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The paper proposes an engineering calculation method, on the basis of which it was proposed to use three ultrafiltration units connected in series for the ultrafiltration separation of cheese whey components. These installations operated in a continuous cycle, which contained membrane devices with the calculated parameters. This paper describes a scheme for obtaining whey protein concentrate from cheese whey formed during the processing of milk into rennet cheese. The scheme works on a tubular ultrafiltration apparatus - it was accepted for development at ChS VERO LLC. In our proposed scheme, an electrodialysis unit is used, since this unit has more advantages than others. The advantage of the electrodialysis unit is the demineralization of technological solutions with a high dry matter content (concentrated whey, gelatin, sugar syrup, chicory syrup, glycerin) and tolerance. The productivity of the selected electrodialysis plant allows the concentrated volume to be brought to a demineralization level of 80% in about 1 hour. The work describes in detail the scheme of the concentration line for LLC "VEKSHA" and LLC "ChS" VERO "with obtaining dry whey concentrate, including a tube-type ultrafiltration apparatus. Also substantiated is the value determined by the ratio of the results of production and labor costs and funds for the production of cheese whey for LLC "ChS" VERO "and LLC" VEKSHA ". The expected economic effect from the introduction of the line will be 4200 thousand rubles. for LLC "VEKSHA" and 980 thousand rubles. for LLC "ChS" VERO "per year in prices of 2021.

Results are presented from studying active and drainage layers of composite ultrafiltration polysulfone and polyethersulfone membranes via thermogravimetry (TG), differential scanning calometry (DSC), and X-ray diffraction analysis in the air-dried state and after exposure to transmembrane pressure and permeate diffusion. It is found that thermal effects of polymer layers are observed on the TG and DSC curves of the composite membrane samples. The thermal properties of Lavsan (PET) are apparent in the temperature range of 32 to 240°C; those of polysulfones, from 240 to 450°C. Deconvolution of endothermic peaks shows that the peak at Tgt = 64.1°C correlates with glass transition temperature; the peak at Tm = 188.4°C, with the melting of PET crystallites according to the empirical rule of two thirds: Tgt ≈ 2/3Tm. Degradation of both PET and polysulfone macromolecules starts at T = 450°С. It is shown that transmembrane pressure and the diffusion of water alter the chemical composition of Lavsan in ~50% of its mass as a result of hydrolysis. X‑ray diffraction measurements of the active membrane layer at 2θ ≈ 17.5° confirms the amorphous structure of polysulfones. The shift of the diffraction angle toward large angles 2θ ≈ 19.24° for PS indicates an increase in the packing density of macromolecules in amorphous formations of the working sample. It is concluded that the density of packing falls for polyethersulfone at 2θ ≈ 17.34°.

A pressure-driven electrolytic membrane system of drum type is proposed. Solutions may be effectively separated by combining the pressure-driven electrolytic membrane technique with water cooling of the electrode. The drainage channels from the anode and cathode regions are independent. A method is proposed for calculating the strength of the system’s housing. The required thickness of the outer wall and the fiberglass flanges is determined.

An analytical review on the study of structural changes in membranes is presented. Ultrafiltration films of polytetrafluoroethylene membranes in the temperature range from 30 to 500°С are investigated by thermogravimetry. An analysis of the thermal data is carried out, which indicates that in the temperature range from 100 to 215°C, the first stage of destruction occurs, where the value of the lost mass for the air-dry sample is 33%, and for the water-saturated sample, the mass loss is 10%, which is 3 times less than the first sample. For the working sample, a slow process of mass change is observed in a wide temperature range from 100 to 410°C, which with total weight loss is about 9%. The second stage of destruction occurs in the temperature range from 410 to 500°C with a loss of mass for an air-dry sample of 61 and 85% for a water-saturated sample, and the working sample loses 86% of its mass. The data on X-ray crystallography (X-ray crystallography) allow us to conclude that the effect of water and transmembrane pressure leads to a significant change in the morphology of polymer molecules at the supramolecular level. If for an air-dry sample of a polytetrafluoroethylene ultrafiltration membrane, a diffuse nature of the reflection with a maximum at 2θ = 12° is observed, then for a water-saturated sample an intense diffraction peak appears at 2θ = 17° against the background of an amorphous halo. For the working sample, the reflection has a compact structure with a sharp asymmetric peak at 2θ = 13.8°. Complementary methods of TG (thermogravimetry), DSC (differential scanning calorimetry), X-ray diffraction analysis (XRD), and gravimetry have established that conformational changes in molecules in the polytetrafluoroethylene-membrane matrix occur as a result of the detachment of side monomers or oligomers and their sublimation from the film volume under the influence of transmembrane pressure and the interaction of water molecules.

This work has investigated changes in crystallinity and amorphism in the surface layers of commercial microfiltration films. Experimental studies of supramolecular formations and changes in the structure of microfiltration films were carried out by differential scanning calorimetry and X-ray diffractometric measurements in reflection geometry in the region of large angles. In the process of water swelling of semipermeable films of the MMPA, MPS, and МFFK types, a change in the structure of the lattice of the films is observed due to an increase in the interatomic distance, that is, the size of the pore diameter is likely to change throughout the structure of both the active layer and the film substrate. The observed changes in the supramolecular structure of the films upon swelling occur to a greater extent due to the disordering of macrochains in all layers of the films. The decrease in the degree of crystallinity of the films upon sorption of water is most likely associated with the redistribution of the ratio between the number of perfect crystalline phases in polyamide crystallites with different values of the enthalpy of melting.

A method is developed for calculating the values of concentration polarization during the separation of an aqueous solution containing anionic surfactants for ultrafiltration membranes with ideal and non-ideal rejection coefficients in a wide range of changes in the values of the diffusion Peclet number.

The paper presents two methods for identifying microstructural heterogeneities on the surface of OFAM-K and OPMN-P nanofiltration membranes. Optical microscopy in combination with the AutoCad 2016 computer-aided design system and standard Microsoft Excel 2010 tools allows one to investigate microstructural heterogeneities of initial samples of OPMN-P and OFAM-K nanofiltration membranes. A method that enables the automated calculation of the average diameter of the fouling of semi-permeable membranes and the fouling coefficient of porous bodies is also developed. Using the capabilities of the Matlab 2017 software package, the application of modern tools to accomplish the set goal of the work is shown. Practical implementation of the method is exemplified by the nanofiltration process with semi-permeable polymer membranes of OFAM-K and OPMN-P types. The automated method combining optical microscopy studies, Otsu image processing, and software implementation in Matlab 2017 and optical microscopy in combination with the AutoCad 2016 computer-aided design system and standard Microsoft Excel 2010 tools, which more accurately reveals the structural heterogeneities of OFAM-K and OPMN-P nanofiltration membranes, are compared.

The kinetic and thermal processes occurring during the separation of model solutions using electrodialysis equipment have been investigated. The design drawbacks of the developed apparatus that can affect the efficiency and quality of the solutions separation have been revealed.

The design of a roll-type electrobaromembrane apparatus has been developed, in which a high efficiency of mixing of multicomponent solutions is ensured when separating colloidal process fluids and waste water from chemical industries. A method for calculating the total area of membranes in an electrobaromembrane apparatus, taking into account the areas of roll and tubular elements, has been developed.

For the qualitative application of ultrafiltration processes for the concentration and purification of food solutions, both experimental studies and a mathematical description of the processes of the membrane separation process of solutions from the standpoint of the development of computational mathematical models are required. In this work, by analytical solution of equations, that is, by the method of finite differences, mathematical equations are solved. To obtain the system, the flow continuity equations, convective diffusion equations, Navier-Stokes equations and flow equations with boundary conditions were solved in order to build a mathematical model of the process of ultrafiltration protein concentration in cheese whey in the production of rennet cheeses. As a result of the analytical solution of the equations, a system of mathematical equations was obtained that allows one to construct a profile of changes in the flow rates of the solution along the cross-section of the intermembrane channel and to determine the protein concentration in cheese whey along the length of the tubular ultrafiltration element BTU 05/2 of industrial type. The obtained mathematical model makes it possible to theoretically describe the process of ultrafiltration protein concentration in cheese whey along the entire length of the membrane channel of the tubular element under laminar and transient regimes of solution flow. The resulting system of mathematical equations makes it possible to find the numerical values of the mass flow rate of cheese whey, make it possible to calculate the specific output flow when the transmembrane pressure changes and to calculate the concentration of solutes in the secondary milk raw materials on the left and right ultrafiltration membrane of the intermembrane channel. The adequacy of the developed mathematical model was carried out by comparing the calculated and experimental data on the specific output flow when the transmembrane pressure in the intermembrane channel changes from 0.1 to 0.25 MPa with ultrafiltration concentration of cheese whey. The deviation of the calculated data found by the mathematical model from experimental studies obtained on a semi-industrial tubular ultrafiltration plant BTU 05/2 using semipermeable membranes, in which the active layer is made of fluoroplastic, hemisulphone and polyethersulfone, did not exceed 10%.

Electrochemical and transport characteristics of systems equipped with OPMN-P and OFAM-K membranes during operation in electronanofiltration cell are studied experimentally. The reasons for changes in the characteristics of membrane systems under the influence of various factors in the process of electronanofiltration of solutions that simulate the ionic composition of the ammonium-nitrate- and potassium-sulfate-containing solutions from electroplating and mineral fertilizers production, as well as the process media of the Livshits АО ТАGAT electroplating plant, are revealed. The change in the local conductivity of the solution in the intermembrane channel and, as a consequence, the increase in current density at the studied solution electronanofiltration is shown to be connected with the flow restriction in the electrochemical cell and the solution heating. Analysis of the systems’ electrochemical characteristics during the electronanofiltration the galvanic-production process media gave the degradation range of the OPMN-P semi-permeable membrane active layer (15–30 V) because of surplus of the operation range certified value pH > 12. Improving of the transport characteristics of membrane systems during electronanofiltration of aqueous solutions (ammonium nitrate, and potassium sulfate) is associated with the increase in the pressure differential. Increase of the voltage in the electronanofiltration cell leads to decrease in the outlet flow for the near-anodic membrane OFAM-K and increase in the outlet flow for the near-cathoduc membrane OPMN-P. This is associated with the displacement of the pH value of the near-anodic permeate toward acidic environment; of the near-cathodic permeate, toward alkaline environment. It is found that during the electronanofiltration of the electroplating process media the surface of the near-cathodic membrane OPMN-P is coated with the Fe(OH)2 and Fe(OH)3 precipitates due to supersaturation. The precipitates act as an absorber of Zn2+, [Zn(OH)4]2–, and other ions at a constant pressure differential P = 1.6 MPa, which leads to the dynamic membrane formation. Empirical equations for the calculating of the specific outlet flux and the retention coefficient are proposed basing on the analysis of experimental data obtained during the membrane separation of the studied solutions under the action of the pressure differential and voltage.

We perform X-ray diffractometry, electron-microscopic, and kinetic studies of the surface layers of UAM-50 and UAM-100 ultrafiltration membranes. The crystallinity of the membranes is studied by X-Ray diffraction in the region of large angles 2θ from 2° to 40°, using a DRON-3 diffractometer with modern methods of the computer processing of experimental data. Comparative analysis of the X-ray diffraction patterns reveal the coincidence of the diffraction angles for the working and air-dry samples of ultrafiltration membranes, while the membrane samples have three pronounced maxima located approximately in the angular range from 17.50° to 25.60°. The crystallinity for the air-dry samples is 68% for UAM-50 and 74% for UAM-100, and for the working samples, it is 32 and 41% for UAM-50 and UAM-100, respectively. Investigations of the surface of drainage layers of the UAM-50 and UAM-100 ultrafiltration membranes are carried out by scanning electron microscopy. The thickness of the active layer is 27 nm for the UAM-50 membrane and 15 nm for the UAM-100 membrane. Pores of different sizes are visible on the surface of the active layer of the membrane; the pore sizes range from 2.5 to 40 nm for UAM-50 and from 10 to 40 nm for UAM-100. Kinetic studies of the ultrafiltration membranes confirm that they have an asymmetric pore structure. Small pores in the membrane trap contaminant molecules, while large pores allow the permeate to pass quickly to a more open permeate carrier, that is, a purified solution. The water permeability of the working membrane increases with an increase in the transmembrane pressure due to an increase in the driving force of the process and rearrangement of the crystal structure (a decrease in the size of crystals in the working sample of the membrane) and a decrease in the crystallinity of the membranes.

The electrodialysis method is used to recover iron, nickel and copper from waste water generated in the manufacture of printed circuit boards. The objects of study were ion-exchange membranes PC Acid 60 (PCCell GmbH) and CM (H) RALEX® (MEGA) and model solutions containing heavy metal ions (Fe3+, Ni2+, and Cu2+) and SO42– и NO3– anions. The time dependences of the retention coefficients of the Fe3+, Ni2+, and Cu2+ cations were constructed, the degree of treatment of the solutions to remove the SO42– и NO3– anions was determined, and the ion fluxes and ion transport numbers were calculated. On separating solutions containing one and all three salts of the target metals, the retention coefficients of Ni2+ and Cu2+ cations differ significantly, whereas those of Fe3+ cations, on the contrary, differ by no more than 2–3%. On separating a multicomponent three-salt solution, the retention coefficients of Ni2+ and Cu2+ cations are decreased in comparison with the corresponding values for single-salt solutions. For the purpose of exhaustive metal recovery, the electrodialysis separation of multicomponent solutions is the most efficient method, as applied to Fe3+ and Cu2+ cations.

A design of a tubular electrobaromembrane apparatus for cleaning industrial solutions of chemical plants is developed. An optimized version of the apparatus with an effective solution separating area is presented and the volume of the body components and the mass of the body are calculated. The economic merits of the materials for fabrication of the apparatus for electrobaromembrane and baromembrane separation are compared. The merits of the developed apparatus design are enlarged solution separation area, increased throughput, improved solution separation quality, and reduced material content per unit volume of the apparatus.

The influence of the structure of the surface cellulose acetate layer on the transport characteristics of ultrafiltration composite membranes is considered using the methods of IR spectroscopy and of scanning electron microscopy. The amorphous phase of ultrafiltration cellulose acetate composite membranes is formed at a certain stage of the technological cycle of obtaining a composite membrane. IR spectra are presented where the forms of the absorption bands of valence vibrations of hydroxylic groups at ν = 3339.14–3366.2 cm–1 alter the asymmetry parameter from ~1 for an air-dry sample and to 0.79 for a water-saturated one, which allows the assertion of formation of volumetric supermolecular structure of a cellulose acetate layer of an air-dry sample by two types of hydrogen bonds and dipole–dipole interactions of carbonyl groups. The decrease of the asymmetry parameter to 0.79 of the absorption bands of hydroxylic groups and of the intensity of absorption bands of methyl groups by 2.56, 3.3, and 3.8 times in water saturated samples of membranes occurs because of the destruction of supermolecular structure and reorganization of hydrogen bonds between the active groups of cellulose acetate and molecules of water. The data obtained by the method of scanning electron microscopy allow one to note that the surface layer of ultrafiltration membranes has an asymmetric pore structure. The surface layer of a membrane can be divided into two components: a selectively permeable layer with pores of small size and a pore substrate, in which the pores increase in their diameter as they approach the substrate.

A tubular electrochemical membrane apparatus that enables efficient mixing of chemical plant solutions to be separated and of colloidal process solutions is designed and a procedure for calculating the total working area of the membranes in a tubular electrobaromembrane apparatus is developed. The areas of the cathodic and anodic membranes are calculated.

This paper presents an analytical overview of the study of the kinetic and physicochemical characteristics of composite membrane films. UAM-100, UAM-150, and MGA-95 composite films have been studied using thermogravimetry in the temperature range from 30 to 300°C. A kinetic analysis of experimental data by the Freeman–Carroll method is carried out. It was found that hydrated water for all the studied semi-permeable films evaporates in the temperature range from ~95 to ~180°C. Comparison of the ratios of the amount of removed water in the film samples correlates with the geometric parameters of the pores. The values of the activation energy and the pre-exponential factor (E = 26.9 kJ/mol and ln(A ≈ 6.3 (min–1)) in the range 0.2 < α < 0.7 of the degree of dehydration indicate the same regularity in the distribution of water molecules in the polymolecular layer for all composite films. The high dehydration values, e.g., for a sample of a composite semipermeable film MGA-95 at the temperature of the maximum on the thermogravimetry curve (Tmax = 169.6°C) indicate that water molecules form hydrogen bonds both with ionogenic groups of cellulose acetate and with each other.

Experimental studies and analysis of the effect of transmembrane pressure on the composite porous film material of OFAM-K, OPMN-P membranes and their components by differential scanning calorimetry (DSC), X-ray diffraction analysis and optical microscopy are presented. Investigations of nanofiltration composite materials by differential scanning calorimetry make it possible to study thermal effects that cause changes in the structure and phase transformations with increasing temperature in the membrane sample. X-ray diffraction analysis of the crystalline and amorphous regions of composite films using the radial distribution function allow the change in the unit cells in the membrane polymer sample due to an increase in the interatomic distances to be established. The crystallinity in a membrane sample exposed to transmembrane pressure increases from 44 to 55% due to the appearance of an additional crystalline phase in the film. Optical microscopy studies of the membrane substrate show a morphological feature that resembles fiber compaction, as well as the presence of microscopic voids, which can ultimately be explained by the presence of more knitted fibers in some areas of the membrane.

A comparative study of the application of membrane, electromembrane and electrobaromembrane technologies for various industries in the field of wastewater treatment and technological solutions is presented. The principle of classification of membrane separation processes is formulated. The characteristic periods of the solvent transfer stimulation were determined. Based on the experimental data obtained on the permeability of the solvent through the MGA-80P and MGA-95 membranes, empirical dependences are proposed that describe the kinetic characteristics of the dependence from transmembrane pressure and temperature effects.

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 classification of chemical purification technologies, membrane processes, depending on the pore size in membranes is given. It has been established that environmentally friendly membrane methods for separating liquid media are an alternative to traditional methods for separating technological solutions and industrial waste waters.

The paper presents the results of experimental data on the kinetic characteristics of ultrafiltration tubular elements, such as the output specific flow, retention coefficient, diffusion permeability coefficient, distribution coefficient. To study the purification of milk whey, we used tubular ultrafilters BTU 05/2 with membrane material fluoroplast (F), polyethersulfone (PESF), polysulfone (PS). For theoretical calculation of the retention coefficient, output specific flux, diffusion permeability coefficient, distribution coefficient, mathematical expressions were developed and empirical coefficients were obtained. The developed mathematical expression describes the experimental data with good reliability. The obtained experimental and calculated data can be used with high reliability in calculating mass-transfer fluxes of substances through a semi-permeable membrane, as well as in engineering methods for calculating and predicting efficiency, and using membrane processes for concentrating serum. The protein concentration in real milk whey was determined by formol titration. On the basis of the studies carried out, the dependence of the growth of the output specific flow on pressure was established, that the optimal pressure for concentrating milk whey on the ultrafiltration membranes we have chosen is 0.25 MPa. For three types of ultrafilters, the experimental value of the coefficient was within 99% for protein. For the theoretical calculation of the retention coefficient, a program in the MAXIMA language was developed and registered. Due to the method of applying the membrane to the reinforcing element, the membrane material polyethersulfone (PESF) and polysulfone (PS) have a substrate, due to which they sorb more substances on themselves, because of this, the diffusion permeability coefficient and the distribution coefficient are much higher than that of a filter element with membrane made of fluoroplastic (F), which does not have a substrate.

The paper considers works on methods for calculating design and technological parameters, design of membrane equipment, research of technological features of membrane devices, selection of design schemes, methods for calculating strength and stiffness. A method has been developed for calculating mechanical loads and determining the thickness of plates and toroidal shells of a membrane apparatus of the combined type, which makes it possible to assess the strength properties of apparatus of this class. An example of a calculation, which makes it possible to assess the adequacy of the application of this technique to devices of the combined type, is given.

A procedure has been developed for calculating end flanges of a flat-chamber type of electrobaromembrane apparatus weakened by a porthole for feeding solution to be separated in accordance with permissible stresses, taking account of the loading time.

Experimental data have been obtained, and the characteristics of the moisture content and permeability of cellulose acetate porous materials were analyzed via thermal action. Dynamic thermogravimetric analysis found that the destruction process in an air-dry sample of the membrane begins at 21°C. It is accompanied by a 2% weight loss and an endothermic effect. The destruction ends at 50°C. With a subsequent increase in temperature, the manifestation of endothermic effect continues a temperature of 120–175°C with the maximum rate of mass loss at 146°C. The weight loss ends at about 190°C and is 6.5%. The study of MGA-80 and MGA-95 porous cellulose acetate films at transmembrane pressure upon temperature exposure showed that the permeability and specific output flow to water increase as the temperature rises to 50°C. Analysis of dependences of the specific output flow on temperature revealed that the specific output flow to water increases by ~18% upon an initial temperature rise of 10°C. This is due to structural changes in the cellulose acetate layer. A further increase in temperature by 15°C leads to an increase in permeability by ~10%. These phenomena are associated with the process of structural transformation in the active layer and the polymer substrate of the MGA-95 and MGA-80P membranes, respectively.

The periodic method for the production of suspension polymethylmethacrylate of injection molded grades has a number of significant drawbacks: it does not ensure the stability of the properties of the finished product in various batches, it involves significant manual labor. The designs of reactors for carrying out the process in a continuous mode are proposed. These designs allow ensuring the stability of the properties of the finished product, excluding the granulation operation in the manufacture of polymethylmethacrylate products. A mathematical model of the structure of flows in the reactor using the mathematical apparatus of stationary processes and Markov chains has been developed. The proposed reactor can be used by factories of the chemical industry for the polymerization of methyl methacrylate and its copolymers, as well as, possibly, for the polymerization of other monomers that form similar reaction systems.

A developed design of a combined-type electro-baromembrane apparatus for separating solutions into two successive circuits is presented. As well as allowing differential ion separation in the flows of cathode and anode permeate in the form of bases and acids at the first stage of separation, the baromembrane design leads to reduced hydraulic resistance per unit volume and improved solution separation efficiency. The methodology used for calculating the technological characteristics of the apparatus is described.

The paper presents the structural organization of the surface (selective) layer. The amorphous phase of the cellulose acetate composite membrane is formed at a certain stage of the technological cycle of producing the cellulose acetate membrane. It presents a mass of broken, entangled, and twisted macromolecular chains connected by a network of hydrogen bonds of various strengths. Analysis of the IR spectra, where the shapes of the absorption bands of the valence vibrations of hydroxyl groups at ν = 3339.14–3366.2 cm–1 with the asymmetry coefficient varying from ~1 for a dry sample to 0.79 for a wet sample, suggests that the bulk supramolecular structure of the cellulose acetate layer of the air-dry sample is formed by two types of hydrogen bonds and the dipole–dipole interactions of the carbonyl groups. The interactions of macromolecules in the equatorial plane are formed by a network of hydrogen bonds of the OH…O type with the participation of a single hydroxyl group of the pyranose ring in cellulose acetate. In the axial direction, the supramolecular structure is organized through the hydrogen bonds of the CH…O=C type between the methane and carbonyl groups, as well as possibly the dipole–dipole interactions between the coplanar ordered dipoles of the C=O groups. The coefficient of asymmetry of the absorption bands of hydroxyl groups is reduced to 0.81–0.79 and the intensity of the absorption band of methyl groups is reduced by factors of 2.56, 3.3, and 3.8 in water-saturated samples due to the destruction of the supramolecular structure and the reorganization of the hydrogen bonds between the active groups of cellulose acetate and water molecules. The absence of an absorption band of ν = 873.53–851.9 cm–1 in the water-saturated samples indicates a conformational rearrangement of the macromolecules into a linear form with the formation of narrow mesopores of cellulose acetate between the macromolecules.