Flux decline in protein ultrafiltration

This paper examines the link between flux decline and protein which becomes deposited (bound) onto the membrane in protein ultrafiltration. For the conditions studied deposition kinetics were relatively slow, with the rate dependent on feed concentration but the “plateau” (steady-state) amount insensitive to this parameter. The amount of deposition was dependent on system hydrodynamics, membrane type and solution environment. Specific resistances of the deposited layer and the labile boundary layer were measured by analysis of unstirred and stirred permeation rates. A semi-empirical relationship, including the deposition kinetics and the deposited layer resistance, gives reasonable prediction of the observed flux decline.     

Three layer membrane model for characterizing ultrafiltration membranes

To characterize ultrafiltration membranes, it is important to understand their intrinsic, macromolecular-rejection properties. Defining these properties in terms of a membrane's permselectivity parameters requires an understanding of the mass transfer of the solute at the membrane interface. The solute concentration is difficult to measure experimentally, and has been previously estimated using various forms of a mass transfer coefficient. In this paper, we present an analytical, steady-state model for predicting ultrafiltration solute concentrations at the membrane interface from experimentally measured parameters and known solute physical properties - without the use of a mass transfer correlation. We then extend the model by looking at mass transfer through the membrane itself, in order to predict membrane permselectivity parameters.     

Influence of gel layer rheology on ultrafiltration flux of wheat starch effluent

Ultrafiltration flux rates of wheat starch effluent in a tubular membrane system revealed unusual values of the exponents in the mass transfer model (Sh = a Reⁿ Sc^m). For turbulent flow the values of the exponent n ranged from 0.2 to 0.9 and m from 0.0 to 0.35 depending on the relative amounts of protein, pentosans and suspended solids in the wheat starch effluent. Samples of the gel layer exhibited theological behaviour ranging from pseudoplastic to Newtonian depending on the suspended solids content of the effluent. The thickness of the gel layer was evaluated for the different patterns of gel layer rheology and applied in a pressure-driven filtration model. The resistance of the gel layer was found to be the dominant resistance. The variation in the values of the exponent n was ascribed to the permeability and compaction differences of the different composition gels. Concentration runs were performed in which enzymatic hydrolysis of the concentrate with hemicellulase reduced the viscosity of the concentrate from 48 to 11 mPa-sec at 70°C and the flux rate was enhanced by 200%.     

Flux decline in crossflow microfiltration and ultrafiltration: experimental verification of fouling dynamics

The theory of fouling dynamics in crossflow membrane filtration is compared with ultrafiltration experiments with suspensions of 0.12 μm silica colloids. It has been experimentally verified that colloidal fouling in crossflow filtration is a dynamics process from non-equilibrium to equilibrium and that the steady state flux is the limiting flux. With the cake concentration c_g identified from an independent experiment and the specific cake resistance calculated by Carman–Kozeny equation, the time-dependent flux and the time to reach steady state in the experiments of this study are correctly predicted with the theory of fouling dynamics.     

Flux improvement by Dean vortices: ultrafiltration of colloidal suspensions and macromolecular solutions

Coiled and straight hollow-fibre modules have been built and tested; the permeate flux obtained in ultrafiltration with these two geometries is compared for two feeds: a colloidal bentonite suspension and a dextran solution. In the case of colloidal suspensions, the secondary flows induced by the coiled geometry allow fouling to be reduced and the permeate flux is multiplied by a factor of up to 2. An empirical relationship is proposed to express the limiting flux of permeate as a function of both the velocity and some geometrical parameters of the coiled modules. Analogous results are obtained during the ultrafiltration of dextran. It is also shown that under certain conditions almost no deposit was formed; the permeate flux under these conditions is three times higher for coiled modules than for straight ones. For a given energy expenditure and ultrafiltration process, the gain in permeate flux can reach a factor of 1.8.     

Osmotic pressure,atomic pressure and the virial equation of state of polymer solutions: Monte Carlo simulations of a bead-spring model

A recently introduced coarse-grained model of polymer chains is studied analyzing various contributions to the pressure as obtained from the virial theorem as a function of chain length N, temperature T and density ϕ. The off-lattice model of the polymer chains has anharmonic springs between the beads, but of finite extensibility, and the Morse-type interaction between beads is repulsive at very short distances and attractive at intermediate distances. Solvent molecules are not explicitly included. It is found that the covalent forces along the chain (modelled by the spring potentials) contribute a negative term to the pressure, irrespective of temperature, which vanishes linearly in ϕ as ϕ → 0. In contrast, both contributions to the pressure due to intrachain nonbonded forces and due to forces between different chains change sign from high temperatures (T ≫ θ, θ the theta-temperature) where they are positive, to low temperature where both parts of the pressure become negative. It is shown that the total pressure has the expected behavior with temperature near the θ-temperature, i.e., Δp ≡ p_tot − k_B · T_p ∼ (T − θ). We study also the concentration and chainlength dependence of the various contributions to the pressure in the good solvent regime and interpret them with scaling predictions.     

A general gel layer model for the transport of colloids and macroions in dilute solution

A general boundary element methodology for studying the dilute solution transport of rigid macroions that contain gel layers on their outer surfaces is developed and applied to several model systems. The methodology can be applied to particles of arbitrary size, shape, charge distribution, and gel layer geometry. Account is also taken of the steady state distortion of the ion atmosphere from equilibrium, which makes it applicable to the transport of highly charged structures. The coupled field equations (Poisson, ion-transport, low-Reynolds-number Navier-Stokes, and Brinkman) are solved numerically and from this, transport properties (diffusion constants, electrophoretic mobilities, excess viscosities) can be computed. In the present work, the methodology is first applied to a gel sphere model over a wide range of particle charge and the resulting transport properties are found to be in excellent agreement with independent theory under those conditions where independent theory is available. It is then applied to several prolate spheroidal models of a particular silica sol sample in an attempt to identify possible solution structures. A single model, that is able to account simultaneously for all of the transport behavior, which does not undergo significant conformational change with salt concentration, could not be found. A model with a thin (相似文献   

Quantification of solid pressure in the concentration polarization (CP) layer of colloidal particles and its impact on ultrafiltration

Here we describe the nature and implications of the "concentration polarization" (CP) layer that is formed during ultrafiltration of colloidal particles using a new approach in which the solid pressure, which arises from inter-particle interactions, and the inherent osmotic pressure are separately considered. The approach makes use of the particle transport mass balance between the convective and diffusive fluxes. The particle convection rate is hindered when inter-particle interactions take effect by reducing the particle velocities while the particle diffusion is solely controlled by the Brownian motion. An increase in solid pressure accounts for the reduction of the water potential caused by the relative motions of the particles and the surrounding water. A cell model is adopted to relate the local solid pressure with the local solid fraction and inter-particle interactions. The inter-particle interactions critically determine the form of particle accumulation (i.e. CP or gel/cake) on the membrane. The Shirato-Darcy equation is employed to relate the rate of increase in solid pressure, the relative liquid velocity and the solid fraction. Numerical integration approaches are employed to quantify the properties of the CP layer during both the development as well as the steady state phases (with steady state normally being achieved in a few minutes). The solid fractions are always no higher than those obtained when the inter-particle interactions are not considered. The decrease of the water potential caused by CP formation leads to the increase of both the solid pressure and the osmotic pressure. The dependence of the solid pressure on the solid fraction is usually stronger than that of the osmotic pressure. It is thus apparent that the solid pressure would be expected to dominate water potential reduction for solid fractions above a certain value though the solid pressure will be negligible when the solid fraction is relatively low.     

Free-solvent model shows osmotic pressure is the dominant factor in limiting flux during protein ultrafiltration

In protein ultrafiltration (UF), the limiting flux phenomenon has been generally considered a consequence of the presence of membrane fouling or the perceived formation of a cake/gel layer that develops at high operating pressures. Subsequently, numerous theoretical models on gel/cake physics have been made to address how these factors can result in limiting flux. In a paradigm shift, the present article reestablishes the significance of osmotic pressure by examining its contribution to limiting flux in the framework of the recently developed free solvent osmotic pressure model. The resulting free-solvent-based flux model (FSB) uses the Kedem–Katchalsky model, film theory and the free solvent representation for osmotic pressure in its development. Single protein tangential-flow diafiltration experiments (30 kDa MWCO CRC membranes) were also conducted using ovalbumin (OVA, 45 kDa), bovine serum albumin (BSA, 69 kDa), and immuno-gamma globulin (IgG, 155 kDa) in moderate NaCl buffered solutions at pH 4.5, 5.4, 7 and 7.4. The membrane was preconditioned to minimize membrane fouling development during the experimental procedure. The pressure was randomly selected and flux and sieving were determined. The experimental results clearly demonstrated that the limiting flux phenomenon is not dominated by membrane fouling and the FSB model theoretically illustrates that osmotic pressure is the primary factor in limiting flux during UF. The FSB model provides excellent agreement with the experimental results while producing realistic protein wall concentrations. In addition, the pH dependence of the limiting flux is shown to correlate to the pH dependency of the specific protein diffusion coefficient.     

Osmotic pressure and structures of monodisperse ordered foam

We present an experimental and numerical study of the osmotic pressure in monodisperse ordered foams as a function of the liquid fraction. The data are compared to previous results obtained for disordered monodisperse and polydisperse concentrated emulsions. Moreover, we report a quantitative investigation of the transition from a bubble close packing to a bcc structure as a function of the liquid volume fraction. These findings are discussed in the context of theoretical models that have been proposed in the literature.     

Prediction of dynamic permeate flux during cross-flow ultrafiltration of polyethylene glycol using concentration polarization-gel layer model

A tubular ultrafiltration model which couples the formation of a cake layer on the membrane surface and the presence of a polarized layer above the cake has been developed, which contains a single constant and the cake layer resistance to be evaluated from experiments. In the model, the tangential flow of feed material is assumed to induce a shearing effect on the cake layer resulting in the re-entrainment the particles into the bulk stream. The validity of the model over a range of cross-flow velocity, transmembrane pressure (TMP) and solute concentration was confirmed using experimental permeate fluxes obtained from the ultrafiltration of polyethylene glycol. Excellent prediction is observed for solute concentrations above some critical value at which a well developed cake layer is believed to have been formed. For concentrations below this value, the model under predicted the steady-state permeate fluxes. By ignoring the presence of the polarized layer, the model always over predict the dynamic fluxes.     

A constant flux based mathematical model for predicting permeate flux decline in constant pressure protein ultrafiltration

This paper discusses a novel approach for predicting permeate flux decline in constant pressure ultrafiltration of protein solutions. A constant pressure process is assumed to be made up of a large number of small, sequential, constant flux ultrafiltration steps: the flux decreasing due to fouling and other related factors at the end of each step. The advantage of this approach is that constant flux ultrafiltration is easier to study, characterize, and model than constant pressure ultrafiltration. Consequently model parameters can be obtained in reliable and reproducible manner. Constant pressure ultrafiltration is dynamic in nature since both the magnitude of osmotic back-pressure and the extent of membrane fouling decrease as the permeate flux decreases with time. The proposed model takes into consideration the interplay between permeate flux, concentration polarization, and membrane fouling. The model demonstrates that the initial rapid flux decline is due to a combination of concentration polarization and membrane fouling while during the remaining part of the process, the effect of concentration polarization becomes negligible. The model also shows that concentration polarization affects the initial flux decline only at higher transmembrane pressures. This model which was validated using experimental data is conceptually simpler than other available models and easy to use. In addition to its value as a predictive tool it would particularly be useful for deciding appropriate start-up conditions in ultrafiltration processes.     

Osmotic pressure and polymer size in semidilute polymer solutions under good-solvent conditions

We consider the lattice Domb-Joyce model at a value of the coupling for which scaling corrections approximately vanish and determine the universal scaling functions associated with the osmotic pressure and the polymer size for semidilute polymer solutions (c/c( *)相似文献   

Fouling during the cross-flow ultrafiltration of proteins: a mass-transfer model

A model was designed to predict the effect of pH and ionic strength on fouling in the cross-flow ultrafiltration (UF)of protein solutions. Ilias and Govind’s numerical approach for concentration polarisation was combined with the Stokes–Einstein generalised equation and Bowen and Jenner’s osmotic pressure model. Coagulation was predicted when the mass-transport equation diverged to concentrations higher than that of the maximum osmotic pressure. This occurred at concentrations exceeding that of the maximum diffusivity, when diffusion became too weak to resist drag forces. In this case, one or more monolayers of protein deposited. The model was experimentally tested with 1 g/l BSA and Amicon H1P30-20 modules, for a range of pressures, ionic strengths and pH.     

Theoretical analysis and verification of concentration distribution model in the ultrafiltration process

Based on the assumed flat model, Navier-Stokes equation for two-dimensional laminar flow fluid and the theory for diffusion and mass transfer, we obtained theoretical results with regarding to the concentration distribution in separation process by mass transfer model in the ultrafiltration process. Through theoretical analysis and experimental verification of concentration distribution, it was known that this model could not only preferably describe the concentration distribution of ultrafiltration process but also forecast concentration polarization phenomenon.     

Osmotic pressure of micellar sodium dodecyl sulfate solutions in the presence of NaCl

The concentration dependence of osmotic pressure π_s of micellar solutions of an ionic surfactant in the presence of a background electrolyte is theoretically considered in terms of the Debye-Hückel theory with due regard for the premicellar association and interaction of micelles. On the basis of the quasi-chemical theory of micellization, the system composition is determined and the thickness of the electrical double layer of micelles is calculated. Within the framework of a cell model and the ideas of the molecular and ion-electrostatic interaction of micelles, which varies in relation to the degree of micellization, osmotic pressure in a sodium dodecyl sulfate-0.01 M NaCl system is calculated during variations in the overall surfactant concentrations. The results obtained are in good qualitative and quantitative agreement with available experimental data. At the same time, the results of calculating π_s values in terms of the Debye-Hückel theory without consideration for the interaction of micelles do not allow explanation of the experimental regularities.     

The osmotic pressure of concentrated protein and lipoprotein solutions and its significance to ultrafiltration

Side-by-side measurements were made of osmotic pressure and ultrafiltration flux from a stirred cell for separate saline solutions of the proteins, bovine serum albumin, bovine fibrinogen, human low density lipoprotein and for polyethylene oxide .in distilled water. Albumin osmotic pressures were large enough to conclude that concentration polarization limits ultrafiltrate flux mostly by decreasing the driving forceΔP -Δπ. For the other large macrosolutes, concentrated-solution osmotic pressures were so small that polarization probably limits flux at the usual levels of applied pressure by adding a hydrodynamic resistance (gel layer) in series with the membrane resistance.     

Resistance in series model for micellar enhanced ultrafiltration of eosin dye

A study has been performed to quantify the extent of flux decline during micellar enhanced ultrafiltration (MEUF) of an acid dye (eosin red) using hexadecyl (cetyl) pyridinium chloride as the cationic surfactant. Effects of the operating conditions, e.g., transmembrane pressure drop and feed-surfactant-to-dye ratio, on the permeate flux profile and observed retention have been investigated in an unstirred batch ultrafiltration (UF) cell. A simple resistance-in-series model has been used to quantify the flux decline. From the flux decline history, it has been found that the membrane permeability decreases rapidly due to reversible pore blocking and further flux decline is caused by the growth of a gel-type layer over the membrane surface. The different resistances and growth kinetics of the gel layer have been investigated as functions of the operating conditions.