Theoretical Substantiation of Concentration Polarization in Electrochemical Baromembrane Processes for the Purification of Copper-Containing Solutions from Galvanic Plants

In this paper, a method of optimizing two functions at once, such as maximum specific solvent flux (water permeability) J_{v max} and minimum concentration polarization θ_min by using a complex criterion Ф and criterial functional restrictions is proposed to determine J_{v max} and θ_min depending on the application of electrical current and the hydraulic permeability coefficients of a solvent. The equations of optimizing the functions of specific solvent flux J_v and concentration polarization θ are given in an analytical form without empirical correction coefficients to simplify the process of optimization. The maximum deviations between the analytically and experimentally found values are less than 3% for J_v and 2% for θ_min.