Gel Polarization Model Research Articles

Influence of Unsteady State Dynamics on the Rejection of Cadmium (II) by Ultrafiltration

The unsteady-state permeate flux response to a step change in the transmembrane pressure in a stirred ultrafiltration cell was studied. The changes in the gel-layer concentration and gel-layer growth, with the change in the transmembrane pressure were studied. Metal solutions were prepared in a polymeric solvent, and the dynamics of the operating parameters on this process were studied. The process, a hybrid process called Polymer Enhanced Ultrafiltration, (PEUF) was modeled mathematically and validated using experimentation for the change in the transmembrane pressure and concentration of the polymeric solvent added. The permeate flux was modeled using gel-polarization model and first principles model which was solved using MATLAB’s PDE and ODE solver subroutines.

Application of mathematical analysis on dialysis.

Hemodialysis is a blood purification method based on solute removal by diffusion and incorporates filtration to improve the efficiency of water removal and removal of high molecular weight substances. It is now a well-established treatment, due to the improved performance of dialyzers. This review outlines the development process of dialyzers, focusing on the application based on the mathematical analysis. First, phenomena occurring in the vicinity of the dialysis membrane are explained using a film model for diffusion and a gel polarization model for filtration. Then, currently established dialyzer designs are introduced using mathematical analysis. Furthermore, the design of dialyzers to promote internal filtration, the designs of hemodiafilters suitable for online hemodiafiltration (HDF), and the design of compact dialyzer for are also presented.

Process Analytical Technology (PAT) Implementation for Membrane Operations in Continuous Manufacturing of mAbs: Model-Based Control of Single-Pass Tangential Flow Ultrafiltration.

Control of single pass tangential flow ultrafiltration (SPTFF) is crucial for continuous manufacturing of monoclonal antibodies (mAbs). Integrating SPTFF technology into continuous manufacturing trains requires successful resolution of several challenges that arise due to the complexity of mass transfer interactions across multi-membrane configurations, the significant effect of feed material attributes and process variability on flux, and the need for advanced scheduling. In this paper, we propose a real-time, automated monitoring and control strategy for SPTFF in continuous processing of mAbs. The approach leverages a previously developed model for predicting the VCF across an SPTFF module based on the gel polarization model of protein ultrafiltration. A distributed control system (DCS) architecture was created for integrating the monitoring sensors and control elements, including NIRS sensors for concentration monitoring, as well as weighing balances, pressure sensors, pumps, and valves. Two different SPTFF control strategies were developed, firstly for final formulation of the drug product into the drug substance (ultrafiltration and diafiltration), and secondly for in-line concentration between two chromatography steps. Case studies were designed with 15 runs to test the strategy with a range of deviations induced in the feed and process conditions. The retentate concentration was controlled to within 10% of the target value in all runs. The combination of real-time sensor data and model-based control effectively enabled automated and tightly controlled operation of the SPTFF step and is a key enabler of quality by design in continuous mAb manufacturing.

Modelling and optimization of single-pass tangential flow ultrafiltration for continuous manufacturing of monoclonal antibodies

Formulation of biotherapeutics using single pass tangential-flow filtration (SPTFF) is a critical step in continuous manufacturing processes for many drugs including monoclonal antibodies (mAbs). The concentration of the mAb in the final formulation is a critical quality attribute which affects safety and efficacy and is determined by the concentration factor achieved by the process material stream in a single pass through an SPTFF module. Modern SPTFF modules consist of multiple smaller membranes connected in different series and parallel configurations to increase the overall membrane area and residence time of the process material in order to achieve high concentration factors in a single pass. The present work leverages the gel polarization model of protein ultrafiltration to develop a model for the permeate flux vs. time profile of a single membrane inside an SPTFF module based on three key resistances, namely the boundary layer resistance, resistance of the deposited protein layer over time, and intrinsic membrane resistance. Correlations are developed to predict the key mechanistic parameters across the typical operating range of flow rate, bulk concentration and transmembrane pressure in downstream mAb processing steps. The single membrane model is then used as a building block to model complex SPTFF configurations with diverse tree structures, and to facilitate in-silico design of customized SPTFF configurations based on operating targets.

Prediction of long term filtration by coupled gel layer and pore transport model for salt removal using mixed matrix hollow fiber ultrafiltration membrane

Characterization and performance of lanthanum cobalt oxide nanoparticle doped hollow fiber ultrafiltration membrane are reported in this paper. Nanoparticles (1 wt%) having zeta potential −30 mV at pH 7 imparted high surface charge (surface potential ~19 mV) to the hollow fibers. At this composition, the membrane became more hydrophilic with contact angle reduced to 520 from 570 corresponding to without nanoparticles. Permeability of hollow fiber with 1 wt% nanoparticles increased by 40% compared to that without nanoparticle. At this composition, the membrane molecular weight cut off was 4000 Da (with average pore diameter 34 nm) belonging to ultrafiltration range. Rejection of sodium chloride was 47% in 1000 mg/l synthetic solution at transmembrane pressure drop 69 kPa and cross flow rate 20 l/h. Performance of developed hollow fiber membrane was also tested using actual seawater with a rejection of 40% total dissolved solids at 138 kPa at 20 l/h with 15 l/m2h permeate flux. A combined gel polarization and pore flow model was used to quantify the long term flux decline and salt concentration in the permeate as function of time.

Biorefinery of microalgal soluble proteins by sequential processing and membrane filtration

A mild biorefinery process was investigated on the microalga Nannochloropsis gaditana, to obtain an enriched fraction of water soluble proteins free from chlorophyll. After harvesting, a 100g.L−1 solution of cells was first subjected to cell disruption by either high-pressure homogenization (HPH) or enzymatic treatment (ENZ). HPH resulted in a larger release of proteins (49%) in the aqueous phase compared to the Alcalase incubation (35%). In both cases, an ultrafiltration/diafiltration (UF/DF) was then performed on the supernatant obtained from cell disruption by testing different membrane cut-off (1000kDa, 500kDa and 300kDa). After optimising the process conditions, the combination of ENZ→UF/DF ended in a larger overall yield of water soluble proteins (24.8%) in the permeate compared to the combination of HPH→UF/DF (17.4%). A gel polarization model was implemented to assess the maximum achievable concentration factor during ultrafiltration and the mass transfer coefficient related to the theoretical permeation flux rate.

Integrated membrane process for purification and concentration of aqueous Syzygium cumini (L.) seed extract

The aim of the present study was to investigate the potentiality of an integrated membrane process for the purification and the concentration of phenolic compounds from aqueous jamun (Syzygium cumini L.) seed extract. The aqueous seed extract obtained at optimal condition (temperature: 49.2°C, time: 89.4min, and liquid to solid ratio: 51.6:1mL/g) was submitted to cross flow ultrafiltration for initial clarification, followed by concentration using nanofiltration under batch concentration mode. A detailed parametric study was carried out to investigate the effect of various process parameters such as transmembrane pressure, cross-flow velocity (or stirrer speed) on the permeate flux and permeate quality. Using classical film theory, a steady state gel polarization model incorporating the effect of transmembrane pressure difference and viscosity variation was proposed for the prediction of permeate flux during cross flow ultrafiltration of aqueous seed extract. The predicted flux values were successfully compared with the experimental results. Experimental results showed that the operating conditions had significant effect on permeate flux, recovery of polyphenols, purity and antioxidant activity of phenolic extract. Ultrafiltration experiments at lower operating pressures (276 and 414kPa) using 100kDa membrane resulted in the recovery of 59–66.7% of total polyphenol content in the clarified extract with the purity of 49–58.3% starting from an extract purity of 39.2%. The clarified extract could be successfully concentrated about three times higher using 250Da nanofiltration membrane at volume concentration ratio of three. The present study revealed that the UF/NF integrated membranes process was successful in clarifying and concentrating phenolic extract obtained from jamun seed with enhanced purity and antioxidant activity.

Mathematical Modelling for Removal of Mixture of Heavy Metal Ions from Waste-Water Using Micellar Enhanced Ultrafiltration (MEUF) Process

The micellar enhanced ultrafiltration (MEUF) was studied for the removal of heavy metals using a mixture of non-ionic surfactant TWEEN-80 and anionic surfactant sodium dodecyl sulphate (SDS). The gel polarization model and resistance-in-series model were used to estimate the mass transfer coefficient (3 x 10-6 m/s) and the permeate flux. The total metal ion concentration was varied from 1 mM-4 mM and the corresponding effect of the trans-membrane pressure and limiting fluxes were studied. The modified resistance-in-series model was applied to these experimental data to correlate the flux with the feed concentration and applied pressure.

Enhanced Cross-Flow Ultrafiltration of Apple Juice Using Electric Field

Electric field-enhanced cross-flow ultrafiltration of enzyme-treated apple juice is studied in a rectangular cell using a 30 kDa molecular weight cut-off flat sheet polyethersulfone membrane under turbulent flow conditions for various operating conditions. Application of direct current (DC) electric field has resulted in a significant augmentation of permeate flux. Using classical film theory, a steady-state gel polarization model incorporating the effect of electric field and pressure-dependent mass transfer coefficient is proposed for the prediction of permeate flux. From the steady-state model, gel layer concentration, effective diffusivity and effective viscosity of gel-forming solute in apple juice are estimated. A gel layer model based on resistance-in-series theory is proposed and numerically solved to quantify the transient flux decline and development of gel layer thickness over the membrane surface. The model predictions are successfully compared with the experimental results. Practical Applications To the best of our knowledge, quantification of ultrafiltration performance of apple juice in the presence of electric field is attempted for the first time and its modeling for prediction of steady-state flux as well as unsteady-state flux profile has not been reported so far. The present study aims to investigate the potentiality of an electric field-assisted ultrafiltration in the clarification of apple juice for the first time, as an alternative to conventional processing methods. The effects of various operating parameters such as electric field, transmembrane pressure, feed flow rate on the permeate flux and fouling resistance are investigated.

Time-optimal diafiltration processes for Cephalosporin C separated from fermentation broth under constant yield and constant concentration

Cephalosporin C (CPC) fermentation broth is a typical fluid which is filtrated hardly. In order to optimize the CPC diafiltration process under constant yield and constant concentration, a mathematic model is developed to estimate the operation time, where the membrane permeation performance is given by the gel polarization model. The expressions of tmin and the optimal conditions are put forward respectively. Based on the model, the optimization processes for CPC diafiltration to achieve desired yield and concentration have been investigated. Under the conditions of C0=0.1 and the steady state, the values CG=0.65 and β=28.65m3m−2h−1 are extrapolated based on the experiment results. The optimal range of pre-concentration ratio 0.5⩽a⩽0.8 is confirmed. Compared with the overall process time under C0/CG=1/6.5, the fluctuation range of that is more than 40% in the range of 0.08<C0/CG<0.23. Under the time-optimal conditions, both of the desired CPC yield ξ and the average concentration of CPC in filtrate Ct can be controlled properly.

Separation Properties of Wastewater Containing O/W Emulsion Using Ceramic Microfiltration/Ultrafiltration (MF/UF) Membranes.

Washing systems using water soluble detergent are used in electrical and mechanical industries and the wastewater containing O/W emulsion are discharged from these systems. Membrane filtration has large potential for the efficient separation of O/W emulsion for reuses of treated water and detergent. The separation properties of O/W emulsions by cross-flow microfiltration and ultrafiltration were studied with ceramic MF and UF membranes. The effects of pore size; applied pressure; cross-flow velocity; and detergent concentration on rejection of O/W emulsion and flux were systematically studied. At the condition achieving complete separation of O/W emulsion the pressure-independent flux was observed and this flux behavior was explained by gel-polarization model. The O/W emulsion tended to permeate through the membrane at the conditions of larger pore size; higher emulsion concentration; and higher pressure. The O/W emulsion could permeate the membrane pore structure by destruction or deformation. These results imply the stability of O/W emulsion in the gel-layer formed on membrane surface play an important role in the separation properties. The O/W emulsion was concentrated by batch cross-flow concentration filtration and the flux decline during the concentration filtration was explained by the gel- polarization model.

Minimizing the process time for ultrafiltration/diafiltration under gel polarization conditions

Abstract This study examines a generalized ultrafiltration/diafiltration process that is designed to reduce the initial volume of a given process liqueur and to eliminate impurities from the product solution. This theoretical investigation focuses on applications where the permeate flux is given by the gel polarization model. The goal of this paper is to use optimal control theory to determine optimal time-varying diluant addition that minimizes treatment time. We propose a diafiltration model in a dimensionless form with normalized model equations in order to determine general features of optimal diluant utilization strategy. Based on the model, we formulate the optimal control problem and apply the theory of optimal control exploiting the Pontryagin’s minimum principle. We confirm the analytical results by numerical computations using numerical methods of dynamic optimization. We prove that optimal control strategy is to perform a constant-volume diafiltration step at optimal macro-solute concentration that guarantees maximal removal of micro-solute at any time instant. This constant-volume diafiltration step is preceded and followed by optional ultrafiltration or pure dilution steps that force the concentrations at first to arrive to the optimal macro-solute concentration and at last to arrive to the desired final concentrations. Finally, we provide practical optimization diagrams that allow decision makers to determine the optimal diluant control of a given separation task.

Simulation of micellar enhanced ultrafiltration by multiple solute model

Multiple solute ultrafiltration models in micellar enhanced ultra filtration (MEUF) have been studied, for experimental results of selective separation of Cu (II) and Co (II) with anionic surfactant, sodium dodecyl sulfate (SDS) and imino diacetic acid (IDA) as chelating agent using synthetic waste water. This model is based on mass balance analysis coupled with the filtration theory, resistance-in-series model and gel polarization model. This model is characterized by the parameters, membrane resistance Rm, membrane permeability Pm, back transport coefficient Kb, Kbi and mass transfer coefficient ki. These parameters are estimated by using the Levenberg–Marquardt method coupled with the Gauss–Newton algorithm.Due to cross currents caused by the superficial velocity, some solutes are removed from the membrane surface and go into the bulk known as back transport effect. Hence back transport coefficient plays significant role in explaining the extent of micellization. The simulation results show a good agreement with the experimental data of permeate quality and flux. The consideration of negligible gel thickness is suitable for dilute solutions.

Stirred cell ultrafiltration of aqueous micellar TX-100 solutions

Cellulose membranes with different molecular weight cut-offs (MWCO, 5–100 kDa) were used for the filtration of aqueous micellar TX-100 solutions. The experiments were performed in a stirred cell and surfactant concentration and pressure were varied. The gel-polarization model was employed and showed a gel concentration for TX-100 in the range of 150–300 g/L. Ultrafiltration was also carried out with dimethyl itaconate (DMI) and diethyl itaconate (DEI) as dissolved organic compounds and we found that the solute retention was directly associated to the hydrophobicity of the compounds. The flux was not affected as long as the solution appears homogeneous and the formation of a second phase with higher organic content was avoided. In order to use micellar enhanced ultrafiltration (MEUF) for the recovery of hydrophobic catalysts dissolved in aqueous micellar reaction media, a low MWCO membrane, low surfactant concentrations and hydrophilic reactants should be preferred.

Cross-flow microfiltration of dilute macromolecular suspension

The operating condition effects on the cross-flow microfiltration performance of dilute macromolecular suspension were studied. Track-etched membranes of different pore sizes were used to filter blue dextran with a molecular weight of 2000 kDa. Increasing the membrane pore diameter results in higher filtration flux but decreases the dextran rejection coefficient. For filtration using 0.2-μm membrane, an increase in cross-flow velocity or filtration pressure leads to higher filtration flux, but the impact of cross-flow velocity is more significant. A membrane fouling model based on force analysis and membrane pore size reduction caused by dextran adsorption at pseudo-steady state is proposed. The effective membrane pore diameter and pseudo-steady filtration flux under various conditions can then be estimated. On the other hand, the pseudo-steady dextran rejection coefficient increases with increasing cross-flow velocity or decreasing filtration pressure when cross-flow velocity is lower than 0.3 m/s. This can be reasonably explained by the sweeping effect of tangential flow or using the modified gel-polarization model. However, a contrary trend occurs under the conditions with higher cross-flow velocity. This result is attributed to the dextran molecular deformation. The “coil-stretched” deformation of blue dextran molecules can be indicated using the Reynolds number in the permeating flow direction or Deborah number for macromolecular flow through porous media.

Modeling and Simulation of Stirred Dead End Ultrafiltration Process Using the Aspen Engineering Suite

Simulation of pressure-driven membrane process has been carried out considering two different types of solute (silica and dextran) and membrane (partially permeable and totally retentive) in a stirred cell using the Aspen Engineering Suite. One solute, silica, exerts negligible osmotic pressure but the other, dextran, offers adequate osmotic pressure. Silica is very susceptible to form a gel layer while dextran has no such tendency. Two types of membrane are considered for this work. One membrane completely separates solute from the solvent (totally retentive membrane) and the other does it partially (partially permeable membrane). The second type of membrane is regarded as highly compact granulated particle layer which has a different range of porosity. So the diffusivity within the membrane layer is referred to as hindered back diffusion. Osmotic pressure model and gel polarization model have been considered for batch and continuous mode operation. Silica suspension has been simulated with totally retentive membrane and dextran solution is simulated with partially retentive membrane in batch and continuous mode, respectively. The effect of applied pressure, stirring speed, and initial feed concentration on permeate flux, membrane surface concentration, permeate concentration, and true and observed rejection have been studied.

Estimation of the gel layer concentration in ultrafiltration: Comparison of different methods

Fouling is one of the major limitations of membrane applications. Gel layer formation is a common fouling mechanism that increases the membrane fouling resistance. In this work the estimation of the gel layer concentration was performed from experimental values obtained in several ultrafiltration experiments using three methods: the gel-polarization model, the mechanistic model for gel layer formation proposed by Song and an expression of the concentration polarization modulus developed for tubular membranes and turbulent flow. The results were compared and analyzed. Two types of monotubular ceramic membranes with different MWCO (5 and 15 KDa) were used in the experiments. Polyethylene glycol (PEG) of 35,000 Da in distilled water was used as feed. The experiments were performed at different feed flow rates (1–3 m/s), transmembrane pressures (0.1–0.5 MPa), temperatures (15–40EC) and constant feed concentrations (5–15 g/L). Values of the gel layer concentration estimated with the gel-polarization model diff...

Pulsed electric field enhanced ultrafiltration of synthetic and fruit juice

An experimental investigation of electric field assisted clarification of synthetic juice (a mixture of pectin and sucrose) and mosambi ( Citrus Sinensis ( L.) Osbeck) juice using a 30 kDa molecular weight cut-off membrane in cross-flow ultrafiltration mode under laminar flow regime is reported herein. Electric field is applied in both continuous as well as pulse mode. Application of d.c. electric field has resulted in significant enhancement of permeate flux. It has been found that use of pulsed electric field is more advantageous in terms of less energy consumption, no property variations of the permeate and retentate streams and equally effective in terms of flux enhancement as compared to continuous field. A gel polarization model is proposed incorporating continuous as well as pulsed electric field and numerically solved to quantify the permeate flux. Experimental flux values are successfully compared with results from the numerical solution of the model under various operating conditions.

Cross-flow electro-ultrafiltration of mosambi ( Citrus sinensis (L.) Osbeck) juice

An experimental investigation has been undertaken to observe the effect of external electric field on the enhancement of permeate flux during clarification of mosambi ( Citrus sinensis (L.) Osbeck) juice by ultrafiltration. A detailed study has been carried out using a 50 kDa molecular weight cut-off flat sheet polyethersulfone membrane in cross-flow ultrafiltration under laminar flow conditions for a wide range of operating conditions. Use of d.c. electric field resulted in a 32% enhancement of permeate flux. A steady state gel polarization model has been applied to evaluate the gel layer concentration, effective diffusivity and effective viscosity of the juice within the concentration boundary layer, by optimizing the experimental flux data.

Ultrafiltration modeling of multiple solutes system for continuous cross-flow process

A mathematical model suitable for the multiple solutes system in continuous cross-flow ultrafiltration is developed. This model is based on mass balance analysis coupled with the filtration theory (osmotic pressure model, Kozeny–Carman equation), resistance-in-series model and gel polarization model. This model is characterized by the parameters R m , P m , K b , K bi and k i . These parameters are estimated by using the Levenberg–Marquardt method coupled with the Gauss–Newton algorithm based on the experimental data obtained from the treatment of pretreated palm oil mill effluent (POME) as a feed in the pilot plant scale ultrafiltration system. The pretreated POME is composed of a ternary system with the solutes of carbohydrate constituents, crude protein and ammoniacal nitrogen. The simulation results show a good agreement with the experimental data. The proposed model is suitable for predicting the performance of multiple solutes in an ultrafiltration process. The concentration of each solute present is correlated with the COD value of the permeate stream.