of the solution and the character of movement of the phases in a flow apparatus. The mathematical description of the process of ion-exchange solution purification on ionite particles of cylindrical shape in a batch flow apparatus was developed. At the developing mathematical description the following assumptions were used: the ionite is monodisperse, uniform initial distribution of substances in the ionite, the ion exchange equilibrium is described by Henry equation, the rate of the process is limited by both internal and external diffusion, the flow pattern of the liquid phase in the apparatus is described by the perfect mixing model, the solution with the constant volumetric flow rate and the constant concentration of the substance  is supplied to the apparatus, kinetic and hydrodynamic process parameters are constants. Mathematical description includes the following equations: the diffusion equation of ionite, isotherm equation ion exchange, the equation for average concentration of the substance in the ionite, the material balance equation for a perfect mixing flow apparatus, initial and boundary conditions. To solve boundary value problem, we use the integral Laplace transformations. The obtained equation allows to analyze the effect of the volumetric flow rate of the solution supplied to a flow apparatus, the ratio of the volumes of solid and liquid phases in the apparatus, the diameter of the particle, and other parameters of the process on the concentration distribution of a substance along the internal coordinate of the solid. The developed mathematical model is used to study the desorption of copper ions from the modified polycaproamide fiber with sulfuric acid solution.