Extent Of Concentration Polarization Research Articles

Role of imperfections in transfer of organic micro-pollutants through RO/NF membranes: Numerical study

Due to relatively low diffusivities, the rejection of organic micro-pollutants in pressure-driven membrane processes is more affected by Concentration Polarization (CP) than that of typical inorganic ions. On the other hand, it can be more sensitive to various membrane imperfections because the rejection of these solutes by intact membranes can be expected to be quite high. This makes necessary simultaneous accounting for membrane imperfections and Concentration Polarization in Reverse Osmosis and/or Nanofiltration of organic micro-pollutants. This study, for the first time, explores this problem numerically for the model of a single circular opening in a selective layer (the porous support is assumed to remain undamaged). The solute accumulated due to the CP close to the surrounding intact active layer “spills over” to the imperfection, which leads to an enhanced transmembrane solute passage as compared to the classical solution-diffusion-imperfection model assuming this passage to be controlled by the feed concentration. Our analysis reveals that the extent of this “spill-over” depends primarily on the size of imperfection (we studied the range between 0.2 μm and 20 μm) as well as on the ratio of hydraulic resistances of selective and support layers. Smaller imperfections in active layers of membranes with less permeable porous supports have larger impact. The extent of CP away from the imperfection is also important. Contrary to the trend expected for imperfection-free membranes (a better rejection of larger solutes due to a stronger steric exclusion and hindrance), the solute passage through imperfections is demonstrated to be larger for solutes with smaller diffusion coefficients, so in future experiments this can be considered a signature feature of a noticeable impact of imperfections. Quantifying their impact is important for understanding membrane aging, rational selection of membrane cleaning procedures as well as development of better membranes.

Ion Separations Based on Spontaneously Arising Streaming Potentials in Rotating Isoporous Membranes.

Highly selective ion separations are vital for producing pure salts, and membrane-based separations are promising alternatives to conventional ion-separation techniques. Our previous work demonstrated that simple pressure-driven flow through negatively charged isoporous membranes can separate Li+ and K+ with selectivities as high as 70 in dilute solutions. The separation mechanism relies on spontaneously arising streaming potentials that induce electromigration, which opposes advection and separates cations based on differences in their electrophoretic mobilities. Although the separation technique is simple, this work shows that high selectivities are possible only with careful consideration of experimental conditions including transmembrane pressure, solution ionic strength, the K+/Li+ ratio in the feed, and the extent of concentration polarization. Separations conducted with a rotating membrane show Li+/K+ selectivities as high as 150 with a 1000 rpm membrane rotation rate, but the selectivity decreases to 1.3 at 95 rpm. These results demonstrate the benefits and necessity of quantitative control of concentration polarization in highly selective separations. Increases in solution ionic strength or the K+/Li+ feed ratio can also decrease selectivities more than an order of magnitude.

Role of membrane structure on the filtrate flux during monoclonal antibody filtration through virus retentive membranes.

Virus removal filtration is a critical step in the manufacture of monoclonal antibody products, providing a robust size-based removal of both enveloped and non-enveloped viruses. Many monoclonal antibodies show very large reductions in filtrate flux during virus filtration, with the mechanisms governing this behavior and its dependence on the properties of the virus filter and antibody remaining largely unknown. Experiments were performed using the highly asymmetric Viresolve® Pro and the relatively homogeneous Pegasus™ SV4 virus filters using a highly purified monoclonal antibody. The filtrate flux for a 4g/L antibody solution through the Viresolve® Pro decreased by about 10-fold when the filter was oriented with the skin side down but by more than 1000-fold when the asymmetric filter orientation was reversed and used with the skin side up. The very large flux decline observed with the skin side up could be eliminated by placing a large pore size prefilter directly on top of the virus filter; this improvement in filtrate flux was not seen when the prefilter was used inline or as a batch prefiltration step. The increase in flux due to the prefilter was not related to the removal of large protein aggregates or to an alteration in the extent of concentration polarization. Instead, the prefilter appears to transiently disrupt reversible associations of the antibodies caused by strong intermolecular attractions. These results provide important insights into the role of membrane morphology and antibody properties on the filtrate flux during virus filtration.

High-performance 7-channel monolith supported SSZ-13 membranes for high-pressure CO2/CH4 separations

Continuous SSZ-13 zeolite membranes were reproducibly synthesized on the inner surface of 7-channel monolith supports for the first time. Packing density and mechanical strength were much greater than those using normal tubular and disc membranes. The membrane in the central channel of monolith was thinner than these of the side channels. The best monolith supported SSZ-13 membrane (with spacers) showed a CO2/CH4 selectivity of 72 and a CO2 permeance of 163 × 10-8 mol/(m2 s Pa) at pressure drop of 2.0 MPa and feed flow rate of 20 standard L/min for an equimolar CO2/CH4 mixture. Such separation performance was higher than most of zeolite membranes prepared on single-channel tubes or discs. The effects of temperature, pressure drop and fluid state on separation performance of the membranes were investigated. The extent of concentration polarization through monolith supported membrane was modelled by the concentration polarization index (CPI). Increasing feed flow rate and inserting spacers into the channels were effective ways to reduce the negative influence of concentration polarization. The latter way was more effective for our monolith supported membranes than the former because the dead volume was reduced greatly. Carbon dioxide permeance and CO2/CH4 selectivity increased by 24% and 85%, respectively, when the CPI increased from 0.79 (without spacer) to 0.89 (with spacer) at feed flow rate of 20 standard L/min.

Ultrafiltration behavior of monoclonal antibodies and Fc-fusion proteins: Effects of physical properties.

Ultrafiltration (UF) is used for the final concentration and formulation of essentially all antibody-based therapeutics including both monoclonal antibodies (mAbs) and Fc-fusion proteins. The objective of this study was to quantitatively compare the filtrate flux behavior for two highly purified mAbs and an Fc-fusion protein under identical flow and buffer conditions. Filtrate flux data were obtained using a Pellicon 3 tangential flow filtration cassette over a wide range of transmembrane pressures and bulk protein concentrations. Independent experimental measurements were performed to evaluate the protein osmotic pressure and solution viscosity. The maximum achievable protein concentration was directly correlated with the solution viscosity, which controls the pressure drop and extent of back-filtration in the cassette. The filtrate flux data were analyzed using a recently developed model that accounts for the effects of intermolecular interactions and transmembrane pressure gradients on the extent of concentration polarization. These results provide important insights into the factors controlling the filtrate flux during the UF of concentrated protein solutions and an effective framework for the design/analysis of UF processes for the formulation of antibody-based therapeutics. Biotechnol. Bioeng. 2017;114: 2057-2065. © 2017 Wiley Periodicals, Inc.

Experiments and modeling of transport in composite Pd and Pd/Ag coated alumina hollow fibers

The mass transport processes are analyzed for H 2 permeation through Pd and Pd/Ag hollow fiber composite membranes. Experimental measurements of pure gas and two-component feeds quantify the extent of retentate-side transport limitations (concentration polarization) in reducing the hydrogen flux. The effects of membrane thickness, feed composition and flow rate, temperature, and total pressure on the extent of concentration polarization are measured. The data reveal that concentration polarization increases with increasing temperature and total pressure and decreasing hydrogen feed concentration. A hierarchy of transport models of varying complexity is presented. The complex 2D models account for gas-phase axial and retentate-side radial concentration gradients, and both selective transport of hydrogen through the Pd membrane and non-selective transport through membrane defects. Satisfactory agreement between model predictions and experimental data is obtained using experimentally measured parameters. An analysis of the characteristic times of the pertinent transport processes identifies the rate limiting regimes and helps to determine the conditions when gas-phase transport limits the overall productivity. The findings underscore the utility of small diameter fiber supports in providing a high surface to volume ratio and reduced concentration polarization.

Numerical Simulation of Concentration Polarization in a Pervaporation Module

A mathematical model was developed to describe mass transfer in a slit flow channel formed by a thin supported membrane at the bottom and an impermeable stainless steel block at the top in a lab‐scale flat sheet pervaporation membrane module. Boundary layer theory was employed to obtain the mass transfer equations governing mass transport in the liquid boundary layer and in the membrane matrix. Equations of the model were solved numerically with computational fluid dynamics (CFD) techniques. The extent of concentration polarization and its impact upon permeation flux rate under different conditions were examined.

Pulsed galvanostatic control of ionophore-based polymeric ion sensors.

This paper describes a pulsed galvanostatic technique to interrogate ion-selective electrodes (ISEs) with no intrinsic ion-exchange properties. Each applied current pulse is followed by a longer baseline potential pulse to regenerate the phase boundary region of the ion-selective membrane. The applied current fully controls the magnitude and sign of the ion flux into the membrane, thus offering instrumental control over an effect that has become very important in ion-selective electrode research in recent years. The resulting chronopotentiometric response curves essentially mimic traditional ISE behavior, with apparently Nernstian response slopes and selectivities that can be described with the Nicolsky equation. Additionally, the magnitude and sign of the current pulse may be used to tune sensor selectivity. Perhaps most important, however, appears to be the finding that the extent of concentration polarization near the membrane surface can be accurately controlled by this technique. A growing number of potentiometric techniques are starting to make use of nonequilibrium principles, and the method introduced here may prove to be very useful to advance these areas of research. The basic characteristics of this pulsed galvanostatic technique are here evaluated with plasticized poly(vinyl chloride) membranes containing the sodium-selective ionophore tert-butyl calix[4]arene tetramethyl ester and a lipophilic inert salt.

Control of Calcium Sulfate (Gypsum) Scale in Nanofiltration of Saline Agricultural Drainage Water

A methodology for calcium sulfate (gypsum) scale control in nanofiltration of saline waters is presented. The methodology involves the use of both theoretically and experimentally determined parameters. Pitzer's thermodynamic equations for electrolytes are used to determine the gypsum scaling potential of the feed water based on its ionic composition, whereas the extent of concentration polarization at the membrane surface is determined from the film model. A proportionality factor that relates the kinetic difference between the saturation predicted by the gypsum solubility model and the actual crystallization is determined using data from glassware crystallization experiments. The last step involves an experimentally developed parabolic equation relating antiscalant (polyacrylic acid) dose to the normalized concentration factors of the saline solution. These parameters are combined into a single model for predicting the required antiscalant dose to control calcium sulfate scale in nanofiltration membrane...

Theory of concentration polarization in crossflow filtration

A novel theory is developed for concentration polarization of non-interacting particles in crossflow-filtration systems. This theory reveals that the extent of concentration polarization, as well as the behaviour of the permeate flux, are characterized by an important dimensionless filtration number (NF= 4πa3pΔP/3kT). There is a critical value of the filtration number for a given suspension and operational conditions. When the filtration number is smaller than the critical value, a polarization layer exists directly over the membrane surface and the wall particle concentration is determined by the pressure and temperature. At higher filtration numbers, a cake layer of retained particles forms between the polarization layer and the membrane surface. Mathematical models are constructed for both cases and analytical solutions for the permeate flux are derived. An increase in permeate flux with increasing pressure is predicted for all operational conditions.

Generalized analytical solution for the freezing of a supercooled aqueous solution in a finite domain

A generalized analytical solution to the problem of the unidirectional planar freezing at a constant temperature of a supercooled aqueous solution of finite extent is presented. This solution is valid for both dilute and non-dilute solutions and also at both short and long times. Mathematical approximations are made only to the extent that the mass diffusivity is considered to be independent of concentration. Our theoretical results compare favorably with the experimental results of other investigators and demonstrate that transient non-uniform concentration profiles can exist within the liquid region of systems as freezing progresses and that the volumes of the liquid and solid regions can vary non-linearly with time. The extent of concentration polarization and the velocity of propagation of the liquid-solid interface are found to be functions of the initial degree of supercooling, the mass diffusivity, and the initial size of the system. A comparison is also made between our results for freezing in finite domains and the classical similarity results for freezing in semi-infinite domains.

Effect of imperfect salt rejection on concentration polarization in reverse osmosis systems

A study of the two-dimensional boundary layer equations describing reverse osmosis in a flat membrane duct reveals the existence of maximum concentration polarization phenomenon corresponding to a particular value of salt rejection ratio, which is contrary to the common belief that the extent of concentration polarization always increases as membranes become more perfect. A one-dimensional model is used to analyze the same problem and explicit relationship between membrane characteristics, operating variables and the presence of maximum concentration polarization is presented.

Simultaneous development of velocity and concentration profiles in reverse osmosis systems

A mathematical analysis for the simultaneous development of the velocity and concentration profiles in a reverse osmosis system consisting of two parallel flat membranes is presented. This analysis, based on boundary layer theory, takes into account the nonlinear effects created by the fact that the water flux produced varies in the longitudinal direction. The initial velocity and concentration profiles are assumed to be uniform and the analysis is resctricted to two dimensional, steady state laminar flows with constant physical properties. The momentum and diffusion equations, coupled through both the boundary conditions and the convective terms in the differential equations, are solved simultaneously using the approximate integral method. The analysis is applicable to both the entrance region and the fully developed region at large distances from the conduit inlet. Data are presented on the concentration build-up at the wall for a wide range of parameters and typical results for the water flux produced and productive capacity are given. Since the concentration profile at any value of x + is given as a simple polynomial, the results can be used conveniently to study the relaxation or attenuation, of concentration polarization as a Graetz type problem. Reasonable agreement is observed between the results of the present work and the limited experimental results available in the literature. However, it is shown that some of the reported experimental data were probably significantly influenced by natural convection. It is shown that the extent of concentration polarization may be significantly different depending on whether the velocity profile in the stream entering the membrane section is parabolic or flat. An explanation is offered for the somewhat surprising fact that the water flux is greater and the polarization is less in fully developed flow than when the velocity profile is flat at the system entrance. This effect will be most pronounced in the highly productive membranes which probably will be developed in the future.