Concentration Polarization Conditions Research Articles

The Role of the Gravitational Field in Generating Electric Potentials in a Double-Membrane System for Concentration Polarization Conditions.

Electric potentials referred to as the gravielectric effect (∆ΨS) are generated in a double-membrane system containing identical polymer membranes set in horizontal planes and separating non-homogenous electrolyte solutions. The gravielectric effect depends on the concentration and composition of the solutions and is formed due to the gravitational field breaking the symmetry of membrane complexes/concentration boundary layers formed under concentration polarization conditions. As a part of the Kedem-Katchalsky formalism, a model of ion transport was developed, containing the transport parameters of membranes and solutions and taking into account hydrodynamic (convective) instabilities. The transition from non-convective to convective or vice versa can be controlled by a dimensionless concentration polarization factor or concentration Rayleigh number. Using the original measuring set, the time dependence of the membrane potentials was investigated. For steady states, the ∆ΨS was calculated and then the concentration characteristics of this effect were determined for aqueous solutions of NaCl and ethanol. The results obtained from the calculations based on the mathematical model of the gravitational effect are consistent with the experimental results within a 7% error range. It has been shown that a positive or negative gravielectric effect appeared when a density of the solution in the inter-membrane compartment was higher or lower than the density in the outer compartments. The values of the ∆ΨS were in a range from 0 to 27 mV. It was found that, the lower the concentration of solutions in the outer compartments of the two-membrane system (C0), for the same values of Cm/C0, the higher the ∆ΨS, which indicates control properties of the double-membrane system. The considered two-membrane electrochemical system is a source of electromotive force and functions as an electrochemical gravireceptor.

Low-frequency impedance of ion-exchange membrane with electrically heterogeneous surface

Understanding of the effect of membrane/electrode surface heterogeneity on the electrochemical behavior of membrane/electrode systems in conditions of current-induced concentration polarization is an important issue. In this paper, low-frequency electrochemical impedance spectra (EIS) of electrically heterogeneous ion-exchange membranes (IEMs) are studied experimentally and theoretically. A 2D model for calculating these spectra is proposed. Non-stationary ion transport through a heterogeneous membrane and two adjacent diffusion layers is studied. The corresponding mathematical problem is solved numerically and analytically under conditions of zero DC bias of the applied AC signal. It is shown that at sufficiently low frequencies, the impedance spectrum of a heterogeneous IEM is described by the finite-length-Warburg-type impedance. However, in the range of relatively high frequencies, a nose-shaped element appears on the complex plane plot. This element reflects an increase in the system resistance due to a higher concentration polarization of the boundary solution caused by nonconductive surface areas. An exact analytical solution describing the impedance is found in the case where the diffusivities of anion and cation are the same. The form of this solution is convenient for the experimental data analysis. A good quantitative agreement between the calculated and experimental impedance spectra for several commercial and specially prepared heterogeneous membranes is established.

Evaluation of Transport Properties and Energy Conversion of Bacterial Cellulose Membrane Using Peusner Network Thermodynamics.

We evaluated the transport properties of a bacterial cellulose (BC) membrane for aqueous ethanol solutions. Using the Rr version of the Kedem-Katchalsky-Peusner formalism (KKP) for the concentration polarization (CP) conditions of solutions, the osmotic and diffusion fluxes as well as the membrane transport parameters were determined, such as the hydraulic permeability (Lp), reflection (σ), and solute permeability (ω). We used these parameters and the Peusner (Rijr) coefficients resulting from the KKP equations to assess the transport properties of the membrane based on the calculated dependence of the concentration coefficients: the resistance, coupling, and energy conversion efficiency for aqueous ethanol solutions. The transport properties of the membrane depended on the hydrodynamic conditions of the osmotic diffusion transport. The resistance coefficients R11r, R22r, and Rdetr were positive and higher, and the R12r coefficient was negative and lower under CP conditions (higher in convective than nonconvective states). The energy conversion was evaluated and fluxes were calculated for the U-, F-, and S-energy. It was found that the energy conversion was greater and the S-energy and F-energy were lower under CP conditions. The convection effect was negative, which means that convection movements were directed vertically upwards. Understanding the membrane transport properties and mechanisms could help to develop and improve the membrane technologies and techniques used in medicine and in water and wastewater treatment processes.

Management of Energy Conversion Processes in Membrane Systems

The internal energy (U-energy) conversion to free energy (F-energy) and energy dissipation (S-energy) is a basic process that enables the continuity of life on Earth. Here, we present a novel method of evaluating F-energy in a membrane system containing ternary solutions of non-electrolytes based on the Kr version of the Kedem–Katchalsky–Peusner (K–K–P) formalism for concentration polarization conditions. The use of this formalism allows the determination of F-energy based on the production of S-energy and coefficient of the energy conversion efficiency. The K–K–P formalism requires the calculation of the Peusner coefficients Kijr and Kdetr (i, j ∈ {1, 2, 3}, r = A, B), which are necessary to calculate S-energy, the degree of coupling and coefficients of energy conversion efficiency. In turn, the equations for S-energy and coefficients of energy conversion efficiency are used in the F-energy calculations. The Kr form of the Kedem–Katchalsky–Peusner model equations, containing the Peusner coefficients Kijr and Kdetr, enables the analysis of energy conversion in membrane systems and is a useful tool for studying the transport properties of membranes. We showed that osmotic pressure dependences of indicated Peusner coefficients, energy conversion efficiency coefficient, entropy and energy production are nonlinear. These nonlinearities were caused by pseudophase transitions from non-convective to convective states or vice versa. The method presented in the paper can be used to assess F-energy resources. The results can be adapted to various membrane systems used in chemical engineering, environmental engineering or medical applications. It can be used in designing new technologies as a part of process management.

Modelling of the Electrical Membrane Potential for Concentration Polarization Conditions.

Based on Kedem–Katchalsky formalism, the model equation of the membrane potential () generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes at different concentrations. The consequence of concentration polarization is the creation, on both sides of the membrane, of concentration boundary layers. The basic equation of this model includes the unknown ratio of solution concentrations ( at the membrane/concentration boundary layers. We present the calculation procedure ( based on novel equations derived in the paper containing the transport parameters of the membrane (, , and ), solutions (, ), concentration boundary layer thicknesses (, ), concentration Raileigh number (), concentration polarization factor (), volume flux (), mechanical pressure difference (), and ratio of known solution concentrations (). From the resulting equation, was calculated for various combinations of the solution concentration ratio (), the Rayleigh concentration number (), the concentration polarization coefficient (), and the hydrostatic pressure difference ). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m−3 () was on one side of the membrane and on the other side an aqueous NaCl solution with a concentration between 1 and 15 mol m−3 (). It is shown that () depends on the value of one of the factors (i.e., , , and ) at a fixed value of the other three.

Non-linear effects in osmotic membrane transport: evaluation of the S-entropy production by volume flux of aqueous ammonia and sulfuric acid solutions under concentration polarization conditions

Non-linear effects in osmotic membrane transport: evaluation of the S-entropy production by volume flux of aqueous ammonia and sulfuric acid solutions under concentration polarization conditions

Investigating the stability of electrically conductive membranes

Stability of electrically conductive membranes (ECM) is critical for expanding their application in separation-based technologies. In this work, ECMs were synthesized by coating polyethersulfone membranes with carbon nanotubes (CNT) crosslinked to polyvinyl alcohol (PVA) using two types of crosslinkers (succinic acid or glutaraldehyde). ECMs demonstrated a 21% reduction in flux over 4 h under cathodic potential (2 V) in comparison to a 69% reduction in flux for control experiments when filtering a realistic bacterial suspension. Subsequently, the electrochemical, physical, and mechanical stability of the ECMs were explored using chronoamperometry and cyclic voltammetry, an evaluation of polymer leaching from membranes, and micro mechanical scratch testing, respectively. ECMs were shown to be unstable under anodic potentials (2–4 V) with the glutaraldehyde crosslinking demonstrating the highest electrochemical stability. PVA was shown to be a physically unstable crosslinking agent for CNTs under concentration polarization conditions. Instability was moderated by extending CP layers through thicker and less dense nanolayers. ECMs showed higher mechanical stability and resistance to surface damage, in particular when coated with glutaraldehyde. We quantified the relationship between ECM surface instability and their physical and electrochemical properties. In so doing, we provide guidance for making practical and scalable electrically conductive membranes.

Evaluation of the Global S-Entropy Production in Membrane Transport of Aqueous Solutions of Hydrochloric Acid and Ammonia.

The results of experimental studies of volume osmotic fluxes () and fluxes of dissolved substances () in a system containing a synthetic Nephrophan® membrane (Orwo VEB Filmfabrik, Wolfen, Germany) set in a horizontal plane are presented. The membrane separated water and aqueous HCl or ammonia solutions or aqueous ammonia and HCl solutions. It was found that for the homogeneity conditions of the solutions and depend only on the concentration and composition of the solutions. For concentration polarization conditions (where concentration boundary layers are created on both sides), and depend on both the concentration and composition of the solutions and the configuration of the membrane system. The obtained results of the and flux studies were used to assess the global production of entropy for the conditions of homogeneity of solutions (), while and —to assess the global production of entropy for concentration polarization conditions ). In addition, the diffusion-convective effects and the convection effect in the global source of entropy were calculated. The concentration polarization coefficient was related to modified concentration Rayleigh number, e.g., the parameter controlling the transition from non-convective (diffusive) to convective state. This number acts as a switch between two states of the concentration field: convective (with a higher entropy source value) and non-convective (with a lower entropy source value). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport.

Membrane Transport in Concentration Polarization Conditions: Evaluation of S-Entropy Production for Ternary Non-Electrolyte Solutions

Abstract A model of the S-entropy production in a system with a membrane which separates non-electrolyte aqueous solutions was presented. The differences between fluxes in non-homogeneous and homogeneous conditions for volume and solute fluxes, respectively, are non-linear functions of the glucose osmotic pressure difference (OPD) in ranges dependent on the initial ethanol OPD. A decrease of ethanol OPD causes a shift of this range into the lower values of glucose OPD; this shift is also observed for negative values of glucose and ethanol OPDs. The coefficient of concentration polarization of the membrane as a function of glucose OPD has a sigmoidal shape. For suitably great negative values of glucose OPD this coefficient is very small, while for suitably high positive glucose OPD this coefficient is equal to 0.5. An increase of ethanol OPD at the initial moment causes a shift of this curve towards the direction of positive values of glucose OPD. In turn the S-entropy production in non-homogeneous conditions has low values for negative values of glucose OPD (convective range) while for suitably high positive glucose OPD it has greater values (diffusive and convective range). A change of ethanol OPD at the initial moment causes a shift of this curve along the horizontal axis.

Nanofiltration of saline oil-water emulsions: Combined and individual effects of salt concentration polarization and fouling by oil

This study employed NF270 nanofiltration membranes and SDS-stabilized hexadecane to identify mechanisms of membrane fouling by highly saline oil-water emulsions. Concentration dependencies of NaCl reflection coefficient σ and NaCl permeability coefficient B were measured and used to determine the separate contributions of osmotic pressure and fouling to the overall flux decline. The NaCl permeability coefficient asymptotically converged to the same steady state value across a range of feed salinities and concentration polarization conditions. The measured near-hyperbolic dependence of the reflection coefficient on the transmembrane concentration differential (σΔπm≈ const) negated the effect of concentration polarization on permeate flux. Oil caused an abrupt decrease in permeate flux but only for more saline feeds (seawater level and higher), which was interpreted as a result of membrane surface sealing by coalesced oil. Headloss analysis showed that over the longer term, the additional hydraulic resistance due to a layer of oil droplets on the membrane surface became the dominant fouling mechanism.

The Rr Form of the Kedem–Katchalsky–Peusner Model Equations for Description of the Membrane Transport in Concentration Polarization Conditions

The paper presents the matrix form of Kedem–Katchalsky–Peusner equations for membrane transport of the non-homogeneous ternary non-electrolyte solutions. Peusner’s coefficients and det [] (i, j ∈ {1, 2, 3}, r = A, B) occurring in these equations, were calculated for Nephrophan biomembrane, glucose in aqueous ethanol solutions and two different settings of the solutions relative to the horizontally oriented membrane for concentration polarization conditions or homogeneity of solutions. Kedem–Katchalsky coefficients, measured for homogeneous and non-homogeneous solutions, were used for the calculations. The calculated Peusner’s coefficients for homogeneous solutions depend linearly, and for non-homogeneous solutions non-linearly on the concentrations of solutes. The concentration dependences of the coefficients and det [] indicate a characteristic glucose concentration of 9.24 mol/m3 (at a fixed ethanol concentration) in which the obtained curves for Configurations A and B intersect. At this point, the density of solutions in the upper and lower membrane chamber are the same. Peusner’s coefficients were used to assess the effect of concentration polarization and free convection on membrane transport (the ξij coefficient), determine the degree of coupling (the coefficient) and coupling parameter (the coefficient) and energy conversion efficiency (the coefficient).

The Role of Gravity in the Evolution of the Concentration Field in the Electrochemical Membrane Cell

The subject of the study was the osmotic volume transport of aqueous CuSO4 and/or ethanol solutions through a selective cellulose acetate membrane (Nephrophan). The effect of concentration of solution components, concentration polarization of solutions and configuration of the membrane system on the value of the volume osmotic flux ( in a single-membrane system in which the polymer membrane located in the horizontal plane was examined. The investigations were carried out under mechanical stirring conditions of the solutions and after it was turned off. Based on the obtained measurement results , the effects of concentration polarization, convection polarization, asymmetry and amplification of the volume osmotic flux and the thickness of the concentration boundary layers were calculated. Osmotic entropy production was also calculated for solution homogeneity and concentration polarization conditions. Using the thickness of the concentration boundary layers, critical values of the Rayleigh concentration number (), i.e., the switch, were estimated between two states: convective (with higher ) and non-convective (with lower ). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport.

Influence of membrane sealing in pressure-driven test cells on their performance

This communication demonstrates the relevance of membrane sealing in a test cell to its performance. Membranes need to be sealed, and therefore a more or less signifcant (depending on the test cell design) peripheral part of the membrane is supported directly by the cell body (instead of a permeate spacer). Although it may seem that there should be no fltration through the membrane when it is supported by an impermeable surface, this communication demonstrates that this is not generally true due to fltration along the membrane porous support. To confrm this, experiments were performed with a cross-flow test cell (GE SEPA™ CF II), blocking the membrane hydraulically from beneath in order to simulate the effect of having the membrane supported by an impermeable surface. The results show that the trans-membrane volume flux obtained in all cases is only slightly affected by the membrane blocking. In view of this, in the cell design, care should be taken to reduce such peripheral parts of the membrane to a minimum because it may be technically very difcult to have there the same conditions of concentration polarization as over the membrane part supported by the permeate spacer.

Comparative study of nanofiltration membrane characterization devices of different dimension and configuration (cross flow and dead end)

Comparison of nanofiltration characterization data from literature is challenging due to different hydrodynamics and system designs, which affect membrane retention. In this study, stirred cell (SC), micro and macro cross flow systems (micro and macro CF) with different configuration were used to measure salt and organic tracer retention. Minimal concentration polarization conditions were applied in order to:1)evaluate comparability of the systems for characterization of membrane pore radius and molecular-weight-cut-off,2)understand the impact of system configuration and operation on mass transfer,3)compare salt retention at laboratory scale with the retention of spiral wound module.Results indicated that system dimension was the most important parameter to affect the mass transfer and the concentration of both salt and organic tracers on the membrane surface (Cm) in the macro CF system. Indeed, the higher channel length to width ratio of macro CF was related to reduced mass transfer and higher Cm. However, a comparability of the three systems was observed by operating at low flux (below 80 L/m2h) and higher cross flow velocity (above 0.4 m/s), where the lowest concentration polarization conditions were maintained. This is valid taking into account the variation of hydrodynamics (e.g. relation of Sherwood number and Reynolds range), which is intrinsically related to the different operation modes of dead end and cross flow. This study gives a novel contribution to improve the accuracy of membrane characterization methodologies and to identify suitable operative conditions for testing new membrane materials at small scale.

Evaluation of S-Entropy Production in a Single-Membrane System in Concentration Polarization Conditions

S-entropy source of membrane system was described based on linear non-equilibrium thermodynamics. The volume and diffusive fluxes of non-electrolyte solutions and osmotic and hydrostatic forces in this system were considered. Formulas describing the intensity of S-entropy production were derived for concentration polarization conditions and for homogeneous solutions. To show the influence of concentration polarization on the value of the S-entropy source, the expressions for the quotient and difference of S-entropy source were used in conditions of concentration polarization and homogeneous solutions. On the bases of elaborated formulas, the S-entropy sources as functions of osmotic and hydrostatic forces for homogeneous solutions and for solutions with concentration polarization of the membrane were calculated. Two-dimensional surfaces presented in this paper characterize second-order form of entropy source as a function of forces on the membrane.

The role of mechanical pressure difference in the generation of membrane voltage under conditions of concentration polarization.

The mechanical pressure difference across the bacterial cellulose membrane located in a horizontal plane causes asymmetry of voltage measured between electrodes immersed in KCl solutions symmetrically on both sides of the membrane. For all measurements, KCl solution with lower concentration was above the membrane. In configuration of the analyzed membrane system, the concentration boundary layers (CBLs) are created only by molecular diffusion. The voltages measured in the membrane system in concentration polarization conditions were compared with suitable voltages obtained from the model of diffusion through CBLs and ion transport through the membrane. An increase of difference of mechanical pressure across the membrane directed as a difference of osmotic pressure always causes a decrease of voltage between the electrodes in the membrane system. In turn, for mechanical pressure difference across the membrane directed in an opposite direction to the difference of osmotic pressure, a peak in the voltage as a function of mechanical pressure difference is observed. An increase of osmotic pressure difference across the membrane at the initial moment causes an increase of the maximal value of the observed peak and a shift of this peak position in the direction of higher values of the mechanical pressure differences across the membrane.

$$H^{*}$$ H ∗ Peusner’s Form of the Kedem–Katchalsky Equations for Non-homogenous Non-electrolyte Binary Solutions

The paper presents a hybrid matrix form of Kedem–Katchalsky equations that contains Peusner’s coefficients $$H_{ij}^{*}\;(i, j = 1, 2)$$ for the conditions of concentration polarization and $$H_{ij}$$ for homogeneous solutions. The aqueous glucose solutions were analyzed in Nephrophan membrane system with membrane in horizontal plane. The calculations of coefficients $$H_{ij}^{*}$$ were made for the A and B configurations of the membrane system. In the A configuration glucose solution with higher concentration was located below and the solution with lower concentration above the membrane. In configuration B locations of the solutions were reversed. Non-diagonal coefficients of matrix $$[H^{*}]$$ (concentration polarization conditions) were shown to be linearly dependent on average concentration of glucose solution in the membrane. $$H_{12}^{*}$$ in A configuration was lower than in B configuration. Non-diagonal coefficients of matrix $$[H^{*}]$$ were lower than appropriate coefficients of matrix [H] (homogeneous solutions). For diagonal coefficients of matrix $$[H^{*}]$$ coefficient $$H_{11}^{*}$$ is constant and equal to $$H_{11}$$ , whereas $$H_{22}^{*}$$ and $$H_{22}$$ are nonlinearly dependent on average concentration of glucose solution in the membrane. Value of $$H_{22}^{*}$$ in A was lower than in B configuration of the membrane system. Additionally, $$H_{22}^{*}$$ were lower than $$H_{22}$$ . For both A and B configurations and concentration polarization conditions, the coefficients $$H_{12}^{*}$$ and $$H_{22}^{*}$$ of matrix $$[H^{*}]$$ are different for average solution concentrations $${>}5.41\,\hbox {mol}\,\hbox {m}^{-3}$$ due to convective mixing of solutions in B configuration.

Laser interferometric investigation of solute transport through membrane-concentration boundary layer system.

We investigate diffusive transport in a membrane system with a horizontally mounted membrane under concentration polarization conditions performed by a laser interferometry method. The data obtained from two different theoretical models are compared to the experimental results of the substance flux. In the first model, the membrane is considered as infinitely thin, while in the second one as a wall of finite thickness. The theoretical calculations show sufficient correspondence with the experimental results. On the basis of interferometric measurements, the relative permeability coefficient (ζs) for the system, consisting of the membrane and concentration boundary layers, was also obtained. This coefficient reflects the concentration polarization of the membrane system. The obtained results indicate that the coefficient ζs of the membrane-concentration boundary layer system decreases in time and seems to be independent of the initial concentration of the solute.

Removal of Mn(II) compounds from water in electrodialysis desalination

The article has studied the influence of the nature of background electrolyte on kinetics of removal of Mn(II) ions from model solutions in the course of electrodialysis desalination. The possibility of deep removal of manganese from different types of waters until MAC for drinking water (0.05 mg/dm3) at the initial concentration of manganese 3–5 mg/dm3 has been shown. It has been proposed the use of additives of antiscalant ACUMER 2200 in chambers of concentration of electrodialysis unit for preventing deposition of barely soluble manganese compounds on the giving up surface of anon exchange membranes under conditions of strict concentration polarization.

Resistance Coefficients of Polymer Membrane with Concentration Polarization

The Kedem-Katchalsky equations, modified by means of symmetric transformations of Peusner thermodynamic networks, were applied to interpret the membrane transport in concentration polarization conditions. The results from the study demonstrate that the resistance coefficients counted for membrane transport of aqueous solutions of glucose through Nephrophan membrane in horizontal plane are nonlinearly dependent on mean concentration of glucose in the membrane \({(\bar{C})}\) . It was also shown that the threshold value of concentration \({(\bar{C}_{cr})}\) existed, and for \({\bar{C} > \bar{C}_{cr}}\) , the resistance coefficients depend, while for \({\bar{C} < \bar{C}_{cr}}\) , they do not depend on the membrane system configuration. Increase of mean glucose concentration in the membrane (in the range \({\bar{C} > \bar{C}_{cr})}\) causes decrease of difference between resistance coefficients of the membrane system in homogeneous conditions (solutions mechanically stirred) and in conditions with hydrodynamic instabilities (configuration B). Besides increase of mean glucose concentration in the membrane (in the range \({\bar{C} > \bar{C}_{cr})}\) causes increase of the difference between resistance coefficients for membrane system with concentration polarization without hydrodynamic instabilities (configuration A) and membrane system in homogeneous conditions.