"Breakthrough" osmosis and unusually high power densities in Pressure-Retarded Osmosis in non-ideally semi-permeable supported membranes

Osmosis is the movement of solvent across a membrane induced by a solute-concentration gradient. It is very important for cell biology. Recently, it has started finding technological applications in the emerging processes of Forward Osmosis and Pressure-Retarded Osmosis. They use ultrathin and dense membranes supported mechanically by much thicker porous layers. Until now, these processes have been modelled by assuming the membrane to be ideally-semipermeable. We show theoretically that allowing for even minor deviations from ideal semipermeability to solvent can give rise to a previously overlooked mode of “breakthrough” osmosis. Here the rate of osmosis is very large (compared to the conventional mode) and practically unaffected by the so-called Internal Concentration Polarization. In Pressure-Retarded Osmosis, the power densities can easily exceed the conventional mode by one order of magnitude. Much more robust support layers can be used, which is an important technical advantage (reduced membrane damage) in Pressure-Retarded Osmosis.Peer ReviewedPostprint (published version

.“Breakthrough” osmosis in “leaky” supported membranes: A breakthrough in PRO?

It is shown theoretically that allowing for a certain (even quite small) extent of membrane “leakiness” (deviations from ideal perm-selectivity) can give rise to a previously overlooked mode of “breakthrough” osmosis in thin polymeric membranes supported mechanically by porous layers. This result is obtained by using the well-established Spiegler-Kedem model for the description of solute and volume transfer across the membrane barrier layer and the classical convection-diffusion equation for modelling the solute transfer within the porous support layer. The use of these simple modelling tools enables one to obtain transparent analytical solutions and simple criteria for the occurrence of the “breakthrough” mode. In particular, we show that it occurs only in the PRO configuration (barrier layer facing the concentrated solution), only when the solute concentration in the dilute solution is very low and only when the draw-solution concentration is sufficiently high (exceeds a threshold value). We demonstrate that in this mode the rate of osmosis is very large (compared to the conventional mode) and practically independent of the diffusion permeance of the support layer. This opens interesting opportunities in the utilization of this phenomenon in Pressure-Retarded Osmosis (PRO) because the support layers can be made much more robust mechanically without compromising the PRO performance by the Internal Concentration Polarization. Besides, the estimated power densities achievable in the “breakthrough” mode can easily exceed by one order of magnitude those predicted in the conventional mode. This can help resolve two principal problems encountered in PRO: insufficient power density and mechanical collapse of thin and loose membranes into the openings of dilute-side spacers. Our analysis shows that for the “breakthrough” mode to occur the membrane must combine a certain extent of “leakiness” (solute reflection coefficients of ca. 0.95 – 0.995) with sufficiently low diffusion permeability. Reliable experimental detection of minor deviations from ideal perm-selectivity can be difficult (primarily in view of concentration-polarization phenomena). Therefore, it is not clear if the corresponding membranes currently exist. Nonetheless, this analysis provides membrane material scientists with clear guidance on the desired properties of membranes that could become a potential game-changer in renewable energy

Evaporation-driven electrokinetic energy conversion: critical review, parametric analysis and perspectives

Energy harvesting from evaporation has become a hot topic in the last couple of years. Researchers have speculated on several possible mechanisms. Electrokinetic energy conversion is the least hypothetical one. The basics of pressure-driven electrokinetic phenomena of streaming current and streaming potential have long been established. The regularities of evaporation from porous media are also well known. However, coupling of these two classes of phenomena has not, yet, been seriously explored. In this critical review, we will recapitalize and combine the available knowledge from these two fields to produce a coherent picture of electrokinetic electricity generation during evaporation from (nano)porous materials. For illustration, we will consider several configurations, namely, single nanopores, arrays of nanopores, systems with reduced area of electrokinetic-conversion elements and devices with side evaporation from thin nanoporous films. For the latter (practically the only one studied experimentally), we will formulate a simple model describing correlations of system performance with such principal parameters as the nanoporous-layer length, width and thickness as well as the pore size, pore-surface hydrophilicity, effective zeta-potential and electric conductivity in nanopores. These correlations will be qualitatively compared with experimental data available in the literature. We will see that experimental data not always are in agreement with the model predictions, which may be due to simplifying model assumptions but also because the mechanisms are different from the classical electrokinetic energy conversion. In particular, this concerns the mechanisms of conversion of evaporation-driven ion streaming currents into electron currents in external circuits. We will also formulate directions of future experimental and theoretical studies that could help clarify these issues.Comment: 41 pages, 7 figure

Implications of inhomogeneous distribution of concentration polarization for interpretation of pressure-driven

A number of CFD studies have demonstrated that there is a considerable inhomogeneity of extent of Concentration Polarization (CP) over the membrane surface especially in spacer-filled feed channels. However, the consequences of this inhomogeneity for the interpretation of measurements of solute rejection in pressure-driven membrane processes have received little attention. This study uses a simple model of locally-1D CP combined with a postulated probability distribution of unstirred-layer thickness over the membrane thickness. In this way, we obtain transparent analytical results and can consider qualitative consequences of inhomogeneous distribution of CP over membrane surface. Our analysis shows that disregarding the CP distribution under-estimates the CP of strongly positively-rejected solutes and over-estimates the CP for the negatively-rejected ones. This observation is especially important for the interpretation of ion rejection from multi-ion solutions in nanofiltration where strong positive and pronounced negative rejections can occur simultaneously for solutes of different charges. We conclude that for reliable interpretation of pressure-driven membrane measurements it is desirable to reduce the inhomogeneity of CP distribution to a minimum in membrane-testing devicesPeer ReviewedPostprint (author's final draft

Current-induced ion concentration polarization at a perfect ion-exchange patch in an infinite insulating wall

This research examines, theoretically, the ion concentration polarization, ion fluxes, and electrostatic fields near an ion- exchange patch in the wall of an electrified fluidic channel. These phenomena are important in related microfluidic ion- preconcentration systems. Under an electric field, counter ions enter the ion-exchange patch at one side and leave at the other, with salt depletion occurring near the entrance and accumulation near the exit. The high patch conductivity and the concentration profiles lead to local electric field perturba- tions that may facilitate preconcentration. This study includes analytical expressions of ion concentrations and electrochemical potentials at small to moderate electric fields, as well as numerical simulations. Additionally, a simple matrix of poly- nomial coefficients (obtained via fitting of numerical data) enables analytical calculation of the two-dimensional concen- tration profiles at all electric fields within the range investigated in the numerical simulations. This is possible because a single dimensionless parameter controls this problem.Postprint (updated version

ElectroOsmoDialysis

Concentration Polarization (CP) and limiting-current phenomena are well-known to limit the productivity of electrodialysis by reducing the current efficiency at higher current densities. Considerable effort has been devoted to attempts to reduce the CP primarily via intensification of external mass transfer close to the membrane surfaces. However, it is notoriously difficult to stir liquids very close to solid surfaces so intensification of cross-flow hydrodynamics has only limited impact and obviously implies additional energy costs. In conventional electro-membrane systems, limiting-current phenomena occur because salt is delivered to polarized membrane/solution interfaces primarily by diffusion. Its rate is limited since the salt concentration cannot drop below zero. In liquids convection is a much more effective transport mechanism than diffusion. Therefore, much attention has been paid to the so-called electro-convection in electro-membrane processes. Nonetheless at short distances from the membrane surfaces even electro-convection remains predominantly tangential so its rate is limited due to the no-slip condition. Normal convection would be much more effective but in the case of conventional ion-exchange membranes it is very week owing to the extremely low mechanical permeability of these membranes. At the same time, with nano-porous charged diaphragms the limiting current can be effectively suppressed due to the normal electro-osmotic flow [1]. This presentation will show in what way considerable (quasi)normal convective flow through ion-exchange membranes (IEXMs) can be arranged for. This can be achieved via creating relatively scarce microscopic perforations in the otherwise almost impermeable membrane matrix. The transmembrane volume flow can be created in several ways but in this presentation we will consider the scenario of putting a nano-porous layer in series with the perforated IEXM so that the former works as an electroosmotic pump. In this case the liquid flow through the perforated IEXM is predominantly driven by the electroosmotic pressure gradients arising within the nanoporous electroosmotic layer. Via numerical simulations, we will demonstrate that due to this (quasi)normal convection (and corresponding salt delivery to the current-polarized interface), limiting current, indeed, is suppressed. Nonetheless, the CP phenomenon itself does not disappear. With increasing current density the salt concentration tends not to zero but to a finite limiting value, which is a function of system parameters. Evidently, in addition to the decrease in the concentration (similar to the conventional ED) there is a volume transfer across the “sandwich”. If a cell pair is formed by two perforated IEXMs of opposite polarity (each “sandwiched” with its own nanoporous EO layer of opposite surface charge) the volume flows through the composite membranes have opposite directions and can merge into a tangential flow along a channel separating them. Due to this, one can expect increased product recovery as compared to the conventional ED. In view of the important role played by electroosmosis, this novel membrane separation process can be termed ElectroOsmoDialysis (EOD). [1] A. Yaroshchuk, What makes a nano-channel? A limiting-current criterion, Microfluid. Nanofluidics. 12 (2012) 615–624. doi:10.1007/s10404-011-0902-6

Balance-of-force selective accumulation of trace ionic species in hierarchical sub-nano-/nano-/micro-porous structures

Separation of species of close electrochemical mobilities (peptides, isotopes) is of interest for a number of applications. In this presentation, we will explore selective accumulation of ionic species in current-polarized hierarchical sub-nano-/nano-/micro-porous structures. Please click Additional Files below to see the full abstract

Transient membrane potential after concentration step: A novel method for advanced characterization of ion-exchange membranes

Electrically-driven membrane processes find ever more versatile applications. Ion-exchange membranes are central elements of these processes. For their optimization, it is important to have detailed information on the transport and equilibrium properties of ion-exchange membranes, in particular, separate information on the equilibrium (partitioning) and kinetic (diffusivity) properties of membranes with respect to ions. Stationary techniques of membrane characterization (membrane potential, Hittorf technique, DC electrical resistance) provide information only on ionic permeabilities, which are products of partitioning and diffusion coefficients. Non-stationary diffusion is well-known to provide information on the partitioning and diffusion coefficients of a diffusing species via a single time-resolved measurement. In principle, this classical technique can be applied to ion-exchange membranes but the typical use of pure solvent in the receiving compartment implies large trans-membrane concentration differences and strongly non-linear diffusion. This complicates considerably the interpretation. In this communication, we present an alternative scenario of non-stationary-diffusion that can be implemented with moderate to small concentration differences. An ion-exchange membrane is sandwiched with a relatively thick porous support and put in a two-compartment stirred cell. The salt concentration in one compartment is kept stationary. The other compartment initially contains solution of the same concentration. At the start of the measurement, this compartment is rapidly emptied and filled up with a solution of a different concentration. The electrical response to this is tracked with a pair of indicator electrodes. This response is time-dependent because of progressive redistribution of applied concentration difference between the membrane and the porous support and the different ion perm-selectivities of those two media. The rate of signal relaxation is primarily controlled by the diffusion permeability of the membrane but is also affected by the salt partitioning coefficient. From the initially-constant signal one can determine the ionic perm-selectivity of the membrane. Thus, instead of just one parameter (perm-selectivity) available from the conventional measurements of stationary membrane potential we obtain information on 3 important properties of the membrane. This work has been performed within the scope of RED-Heat-to-Power project (Conversion of Low Grade Heat to Power through closed loop Reverse Electro-Dialysis) - Horizon 2020 Programme, Grant Agreement n. 640667

Hydrodynamic dispersion in long microchannels under conditions of electroosmotic circulation: II. Electrolytes

This work describes the steady-state transport of an electrolyte due to a stationary concentration difference in straight long channels under conditions of electroosmotic circulation. The electroosmotic flow is induced due to the slip produced at the charged channel walls. This flow is assumed to be compensated by a pressure-driven counterflow so that the net volume flow through the channel is exactly zero. Owing to the concentration dependence of electroosmotic slip, there is an involved coupling between the solute transfer, hydrodynamic flow and charge conservation. Nevertheless, for such a system the Taylor–Aris dispersion (TAD) theory is shown to be approximately applicable locally within an inner part of the channel for a wide range of Péclet numbers (Pe) irrespective of the concentration difference. Numerical simulations reveal only small deviations from analytical solutions for the inner part of the channel. The breakdown of TAD theory occurs within boundary regions near the channel ends and is related to the variation of the dispersion mechanism from the purely molecular diffusion at the channel ends to the hydrodynamic dispersion within the inner part of the channel. This boundary region is larger at the lower-concentration channel edge and its size increases nearly linearly with Pe number. It is possible to derive a simple analytical approximation for the inner profile of cross-section-averaged electrolyte concentration in terms of only few parameters, determined numerically. Such analytical approximations can be useful for experimental studies of concentration polarization phenomena in long microchannels.Peer ReviewedPostprint (author's final draft

Kinematic and volumetric analysis of coupled transmembrane fluxes of binary electrolyte solution components

The paper deals with relationships between the individual transmembrane fluxes of binary electrolyte solution components and the experimentally measurable quantities describing rates of transfer processes, namely, the electric current, the transmembrane volume flow and the rates of concentration changes in the solutions adjacent to the membrane. Also, we collected and rigorously defined the kinetic coefficients describing the membrane selective and electrokinetic properties. A set of useful relationships between these coefficients is derived. An important specificity of the proposed analysis is that it does not use the Irreversible Thermodynamic approach by analyzing no thermodynamic forces that generate the fluxes under consideration. Instead, all the regularities are derived on the basis of conservation and linearity reasons. The terminology "Kinematics of Fluxes" is proposed for such an analysis on the basis of the analogy with Mechanics where Kinematics deals with regularities of motion by considering no mechanic forces. The only thermodynamic steps of the analysis relate to the discussion on the partial molar volumes of electrolyte and ions that are the equilibrium thermodynamic parameters of the adjacent solutions. These parameters are important for interrelating between the transmembrane fluxes of the solution components and the transmembrane volume flow. The paper contains short literature reviews concerned with the partial molar volumes of electrolyte and ions: the methods of measurement, the obtained results and their theoretical interpretations. It is concluded from the reviews that the classical theories should be corrected to make them applicable for sufficiently concentrated solutions, 1M or higher. The proposed correction is taken into account in the kinematic analysis