The present work examines the hydrodynamic flow pattern in an industrial tubular baromembrane device on the example of commercially available membrane elements at pressures of 1.0–4.0 MPa. ...Experimental response curves and dependence curves of the longitudinal mixing coefficient were obtained as a function of the solution flow rate and the pressure in the membrane module. Based on this information, the criterial equation for calculating the longitudinal mixing coefficient was obtained. Numerical values of empirical coefficients are given, which can theoretically be used to calculate the longitudinal mixing coefficients as well as to predict the values for similar constructions of baromembrane systems operating at high transmembrane pressures.
The results of experimental research on hydrodynamics of solution flow in membrane channel are reported. Response curves correlating flow pattern with solution flow rate, pressure, and type of ...membrane module are obtained. A theoretical analysis of the research results is made with a description of the response curves using criterial equations that correlate empirical coefficients with solution flow rate in the channel, pressure, and type of membrane elements.
The results of the development of a tubular electrobaromembrane apparatus (having a uniform filtration area) to treat electroplating process solutions and wastewater are presented. A technique for ...engineering calculation of the proposed advanced design of an electrobaromembrane apparatus with tubular filter elements for implementing the purification of electroplating process solutions and wastewater is presented, taking into account the design features of the apparatus and the dependence of the permeate flow rate on the parameters of the separation process.
The article presents the results of development of a roll-type electrobaromembrane apparatus for separation of technological solutions of chemical industries with differentiated removal of ions. A ...method is described for engineering calculation of the proposed promising design of a roll-type electrobaromembrane apparatus for separation of technological solutions of chemical and engineering industries, taking account of the hydrodynamics and direction of solution movement.
The article presents the results of a study of mass transfer in the process of electrochemical extraction of iron, magnesium and manganese ions from technological solutions. Mathematical expressions ...are obtained, and numerical values of empirical coefficients are determined for theoretical calculation of specific outflow, retention coefficient, and average mass transfer coefficients of the electrochemical membrane process of separation of technological solutions. The dependence of concentration polarization on solution flow rate, pressure gradient, and concentration is analyzed.
A method for calculating a tubular electrobaromembrane apparatus with a nonuniform filtration area has been developed. Due to the addition of concentric cathode and anode membranes with protrusions ...of increased diameter, the tabular electrobaromembrane apparatus has an increased separation area per unit volume of the apparatus. The developed technique enables one to calculate the volume and weight of the apparatus and its environmental and economic efficiency in the separation of biologically active solutions.
The objectives of this study are to perform the mathematical description of the formation of a sediment layer on the surface of membranes due to concentration polarization on the basis of the ...semi-integral method of solving the convective diffusion equation, to optimize the process of ultrafiltration and determine the sediment layer on the surface of a membrane, and to calculate the membrane operation time and the filtrate volume in a steady-state regime before regeneration. Minimization results show that the lowest function value of 1.32583 and 1.32112 is given by the Wolfram Mathematica software for the Na
3
PO
4
concentrations of 0.5 and 1 kg/m
3
, respectively. It is established that concentration polarization attains the maximum admissible value of 1.32583 and 1.298 for the solutions with concentrations of 0.5 and 1 kg/m
3
at 2.43 and 2.52 s from the beginning of the separation process, respectively. The propagation of concentration polarization throughout the entire channel length requires 5500 and 5710 s, respectively. Afterwards, the membranes require regeneration to maintain the necessary level of purification. In these time periods, 0.191 and 0.173 L of filtrate are formed.
A developed spiral-wound electrobaromembrane apparatus offering increased efficiency of solution separation (due to differentiated removal of cathode permeate and anode retentate, depending on the ...anode or cathode connection scheme) is presented. A method for calculating a spiral-wound electrobaromembrane apparatus with an increased separation efficiency of industrial solutions containing zinc, copper, cobalt, and nickel ions is developed along with an assessment of the economic efficiency of an electrobaromembrane installation by calculating the total energy consumption required to carry out the separation process of a process solution containing heavy metal ions.
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The paper analyzes the state of the problem of the theoretical prediction of the retention coefficient and specific output flow for purification or concentration of industrial solutions throughout ...the cycle of nanofiltration separation of industrial solutions containing metal ions. To predict the nanofiltration process, a mathematical model is developed based on solving the equations of convective diffusion, the Navier–Stokes equation, and the flow continuity equation using a polar coordinate system. The theoretical results obtained as a result of solving the system of equations make it possible to evaluate the quality and productivity of nanofiltration separation by calculating the concentrations in the permeate and retentate tracts and the permeate volume. The adequacy of the developed method is assessed by comparing the data calculated using the model with the experimental data obtained on a nanofiltration unit during the separation of solutions containing Cr
3+
and Zn
2+
cations using semi-permeable membranes OPMN-P and AMN-P.
A mathematical description of the electrobaromembrane process using an approach based on the Nernst–Planck and Poisson–Boltzmann equations is presented. The hydrodynamic conditions in the ...intermembrane channel is taken into account by a dimensionless equation based on the Reynolds criterion and a technique is presented for determining electrobaromembrane separation of solutions, taking into account the kinetics of mass transfer and the hydrodynamics of the flow of a solution in an intermembrane channel. Through the use of the technique the local mass-transfer coefficients along the length of the channel of the membrane module may be determined. The technique may also be used to predict and develop laboratory, pilot and industrial electromembrane instruments and plants.
