Generalized integral and similarity solutions of the concentration profiles for osmotic pressure controlled ultrafiltration

A mathematical model describing the concentration polarization phenomenon during osmotic pressure controlled ultrafiltration is presented. Generalized integral and similarity solutions of the concentration profile in the mass transfer boundary layer are obtained. The parameters governing the shape of the concentration profile vary with time in case of a batch cell and axial distance in a cross flow cell. The model is used to predict the permeate flux and the solute rejection simultaneously during unstirred batch cell and cross flow UF. The results obtained by integral and similarity solutions are compared with the results of detailed numerical solution of the governing equations for both the systems. The predictions of permeate flux from the generalized integral method are also compared with some approximate solutions in order to assess the limitations of the various approximations. UF experiments were performed with Dextran (T-20) in cross flow system and with PEG-6000 and Dextran (T-40 and T-20) in unstirred batch cell. Predictions of the model are in remarkably good agreement with detailed simulation as well as experimental results. Moreover, the integral solution can also account for the variation of diffusivity with solute concentration. Comparisons show that (a) while the generalized integral method is much simpler than the detailed numerical solutions, it is much more general and accurate than other analytical and semi-analytical solutions, and, (b) the proposed solution predicts the osmotic pressure controlled flux decline accurately over a wide range of operating conditions. The expression for gel layer governed UF (constant membrane surface concentration) is found to be an asymptotic case of the present solution.     

Resistance to the permeate flux in unstirred ultrafiltration of dissolved macromolecular solutions

The flux decline during the unstirred ultrafiltration of dissolved macromolecular solutions such as polyethylene glycol and dextran solutions was measured at different pressures from I to 4 x 10⁵ Pa and different bulk concentrations from 0.1 to 0.55 kg/m³ with three types of polysulfone membranes. On the basis of the concept that a concentrated solution layer (not a gel layer) is formed on the membrane surface, the hydraulic resistance of the boundary layer was defined with the help of solvent permeability of dissolved macromolecules. The cake filtration theory was employed to analyze the flux decline behaviour. This simple theory worked well and the effective boundary layer concentrations calculated with the boundary layer resistance model developed here were physically quite reasonable. The calculated boundary layer concentrations depend on the applied pressure. The origin of this dependency might be the step concentration profile assumed in the cake filtration theory.     

The dynamics of polarisation in unstirred and stirred ultrafiltration

Polarisation of a retentive UF membrane has been studied for three types of solute, a colloid (silica sol), a protein (albumin) and a branched chain polymer (Dextran), with and without stirring. For unstirred conditions the data have been analysed by modified constantpressure filtration theory, which gives specific resistances, a, of the solutes consistent with their sizes and conformation. The simple Carman—Kozeny relationship approximates a for the colloid and the protein. For all three solutes a increased with pressure and concentration. Times to steady-state flux for stirred conditions ranged from 10 to 50 seconds, with longest times for the lowest concentrations and the largest solute. The amount of solute in the polarised layer was estimated from the measured cake (gel) resistances and the known specific resistances. Layer thicknesses ranged up to to ? 5 μm for the protein, ? 6μm for the Dextran and ? 20 μm for the silica sol. Slight deviations of flux—time profiles from the filtration model are explained by membrane—solute interactions, such as irreversible pore plugging and reversible pore obstruction.     

Correlation of mass transfer rates for a diffusive sampler with air speed and incidence angle

An accurate measurement of a gas concentration in air by diffusive sampling requires knowing the sampling rate. Both the boundary layer between turbulent ambient air and the sampler and the stagnant air layer inside the sampler impose resistance to the transport of analyte into the sampler. As the boundary layer mass transfer resistance is a function of the air speed and direction of the air movement, the sampling rate also depends on these variables. By the procedure developed here, the boundary layer mass transfer resistance was accurately measured as a function of wind speed and direction, and from these data a basic correlation with dimensionless parameters describing mass transfer was obtained. Deviation of air incidence angle and speed during sampling from the calibration conditions may produce a small positive bias, probably not in excess of 10%. Random variation of incidence angle and air speed while the sampler is in use may also contribute to the variability of this sampling method.     

The influence of the porous support layer of composite membranes on the separation of binary gas mixtures

Thin film composite (TFC) membranes exhibit a high flux for gas and vapor permeation and are viable for a wide range of applications. The high flux may also increase the importance of the resistance of the porous support structure depending on the application and process conditions. A comprehensive modeling approach for TFC membranes is introduced, which considers boundary layer resistances near the membrane surface, solution-diffusion through the coating, and the influence of the porous sublayer. Permeation through the support structure is described by the dusty gas model (DGM) with the support treated as a two-layered structure with a dense but porous skin and a more open substructure.The model accurately describes experimental data on TCE/nitrogen separation using a sweep gas on the permeate side very well. The main resistance towards TCE permeation through two different membranes tested is the porous support. It is shown that changes in the support morphology can greatly enhance the performance of the composite membranes. Model calculations were also performed for vacuum assisted permeation. The pressure drop across the support is considerable depending on the coating thickness. The TCE permeation is again dominated by the resistance of the support layer, which can be reduced by altering the morphological parameters of the structure.The proposed model is able to describe the performance of the composite membrane and to identify optimum process conditions for given performance characteristics. It can be used to aid in the development of membrane structures for enhanced performance.     

New insights in the removal of diluted volatile organic compounds from dilute aqueous solution by pervaporation process

The present work aimed the mass transfer investigation in the removal of organic contaminants from water by the pervaporation process. The terpolymer ethene-propene-diene (EPDM) was used as the selective elastomer. Two classes of model organic solutes were chosen: chlorinated hydrocarbons (trichloroethylene, dichloromethane and trichloromethane) and aromatic ones (toluene, phenol and aniline). Pervaporation tests were carried out using dense and composite membranes with different thickness, solute concentrations and feed flow velocities at room temperature. The liquid boundary layer resistance (i.e., concentration polarization phenomenon) was observed for all solutes. The resistance-in-series model was used to determine liquid and polymer phase resistances. The results obtained indicate that the model would be better written considering the chemical potential gradient as driving force, in order to take into account affinity between water and the organic solutes, as well as their interactions with the polymer selective layer. The rational activity coefficients of the solutes in the polymer phase were determined by inverse gas chromatography (IGC) and related to the mass transfer coefficient in the polymer phase.     

Active control of the depletion boundary layers in microfluidic electrochemical reactors

In this paper, we describe three methods to improve the performance of pressure-driven laminar flow-based microreactors by manipulating reaction-depletion boundary layers to overcome mass transfer limitations at reactive surfaces on the walls, such as electrodes. The transport rate of the reactants to the reactive surfaces is enhanced by (i) removing the depleted zone through multiple periodically-placed outlets; (ii) adding fresh reactants through multiple periodically-placed inlets along the reactive surface; or (iii) producing a spiraling, transverse flow through the integration of herringbone ridges along the channel walls. For approaches (i) and (ii), the network of microfluidic channels needs to be designed such that under the operating conditions used the right amount of boundary layer at each outlet or inlet is removed or replenished, respectively. Here, we report a set of design rules, derived with the help of a fluidic resistance circuit model, to aid in the design of appropriate microfluidic networks. Also, the actual enhancement of the performance of the electrochemical microreactor, i.e. chemical conversion efficiency, using multiple inlets, multiple outlets, or herringbone ridges is reported.     

A continuum model for yttria-stabilized zirconia incorporating triple phase boundary,lattice structure and immobile oxide ions

A continuum model for yttria-stabilized zirconia (YSZ) in the framework of non-equilibrium thermodynamics is developed. Particular attention is given to (i) modeling of the YSZ-metal-gas triple phase boundary, (ii) incorporation of the lattice structure and immobile oxide ions within the free energy model and (iii) surface reactions. A finite volume discretization method based on modified Scharfetter-Gummel fluxes is derived in order to perform numerical simulations. The model is used to study the impact of yttria and immobile oxide ions on the structure of the charged boundary layer and the double layer capacitance. Cyclic voltammograms of an air-half cell are simulated to study the effect of parameter variations on surface reactions, adsorption and anion diffusion.

     

Hollow-fiber-type pore-filling membranes made by plasma-graft polymerization for the removal of chlorinated organics from water

Hollow-fiber-type pore-filling membranes were prepared to reduce the emission of toxic chlorinated organics into the environment. These membranes can remove 1,1,2-trichloroethane (TCE) or dichloromethane (DM) from water, and concentrate them in the permeate. The pore-filling membrane can efficiently remove organics from water because of the suppression of the membrane swelling by the porous substrate matrix, and the fact that it can maintain a high solute diffusivity, because of the linear graft chains that fill the substrate pores. Laurylacrylate (LA) or n-butylacrylate (BA) grafted layers were formed inside the porous hollow-fiber substrate, and the pores were filled with the grafted chains formed from plasma-initiated graft polymerization. The hollow-fiber-type LA-grafted membranes showed extremely high separation properties: a 0.09 wt.% TCE aqueous solution was condensed to 99 wt.% TCE in the permeate. The membrane can remove TCE from a water stream, and at the same time, the membrane can purify the TCE for re-use. The membrane also showed high separation performance for an aqueous DM solution. The mass transfer resistance outside the membrane was estimated by using a concentration polarization model. When the mass transfer coefficient at the membrane and feed stream boundary layer was below 10⁻⁴ m/s, the boundary layer resistance affected the membrane performance. This needs to be taken into account when designing the membrane module and operating conditions.     

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.     

SIZE EXCLUSION CHROMATOGRAPHIC COLUMN PACKED WITH REGENERATED CELLULOSE GELS*

Microporous regenerated cellulose gel particles were prepared by mixing cellulose cuoxam with silk fibroin aspore former, and the mean pore size and pore volume of the pallicles were 525 nm and 7.27 mL g~(-1), respectively. Apreparative size-exclusion chromatography (SEC) column (550 mm×20 mm) packed with the cellulose gel particles wasused for the fractionation of two polysaccharides Dextran 07 (M_w = 7.14×10~4, d= 1.7) and Dextran 50(M_w = 50.5×10~4,d = 3.8) in water phase. The fractionation range of the stationary phase covered M_w from 3×10~3 to 1.1×10~6. The dailythroughput was 2.9 g for Dextran 07 (D07) and 4.3 g for Dextran 50 (D50) with a flow-rate of 1.5 mL min~(-1). The fractionsobtained by using the SEC were analyzed by an analytical SEC combined with laser light scattering (LLS), and thepolydispersity indices of fractions for Dextran 07 and Dextran 50 were determined to be 1.34-1.57 and 1.53-3.36,respectively. The preparative SEC is a simple, rapid, and suitable means not only for the fractionation of polysaccharides inwater but also for other polymers in organic solvents.     

CROSS-FLOW MICROFILTRATION OF BKNTOMTE-IN-WATER DISPERSIONS: EFFECTS OF SUSPENSIONRHEOLOGY

Cross-How filtration of bentonite-in-water suspensions is studied experimentally in a small laboratory device. The Theological behaviour and the filtration resistance in batch filtration are independently established. Both transient and steady-state data indicate channel constriction by a dense cake layer. Quantitative estimates based on measured parameters show that steady-state conditions can be ensured by tangential flow of the dense pseudoplastic bentonite cake. Steady-state is possible when the shear stress at the moving boundary feed suspension/dense cake exceeds appr.l Pa (at lower values of the shear stress the cross-flow microfiltration channel gets plugged). The material characteristics of the dense cake, which determine cross-flow filtration behaviour, are the viscosity and the specific filtration resistance. Indirect estimates of these quantities from measured cross-flow filtration parameters are consistent with results from direct measurements. The data support the convective model of cross-flow microfiltration.     

Motion of a Colloidal Sphere Covered by a Layer of Adsorbed Polymers Normal to a Plane Surface

A combined analytical–numerical study is presented for the slow motion of a spherical particle coated with a layer of adsorbed polymers perpendicular to an infinite plane, which can be either a solid wall or a free surface. The Reynolds number is assumed to be vanishingly small, and the thickness of the surface polymer layer is assumed to be much smaller than the particle radius and the spacing between the particle and the plane boundary. A method of matched asymptotic expansions in a small parameter λ incorporated with a boundary collocation technique is used to solve the creeping flow equations inside and outside the adsorbed polymer layer, where λ is the ratio of the characteristic thickness of the polymer layer to the particle radius. The results for the hydrodynamic force exerted on the particle in a resistance problem and for the particle velocity in a mobility problem are expressed in terms of the effective hydrodynamic thickness (L) of the polymer layer, which is accurate to O(λ²). The O(λ) term forLnormalized by its value in the absence of the plane boundary is found to be independent of the polymer segment distribution and the volume fraction of the segments. The O(λ²) term forL, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the boundary effects on the motion of a polymer-coated particle can be quite significant.     

Analysis of transport through thin film composite membranes using an improved Wheatstone bridge resistance model

The two-dimensional Wheatstone bridge resistance analog model for permeation through thin film composite (TFC) membranes proposed by Karode et al. [5] has been extended to also include the cases where the coating layer thickness is of similar magnitude as the pore radius in the support matrix. The effect of the constriction resistance, i.e. the resistance encountered by the permeating species in traveling in a radial direction to find a pore to diffuse through is highlighted by considering three generic types of TFC membranes: (i) TFC membranes where the support has very low surface porosity; (ii) TFC membranes with moderate support layer surface porosity; and (iii) TFC membranes incorporating an intermediate gutter layer between the top coating and the bottom support. The model predictions are compared with experimental data reported in literature and various effects are highlighted by considering a few hypothetical cases. The calculations indicate that PRISM type membranes do not require pore filling in order to achieve a composite selectivity close to that of the support material as the high constriction resistance due to low surface porosity effectively prevents transport along the less permselective pathway. In case of less permeable but highly selective top layers, the constriction resistance can be significantly decreased by the gutter layer concept resulting in higher permeabilities and selectivities controlled by the coating layer. In general, the constriction resistance becomes dominant when the permeability of the top layer is low or when the support surface porosity is low.     

Preparation of poly(butylcyanoacrylate) drug carriers by nanoprecipitation using a pre-synthesized polymer and different colloidal stabilizers

Classically, drug-loaded poly(alkylcyanoacrylate) colloidal carriers are prepared by the drug entrapment during emulsion polymerization. However, a number of chemically sensitive drugs are unstable in the conditions of polymerization or can be irreversibly inactivated by the highly reactive monomer. Furthermore, the particle size distribution and the molecular weight of formed polymer depend strongly on the polymerization conditions. Here, we investigate the nanoprecipitation approach for the preparation of pure and drug-load poly(butylcyanoacrylate) nanoparticles. This method allows the successful entrapment of lipophilic and chemically labile drugs by avoiding the contact with highly reactive monomers. The anticancer agent chlorambucil is chosen as the model drug for the incorporation and release studies. Pure and drug-loaded nanoparticles are successfully prepared using various stabilizers (Polysorbate 80, Pluronic F68, Dextran 40). The nanoparticles coated with Polysorbate 80 are of highest interest since they could overcome the blood–brain barrier and the multidrug resistance in cancer cells. Such nanoparticles can be easily prepared by the nanoprecipitation approach reported here.     

A discussion on ion conductivity at cation exchange membrane/solution interface

By Gouy–Chapman–Stern–Grahame (CGSG) model, the electric double layer at ion exchange membrane/solution interface consists of two parts: the Stern layer and the diffusion layer. The ions in Stern layer are compacted and considered to be immobile. The relation of diffusion layer mean conductivity K with outer Stern layer potential φ₀, the boundary potential φ_δ and the electrolyte concentration C₀ is educed for symmetric electrolyte system. The results show that K is higher than that of the bulk solution and is greatly influenced by φ₀, φ_δ and C₀.The examination of PE01 cation exchange membrane/solution interface resistance R_e measured by ac impedance technique, shows that R_e value decreases quickly as the KCl electrolyte concentration rises. The effect of electrolyte concentration on the resistance of EDL can be explained by the electrical interactions between ions and charged groups of the membrane. Since the membrane/solution interface resistance is much higher than that of bulk solution, therefore, a further analysis based on the theory developed in this study proves that the ion transfer resistance R_e of membrane–solution interface predominantly occurs at Stern layer as a result of static electrical interaction.     

Direct measurement of concentration distribution within the boundary layer of an ion-exchange membrane

In this study the concentration distributions within the diffusion boundary layer were obtained by directly measuring the potential drops while the currents (under- and overlimiting) passed through the Neosepta CMX cation-exchange membrane (Tokuyama Corp., Japan). Potential drops according to the distance from the membrane surface on the depleted side were measured using a microelectrode to obtain the concentration profile. From the concentration profiles obtained, it was observed that the diffusion boundary layers existed in the range of 300-350 microm, which reasonably coincide with the theoretical diffusion boundary layer thickness calculated from the limiting current density. Although there were some deviations between the concentrations determined from the Nernst model and those from experiments, it was confirmed that the Nernst model effectively depicts the transport phenomena in the ion-exchange membrane system. In addition it was found that the salt concentration at the membrane surface increased when the currents applied exceeded the limiting current. It is thought that the concentration polarization formed in the diffusion boundary layer at currents near or lower than the limiting current was disturbed by a turbulent convection when the current was greater than the limiting current. As a consequence, the concentration at the membrane surface increased to a sufficient level for generation of the overlimiting current.