Hindered Transport Theory Research Articles

Hydrodynamic model for renal microvascular filtration: Effects of physiological and hemodynamic changes on glomerular size-selectivity.

The first step in renal urine formation is ultrafiltration across the glomerular barrier. The change in its nanostructure has been associated with nephrotic syndromes. Effects of physiological and hemodynamic factor alterations associated with diabetic nephropathy (DN) on glomerular permselectivity are examined through a mathematical model employing low-Reynolds-number hydrodynamics and hindered transport theory. Glomerular capillaries are represented as networks of cylindrical tubes with multilayered walls. Glomerular basement membrane (GBM) is a fibrous medium with bimodal fiber sizes. Epithelial slit fiber spacing follows a lognormal distribution based on reported electron micrographs with the highest resolution. Endothelial fenestrae are filled with fibers the size of glycosaminoglycans (GAGs). Effects of fiber-macromolecule steric and hydrodynamic interactions are included. Focusing on diabetic nephropathy, the physiological and hemodynamic factors employed in the computation are those reported for healthy humans and patients with early-but-overt diabetic nephropathy. The macromolecule concentration is obtained as a finite element solution of the convection-diffusion equation. Computed sieving coefficients averaged along the capillary length agree well with ficoll sieving coefficients from studies in humans for most solute radii. GBM thickening and the loss of the slit diaphragm hardly affect glomerular permselectivity. GAG volume fraction reduction in the endothelial fenestrae, however, significantly increases macromolecule filtration. Increased renal plasma flow rate (RPF), glomerular hypertension, and reduction of lumen osmotic pressure cause a slight sieving coefficient decrease. These effects are amplified by an increased macromolecule size. Our results indicate that glomerular hypertension and the reduction in the oncotic pressure decreases glomerular macromolecule filtration. Reduction of RPF and changes in the glomerular barrier structure associated with DN, however, increase the solute sieving. Damage to GAGs caused by hyperglycemia is likely to be the most prominent factor affecting glomerular size-selectivity.

Solute hindrance in non-porous membranes: An ATR-FTIR study

The hindered transport theory (HTT) is widely used to analyze the size-dependence of transport in membranes such as reverse osmosis and nanofiltration, however, serious concerns have been raised recently about its suitability for molecular solutes. To address this concern, the diffusivities of dye molecules (189 to 961Da) in a crosslinked poly(vinyl alcohol) film were measured using ATR-FTIR spectroscopy. Possible errors due to liquid layers on both sides of the film were analyzed and appeared to have a minor effect on the results. The values of diffusion coefficient were found to be in the range 3.3×10−14 to 4.4×10−13m2/s. Based on the pore size of 2.24nm estimated from hydraulic permeability, these values were about 3 orders of magnitude lower than the predictions by HTT. This result strongly suggests that HTT may not be a suitable model for the transport of small molecules in membranes such as RO and NF, pointing to the need for more adequate models.

Does hindered transport theory apply to desalination membranes?

As reverse osmosis (RO) and nanofiltration polyamide membranes become increasingly used for water purification, prediction of pollutant transport is required for membrane development and process engineering. Many popular models use hindered transport theory (HTT), which considers a spherical solute moving through an array of fluid-filled rigid cylindrical pores. Experiments and molecular dynamic simulations, however, reveal that polyamide membranes have a distinctly different structure of a "molecular sponge", a network of randomly connected voids widely distributed in size. In view of this disagreement, this study critically examined the validity of HTT by directly measuring diffusivities of several alcohols within a polyamide film of commercial RO membrane using attenuated total reflection-FTIR. It is found that measured diffusivities deviate from HTT predictions by as much as 2-3 orders of magnitude. This result indicates that HTT does not adequately describe solute transport in desalination membranes. As a more adequate alternative, the concept of random resistor networks is suggested, with resistances described by models of activated transport in "soft" polymers without a sharp size cutoff and with a proper address of solute partitioning.

Interplay between the Transport of Solutes Across Nanofiltration Membranes and the Thermal Properties of the Thin Active Layer

The thin active layer (TAL) of seven nanofiltration (NF) membranes was studied using differential scanning calorimetry, and the membranes were classified into two groups according to the polymer physical state (amorphous or semicrystalline). NF membrane performance in terms of permeate volume flux density and rejection of neutral solutes was investigated in temperature cycles. The modeling of rejection using a hindered transport theory showed irreversible and opposite pore size changes for the two groups of NF membranes when the maximum operating temperature of the cycle exceeded the glass-transition temperature of the TAL. A mechanism of pore deformation is proposed to explain the variation of the solute transport properties as a function of the temperature and the polymer physical state in the TAL.

Effect of Temperature on the Transport of Water and Neutral Solutes across Nanofiltration Membranes

We carry out a detailed experimental and theoretical study of the influence of temperature on nanofiltration performance using the Desal5DK membrane. Experimental results for the permeate volume flux density and rejection of four neutral solutes (glycerin, arabinose, glucose, and sucrose) are presented for temperatures between 22 and 50 degrees C. Solute rejection is modeled using a hindered transport theory that allows us to unveil the crucial role played by changes in the membrane structural parameters (effective pore radius and membrane thickness) due to changes in temperature.

Hindrance Factors for Diffusion and Convection in Pores

It is well-known that solutes in liquid-filled pores of molecular dimensions have reduced diffusivities and are sieved during filtration. For solute molecules that are large enough to act as hydrodynamic particles, these phenomena can be explained by a combination of particle−wall hydrodynamic interactions and steric restrictions. Theoretical expressions that include those effects have been available for many years, but, even for spheres in pores of constant cross-section, certain hydrodynamic information has been lacking until recently. In particular, the local enhanced drag and local lag coefficient for off-axis positions had not been fully characterized, requiring that results for symmetrically positioned particles (“centerline approximations”) be employed in predicting diffusional and convective hindrances. In this paper the current status of hindered transport theory is reviewed for neutral spheres in long cylindrical pores or slits, and it is shown that such approximations are no longer necessary. New expressions are presented for diffusive and convective hindrance factors that are properly averaged over the pore cross-section. The root-mean-square errors in the centerline approximations are 20% and 6%, respectively, for diffusive and convective hindrance factors in cylindrical pores; for slit pores the corresponding errors are 16% and 10%. Comparisons are made between the predictions and recent data obtained by tracking particle positions in microchannels.

Modeling skin permeability to hydrophilic and hydrophobic solutes based on four permeation pathways

Barrier properties of skin originate from low permeability of stratum corneum. The objective of this paper is to compile fundamentally-based analytical expressions that can be used to predict skin permeability to hydrophilic as well as hydrophobic solutes. Solute permeation through four possible routes in stratum corneum including free-volume diffusion through lipid bilayers, lateral diffusion along lipid bilayers, diffusion through pores, and diffusion through shunts was analyzed. Contribution of free-volume diffusion through lipid bilayers was determined using Scaled Particle Theory. This theory relates solute partition and diffusion coefficients to the work required to create cavities in a lipid bilayers to allow solute incorporation and motion. Contribution of lateral lipid diffusion was determined from the literature data. Contribution of pores was estimated using hindered transport theory. This theory assumes that hydrophilic solutes permeate across the skin through imperfections in the lipid bilayers modeled as pores. Finally, contribution of shunts was determined using a simple diffusion model. The model yielded a series of equations to predict skin permeability based on solute radius and octanol–water partition coefficient. Predictions of the model compare well with the experimental data.

Hafnia ceramic nanofiltration membranes: Part II. Modeling of pressure-driven transport of neutral solutes and ions

We use the hindered transport theory for neutral solutes and the macroscopic homogeneous electro-transport theory for ions to predict without any adjustable parameters the limiting rejection of, respectively, four neutral molecules and five binary electrolytes by granular porous hafnia nanofilters. Membrane parameters entering into the theory, namely the membrane effective pore size and effective charge density, are estimated from independent measurements performed on the membrane material. The theory is in reasonably good overall agreement with the rejection measurements performed on hafnia nanofilters using uncharged sucrose and PEG (400, 600, 1000) molecules and 10 −3 M electrolytes (NaCl, NaNO 3, CaSO 4, CaCl 2, and Na 2SO 4) at acidic, neutral, and basic pH values (3, 6, and 9).

Theory of pressure-driven transport of neutral solutes and ions in porous ceramic nanofiltration membranes

Hindered transport theory and homogeneous electro-transport theory are used to calculate the limiting, high volume flux, rejection of, respectively, neutral solutes and binary electrolytes by granular porous nanofiltration membranes. For ceramic membranes prepared from metal oxides it is proposed that the membrane structural and charge parameters entering into the theory, namely the effective pore size and membrane charge density, can be estimated from independent measurements: the pore radius from the measured hydraulic radius using a model of sintered granular membranes and the effective membrane charge density from the hydraulic radius and the electrophoretic mobility measurements on the ceramic powder used to prepare the membrane. The electro-transport theory adopted here is valid when the membrane surface charge density is low enough and the pore radius is small enough for there to be strong electrical double layer overlap in the pores. Within this approximation the filtration streaming potential is also derived for binary electrolytes.

Pore induction in human epidermal membrane during low to moderate voltage iontophoresis: A study using AC iontophoresis

The present study aimed to investigate new pore induction as a flux-enhancing mechanism in human epidermal membrane (HEM) with low to moderate voltage electric fields. The extent of pore induction and the effective pore sizes of these induced pores were to be assessed using a low frequency (12.5 Hz) low to moderate voltage (2.0 to 4.0 V) square-wave alternating current (ac) “passive” permeation method (ac iontophoresis). This ac approach was to allow for inducing and sustaining a state of pore induction in HEM while permitting no significant transport enhancement via electroosmosis; thus, transport enhancement entirely due to new pore induction (enhanced passive permeation) was to be assessed without any contributions from electroosmosis. Good proportionality between the increase in HEM permeability and its electrical conductance was found with the “passive” transport data obtained during square-wave ac iontophoresis using urea as the model permeant. Typically, at 3.0 to 4.0 V, HEM conductance increases (and permeability increases) ranged from around 3- to 30-fold. These results appear to be the first direct evidence that new pore induction in HEM is a significant flux enhancing mechanism under moderate voltage conditions. The extents of pore induction in HEM under low frequency moderate voltage (2.0 to 3.0 V) ac, pulsed direct current (dc), and continuous dc were also compared. The extents of pore induction from square-wave ac and pulsed dc were generally of the same order of magnitude but somewhat less than that observed during continuous dc iontophoresis at the same applied voltage and duration, suggesting less extent of pore induction with reversing polarity or when a brief delay is provided between pulses to allow for membrane depolarization. The average effective pore sizes calculated for the induced pores from the experimental data with urea and mannitol as probe permeants and the hindered transport theory were 12 ± 2 Å, which are of the same order of magnitude as those of preexisting pores determined from conventional passive diffusion experiments.

Characterization of the Transport Pathways Induced during Low to Moderate Voltage Iontophoresis in Human Epidermal Membrane

□ This report describes the results of iontophoresis experiments involving the transport of polar nonelectrolytes across human epidermal membrane (HEM) at a moderate applied voltage of 2.0V and where the data are interpreted via a convective transport model and hindered transport theory. A principal finding is that although HEM iontophoresis at 2.0V resulted in a large increase in HEM porosity, the pore radii of the newly induced pores in HEM as calculated from the iontophoresis data using the hindered transport theory were found to be in the range of 6–12Å. This supports the view that electroporation at these modest applied voltages results in pores with sizes the same order of magnitude but somewhat smaller than those estimated for the preexisting pores in HEM prior to electroporation. This outcome is also important from a practical standpoint, as flux enhancement for large molecules (such as oligonucleotides and polypeptides) arising from electroporation under these conditions would be expected to be significantly less than if the resulting pore sizes were much greater. Providing a “prepulse” of 4.0, 8.0, and 15V prior to the 2.0V iontophoresis generally gave greater increases in HEM conductance (and, therefore, in porosity) but did not significantly change the deduced effective pore radii (around 5–9Å). The alteration during and the recovery of HEM after iontophoresis was also investigated. The recovery behavior was found to be dependent upon both the duration of the applied voltage and the magnitude of its effects: the recovery for a HEM sample that experienced a large increase in electrical conductance during iontophoresis was generally poorer than that for a sample that was more resistant to the electric field. Incomplete recovery was generally observed in experiments with long iontophoresis duration (50min) and with the higher voltages (4.0, 8.0V, and 15V). In these cases, the barrier properties of HEM were more greatly altered as indicated by larger increases in the electrical conductance and passive permeability of HEM after iontophoresis.

Analysis of steric hindrance reduction in pulsed protein ultrafiltration

This study analyzes the effect of transmembrane pressure pulsing on transient steric hindrance for BSA ultrafiltration in an unstirred batch cell using 100,000 MWCO cellulosic membranes. Studies were performed with fresh membranes and membranes preadsorbed with 0.1% IgG for 0.5, 2.25 and 26 hours. The Kedem-Katchalsky model was used to determine the apparent sieving coefficients and estimate the wall concentrations. Hindered transport theory was used to estimate the resulting apparent pore size of the membranes for pulsed and nonpulsed cases. The apparent pore size was increased by 8% when pulsing was used in conjunction with fresh membranes. The intrinsic sieving coefficients were increased by 33% during pulsing. Pulsing also substantially increased the apparent pore size and the initial sieving coefficients for the IgG preadsorbed membrane cases. Based on the initial time data for the IgG preadsorbed membrane cases, it was determined that the presence of IgG on the membranes could affect the concentration of BSA in the permeate. It was also found that transmembrane pressure pulsing could partially eliminate this resistance to BSA permeability.

Using micelles to determine the pore size of UF membranes

To estimate the pore size of ultrafiltration (UF) membranes, a method using micellar filtration is proposed. Lithium dodecylsulfate (LiDS) forms micellar aggregates of spherical shape even at high ionic strength. The surfactant rejection rate of micellar solutions show a remarkable dependence upon the ionic strength (LiCl: 0 to 1 mol/l). From the size dependence of the aggregates on the ionic strength (micelle radius plus ionic atmosphere thickness) and the rejection rate of the micellized surfactant, we determine the mean pore diameter of a 40 kDa UF polysulfone membrane. Obtained results are in accordance with the hindered transport theory through capillaries: small LiDS micelles behave like neutral hard spheres in the presence of excess salt. Microscopic examination of the membrane surface shows a quasi-uniform distribution of pores. Pore surface density can be easily determined, but, due to gold aggregates at the pores entrance, the average mean diameter obtained by this method appears to be too large.