Oscillations with a long periodical time observed in solute transport by diffusion combined with convection through a single hollow-fiber membrane

Solute transport by diffusion combined with convection through a single hollow-fiber membrane fixed on an axis of a circular tube was studied precisely. Purified water and an aqueous solution of a solute were fed at constant flow rates into the circular tube and the lumen of the membrane, respectively, and oscillations with a long periodical time were observed in the concentration of solution discharged from the lumen. Results obtained with varying experimental conditions (different solutes, membranes and flow rates at the lumen inlet and outlet) suggest that the oscillations are related to solute transport caused by convection flow through the membranes.     

Effects of overlapping electric double layer on mass transport of a macro‐solute across porous wall of a micro/nanochannel for power law fluid

Effects of overlapping electric double layer and high wall potential on transport of a macrosolute for flow of a power law fluid through a microchannel with porous walls are studied in this work. The electric potential distribution is obtained by coupling the Poisson's equation without considering the Debye–Huckel approximation. The numerical solution shows that the center line potential can be 16% of wall potential at pH 8.5, at wall potential −73 mV and scaled Debye length 0.5. Transport phenomena involving mass transport of a neutral macrosolute is formulated by species advective equation. An analytical solution of Sherwood number is obtained for power law fluid. Effects of fluid rheology are studied in detail. Average Sherwood number is more for a pseudoplastic fluid compared to dilatant upto the ratio of Poiseuille to electroosmotic velocity of 5. Beyond that, the Sherwood number is independent of fluid rheology. Effects of fluid rheology and solute size on permeation flux and concentration of neutral solute are also quantified. More solute permeation occurs as the fluid changes from pseudoplastic to dilatant.     

Mass transfer limitations at crystallizing interfaces in an atomic force microscopy fluid cell: a finite element analysis

Although atomic force microscopy (AFM) has emerged as the preeminent experimental tool for real-time in situ measurements of crystal growth processes in solution, relatively little is known about the mass transfer limitations that may impact these measurements. We present a continuum analysis of flow and mass transfer in an atomic force microscope fluid cell during crystal growth, using data acquired from calcium oxalate monohydrate (COM) crystal growth measurements as a comparison. Steady-state flows and solute concentration fields are computed using a three-dimensional, finite element method implemented on a parallel supercomputer. Steady-state flow results are compared with flow visualization experiments to validate the model. Computations of the flow field demonstrate how nonlinear momentum transport alters the spatial structure of the flow with increasing flow volume, altering mass transport conditions near the AFM cantilever and tip. The simulations demonstrate that the combination of solute depletion from crystal growth and mass transfer resistance lowers the solute concentration in the region between the tip and the crystal compared with the solute concentration at the inlet of the AFM cell. For example, using experimentally measured growth rates for COM, the solute concentration in this region is 3.1% lower than the inlet value because the solute consumed by crystal growth beneath the AFM tip cannot be replenished fully due to mass transport limitations. The simulations also reveal that increasing the flow rate through the cell does not affect this difference significantly because of the inherent shielding by the AFM tip in proximity with the crystal surface. Models such as the one presented here, used in conjunction with AFM measurements, promise more precise interpretations of measurement data.     

Determination of concentration-dependent transport coefficients in nanofiltration: Experimental evaluation of coefficients

To characterize solute transport in nanofiltration (NF) the Spiegler–Kedem equation requires that two coefficients be determined for two-component solutions (a solute in water), solute permeability ω and reflection coefficient σ. For salts both coefficients strongly and in a complex way depend on concentration, which greatly complicates their evaluation from experiments. For this reason, the parameters are usually assumed constant for a given feed and the concentration dependence is assessed from flux–rejection curves for several feeds. This procedure however ignores the fact that the solute concentration and hence the coefficients significantly vary across the membrane. One way to overcome this inconsistency and address concentration dependence is to use physical models explicitly introducing exclusion mechanism(s) and fitting relevant membrane-specific parameters, such as fixed charge or dielectric properties. This procedure often fails to produce unique values of parameters for a given membrane and different salts. In the present study a new phenomenological approach is proposed and critically analyzed, based on the assumption of a similar concentration dependence of ω and 1 − σ, previously shown to be valid under fairly general conditions, thereby the Peclét coefficient A = (1 − σ)/ω may be assumed to be independent of concentration. The coefficients and their concentration dependence for a given solute may be directly and consistently evaluated by fitting flux–rejection data for several feeds and fluxes to numeric solution of the modified transport equations without the need to invoke specific physical models. The values of transport parameters deduced in this way for representative membranes and salts allow important conclusions regarding the transport mechanism. In particular, the roles of different mechanisms in overall salt exclusion could be addressed directly from the variation of ω or 1 − σ with concentration. On the other hand, the value of the Peclét coefficient, free of the effect of salt partitioning, may be analyzed in terms of hindered transport. Using the proposed method, this value was found to be very small for studied thin-film composite membranes, which may significantly simplify the transport equations.     

Effect of ionic strength and protein concentration on the transport of proteins through chitosan/polystyrene sulfonate multilayer membrane

The influence of ionic strength and protein concentration on the transport of bovine serum albumin (BSA), ovalbumin and lysozyme through chitosan (CHI)/polystyrenesulfonate (PSS) multilayers on polyether sulfone supports are investigated under ultrafiltration conditions. The percentage transmission and flux of BSA, ovalbumin and lysozyme were found to increase with increase in salt concentration in the protein. The percentage transmission of BSA through 9 bilayer membrane was found to increase from 5.3 to 115.6 when the salt concentration was varied from 0 to 1 M. It was observed that 0.1 M NaCl in BSA solution is capable of permeating all the BSA. When the salt concentration in BSA was further increased, a negative solute rejection (solute enrichment in permeate) was found to take place. With 9 bilayer membrane, the percentage transmission of ovalbumin was found to increase from 23.3 to 125.8 when the salt concentration in protein was increased from 0 to 0.05 M. The effect of protein concentration on protein transport is studied taking BSA as a model protein. BSA was rejected by the multilayer membrane at all the studied concentrations (0.25, 0.5, 1 and 2 mg/ml). With increase in feed concentration, maximum rejection of protein occurred at higher number of CHI/PSS bilayers. BSA solution flux was found to decrease with an increase in BSA concentration. This study indicates that it is possible to fine tune the transport properties of proteins through multilayer membranes by varying the concentration and ionic strength of protein solutions.     

Dispersion of charged solute in charged micro‐ and nanochannel with reversible sorption

We study dispersion of a charged solute in a charged micro‐ and nanochannel with reversible sorption and derive an analytical solution for mass fraction in the fluid, transport velocity and dispersion coefficient. Electrical double layer formed on the charged surface gives rise to a charge‐dependent solute transport by modifying the transverse distribution of the solute. We discuss the effect of sorption and electrical double layer on solute transport and show that the coupling between sorption and electrical double layer gives rise to charge‐dependent transport even for a thin double layer. However, in this case, it can be reduced to a simple non‐charge‐dependent case by introducing the intrinsic sorption equilibrium constant.     

An experimental and theoretical study on the interaction of PHBA ions and H2O molecules

We studied the dependence of the Raman spectra on the concentration of PHBA aqueous solution under UV laser excitation. Through analyzing the spectra, we conclude that the interaction between PHBA ions and H(2)O molecules is weak. To further explore the problem, we studied the interaction between PHBA ions and H(2)O molecules by virtue of theoretical calculations, DFT-B3PW91/6-31+g(*) was employed. We draw a coincident conclusion with the experiments and dug out the reasonable interaction model that reflects the actual interaction configuration between PHBA ions and H(2)O molecules. We supply a new thinking for studying interactions between solute molecules and solvent molecules, which also can be applied to interactions between solute molecules and other solute molecules in solutions.     

Optimal strategy to model the electrodialytic recovery of a strong electrolyte

In this work, mostly Nernst–Planck derived relationships were used to simulate the electrodialytic recovery of a strong electrolyte, namely sodium chloride. To this end, it was set up a five-step experimental procedure consisting of zero-current leaching, osmosis, and dialysis, electro-osmosis, desalination, current–voltage and validation tests. The contribution of leaching and solute diffusion across the electro-membranes was found to be negligible with respect to the electro-migration. On the contrary, solvent diffusion tended to be important as the solute concentration difference at the membrane sides increased or current density was reduced. The electro-osmosis and desalination tests yielded the water and solute transport numbers.

By performing several limiting current tests at different solute concentrations and feed flow rates using anionic or cationic membranes, it was possible to determine simultaneously the limiting current intensity, the ratio of the differences between the counter-ion transport numbers in the anion- and cation-exchange membranes and solution, the overall resistance of the electro-membranes, the effective membrane surface area, and the solute mass transfer coefficient.

All these process and design parameters allowed the time course of the solute concentration in the concentrating (C) and diluting (D) compartments, as well as the voltage applied to the electrodes, to be reconstructed quite accurately without any further correction factors. The capability of the above parameters to simulate the performance of the electrodialysis (ED) unit was checked by resorting to a few validation tests, that were performed in quite different operating conditions from those used in the training tests, that is by filling tank C with a low feed volume with a low solute concentration and applying a constant current intensity to magnify the effect of electro-osmosis or by changing the current intensity step-wisely to simulate the continuous-mode operation of a multistage ED unit. Finally, a parameter sensitivity analysis made the different contribution of the process and design parameters to be assessed, thus yielding a straightforward procedure for designing or optimising accurately ED desalination units up to a final salt concentration of about 1.7 kmol m⁻³.     

Studies on emulsion liquid membrane extraction of cephalexin

An experimental study on batch extraction of cephalexin using an emulsion liquid membrane system has been reported. The effects of surfactant, carrier and solute concentrations, phase volume ratio, stirring speed, and counterion concentration on the extraction rate were examined. Surfactant, carrier and diluent used were Span-80, Aliquat-336 and n-heptane–kerosene (1:1), respectively. Under the optimised experimental conditions, emulsion swelling was found to be marginal. By maintaining an appropriate pH gradient in the feed and receiving aqueous phase, facilitated transport could be realised. Selective separation of cephalexin from a mixture of 7-aminodeacetoxy cephalosporanic acid (7-ADCA) could be demonstrated in the emulsion liquid membrane system. A mathematical model based on mass transfer across aqueous boundary layer, interfacial chemical reaction and diffusion in the emulsion globule provides a reasonable fit of the experimental solute concentration versus time profiles in the emulsion liquid membrane system.     

Computer simulation study on the concentration distribution of spherical colloids within confined spaces of well‐defined pores

Aside from the virial expansion and density functional methods, theoretical results on the concentration partitioning behavior for charged colloids within cylindrical pores have not been presented so far. With the increase of relative solute size as well as solute concentration, however, the approximate analytic methods have proven to be unreliable. A suitable Monte Carlo simulation, which is proved as a rigorous technique for concentrated colloids, has been applied in the present study. The concentration profiles within the pore representing the effects of solute concentration as well as solution ionic strength are obtained via a stochastic process, from which the partition coefficient is estimated. Previously developed analyses on the linearized Poisson‐Boltzmann (P‐B) equation are employed for the estimation of long‐range electrostatic interaction. Both the singularity method and the analytical solution with series representation properly determine respective interaction energies between pairs of solute particles and between the solute particle and the pore wall. The effect of solute‐solute and solute‐wall interactions associated with repulsive energy is presented on the partitioning of colloids. Simulation results show that the partition coefficient is evidently enhanced when no particle‐wall interaction exists. Hindered diffusion can be predicted by the simplifying assumption of the centerline approximation analogy, where a dependence on the solute concentration becomes greater as the solution ionic strength decreases.     

Dynamical visualization of "coffee stain phenomenon" in droplets of polymer solution via fluorescent microscopy

In the drying process of polymer solution droplets, we propose an experimental procedure for visualizing the solute concentration profile by combining the fluorescent microscopy with the lateral profile observation. We have conducted a dynamical observation of the transport process of the solute polymer toward the edge that causes the "coffee stain phenomenon". We have found that the polymer concentration increases sharply near the edge, while it remains almost constant in the central region until the last stage of drying. The method is useful to understand the dynamical process that occurs near the contact line.     

OPTIMIZING COLLAGEN TRANSPORT THROUGH TRACK-ETCHED NANOPORES

Polymer transport through nanopores is a potentially powerful tool for separation and organization of molecules in biotechnology applications. Our goal is to produce aligned collagen fibrils by mimicking cell-mediated collagen assembly: driving collagen monomers in solution through the aligned nanopores in track-etched membranes followed by fibrillogenesis at the pore exit. We examined type I atelo-collagen monomer transport in neutral, cold solution through polycarbonate track-etched membranes comprising 80-nm-diameter, 6-μm-long pores at 2% areal fraction. Source concentrations of 1.0, 2.8 and 7.0 mg/ml and pressure differentials of 0, 10 and 20 inH(2)O were used. Membrane surfaces were hydrophilized via covalent poly(ethylene-glycol) binding to limit solute-membrane interaction. Collagen transport through the nanopores was a non-intuitive process due to the complex behavior of this associating molecule in semi-dilute solution. Nonetheless, a modified open pore model provided reasonable predictions of transport parameters. Transport rates were concentration- and pressure-dependent, with diffusivities across the membrane in semi-dilute solution two-fold those in dilute solution, possibly via cooperative diffusion or polymer entrainment. The most significant enhancement of collagen transport was accomplished by membrane hydrophilization. The highest concentration transported (5.99±2.58 mg/ml) with the highest monomer flux (2.60±0.49 ×10(3) molecules s(-1) pore(-1)) was observed using 2.8 mg collagen/ml, 10 inH(2)O and hydrophilic membranes.     

Kinetic models of sorption: a theoretical analysis

The kinetics of sorption from a solution onto an adsorbent has been explored theoretically. The general analytical solution was obtained for two cases. It has been shown that at high initial concentration of solute (sorbate) the general equation converts to a pseudo-first-order model and at lower initial concentration of solute it converts to a pseudo-second-order model. In other words, the sorption process obeys pseudo-first-order kinetics at high initial concentration of solute, while it obeys pseudo-second-order kinetics model at lower initial concentration of solute. The theoretical results (derived equations) show that the observed rate constants of pseudo-first-order and pseudo-second-order models are combinations of adsorption and desorption rate constants and also initial concentration of solute. The obtained theoretical equations are used to correlate experimental data for sorption kinetics of some solutes on various sorbents. The predictions of the theory are in excellent agreement with the experimental data.     

Unexpected inverse correlations and cooperativity in ion-pair phase transfer

Liquid/liquid extraction is one of the most widely used separation and purification methods, where a forefront of research is the study of transport mechanisms for solute partitioning and the relationships that these have to solution structure at the phase boundary. To date, organized surface features that include protrusions, water-fingers, and molecular hinges have been reported. Many of these equilibrium studies have focused upon small-molecule transport – yet the extent to which the complexity of the solute, and the competition between different solutes, influence transport mechanisms have not been explored. Here we report molecular dynamics simulations that demonstrate that a metal salt (LiNO₃) can be transported via a protrusion mechanism that is remarkably similar to that reported for H₂O by tri-butyl phosphate (TBP), a process that involves dimeric assemblies. Yet the LiNO₃ out-competes H₂O for a bridging position between the extracting TBP dimer, which in-turn changes the preferred transport pathway of H₂O. Examining the electrolyte concentration dependence on ion-pair transport unexpectedly reveals an inverse correlation with the extracting surfactant concentration. As [LiNO₃] increases, surface adsorbed TBP becomes a limiting reactant in correlation with an increased negative surface charge induced by excess interfacial NO₃⁻, however the rate of transport is enhanced. Within the highly dynamic interfacial environment, we hypothesize that this unique cooperative effect may be due to perturbed surface organization that either decreases the energy of formation of transporting protrusion motifs or makes it easier for these self-assembled species to disengage from the surface.

A forefront of research in separations science (specifically liquid–liquid extraction) is the study of transport mechanisms for solute partitioning, and the relationships that these have to solution structure at the phase boundary.     

低密度溶液中溶剂的重组织性质

分析了溶液的微观结构,结果表明,单个溶质粒子影响其周围的溶剂的结构,溶质粒子间的相互作用也将影响溶剂的结构,溶质对溶剂结构的影响称作溶剂的重组织.提出了二阶重组织能及二阶重组织熵等概念,可以描述在两个溶质粒子发生碰撞时对其周围溶剂结构的影响.利用二元系的集团展开理论,给出了溶剂的一阶、二阶重组织能和重组织熵的表达式.统计热力学分析给出了溶剂-溶剂径向分布函数与溶质和溶剂化学势之间的关系,给出了无限稀溶液模型是否成立的宏观判据.提出的理论可用于低密度的二元溶液.     

Numerical investigation of the solute dispersion in finite-length microchannels with the interphase transport

This paper utilizes a combined approach of the convection-diffusion theory and the moment analysis to conduct a comprehensive investigation of the solute dispersion under the influence of the interphase transport in finitely long inner coated microchannels. The present work has threefold novel contributions: (1) The 2D solute concentration contours in the stationary phase are calculated for the first time to facilitate the understanding the role of the interphase transport in the solute dispersion in the mobile phase. (2) The skewness of the elution curves is investigated to guide the control of solute band shape at the channel outlet. (3) The 2D diffusion-convection theory and zero-dimensional (0D) moment analysis complement each other to present a characterization of the solute dispersion behaviors more comprehensive than that by either of the two methods alone. Parametric studies are performed to clarify the effects of four major parameters related to the interphase transport (i.e., stationary phase Péclet number, interphase transport rate, partition coefficient, and stationary phase thickness) on the solute dispersion characteristics. The results from this study provide a straightforward understanding of the effects of interphase transport on the solute dispersion in finitely long microchannels and are of potential relevance to the design and operation of the microfluidics-based analytical devices.     

Modelling of the pore size distribution of ultrafiltration membranes

A dilute aqueous solution of polydisperse neutral dextrans was used to determine the sieving properties (flux and rejection) of porous polyacrylonitrile membranes. Gel ermeation chromatography was used to measure the solute mole and concentration in the permeate. From these data, rejection coefficients were calculated as a function of solute molecular size. A mathematical model was then developed to relate the flux and solute rejection to pore size distribution and the total number of pores, based upon the assumption that solute rejection was the result of purely geometric considerations. As a first approximation, a solute molecule was considered either too large to enter a membrane pore, or if it entered, its concentration in the permeate from that pore, as well as the solvent flux through the pore, were not affected. This model also considered the effects of steric hindrance and hydrodynamic lag on the convection of solute through a membrane. The shape and sharpness of pore size distributions were found to be useful in comparisons of ultrafiltration membranes.     

Spin amplification in solution magnetic resonance using radiation damping

The sensitive detection of dilute solute spins is critical to biomolecular NMR. In this work, a spin amplifier for detecting dilute solute magnetization is developed using the radiation damping interaction in solution magnetic resonance. The evolution of the solvent magnetization, initially placed along the unstable -z direction, is triggered by the radiation damping field generated by the dilute solute magnetization. As long as the radiation damping field generated by the solute is larger than the corresponding thermal noise field generated by the sample coil, the solute magnetization can effectively trigger the evolution of the water magnetization under radiation damping. The coupling between the solute and solvent magnetizations via the radiation damping field can be further improved through a novel bipolar gradient scheme, which allows solute spins with chemical shift differences much greater than the effective radiation damping field strength to affect the solvent magnetizations more efficiently. Experiments performed on an aqueous acetone solution indicate that solute concentrations on the order of 10(-5) that of the solvent concentration can be readily detected using this spin amplifier.     

Influence of protein–protein interactions on bulk mass transport during ultrafiltration

Bulk mass transfer limitations can have a significant effect on the flux and selectivity during membrane ultrafiltration. Most previous studies of these phenomena have employed the simple stagnant film analysis, but this model is unable to account for the effects of solute–solute interactions on mass transport. We have developed a generalized framework for multicomponent mass transfer that includes both thermodynamic and hydrodynamic (frictional) interactions. Thermodynamic (virial) coefficients were evaluated from osmotic pressure data for albumin (BSA) and immunoglobulins (IgG), while hydrodynamic interaction parameters were determined from filtrate flux data obtained in a stirred cell using fully retentive membranes. The protein concentration profiles in the bulk solution were evaluated by numerical solution of the governing continuity equations incorporating the multicomponent diffusive flux. This model was used to analyze flux and protein transmission data obtained for the filtration of BSA and IgG mixtures through partially permeable membranes. The model accurately predicted the large reduction in flux and BSA transmission upon addition of IgG. These effects were due to the coupling between BSA and IgG mass transfer caused by protein–protein interactions.     

Osmotic phenomena in application for hyperbaric oxygen treatment

Hyperbaric oxygen (HBO) treatment defines the medical procedure when the patient inhales pure oxygen at elevated pressure conditions. Many diseases and all injuries are associated with a lack of oxygen in tissues, known as hypoxia. HBO provides an effective method for fast oxygen delivery in medical practice. The exact mechanism of the oxygen transport under HBO conditions is not fully identified. The objective of this article is to extend the colloid and surface science basis for the oxygen transport in HBO conditions beyond the molecular diffusion transport mechanism. At a pressure in the hyperbaric chamber of two atmospheres, the partial pressure of oxygen in the blood plasma increases 10 times. The sharp increase of oxygen concentration in the blood plasma creates a considerable concentration gradient between the oxygen dissolved in the plasma and in the tissue. The concentration gradient of oxygen as a non-electrolyte solute causes an osmotic flow of blood plasma with dissolved oxygen. In other words, the molecular diffusion transport of oxygen is supplemented by the convective diffusion raised due to the osmotic flow, accelerating the oxygen delivery from blood to tissue. A non steady state equation for non-electrolyte osmosis is solved asymptotically. The solution clearly demonstrates two modes of osmotic flow: normal osmosis, directed from lower to higher solute concentrations, and anomalous osmosis, directed from higher to lower solute concentrations. The fast delivery of oxygen from blood to tissue is explained on the basis of the strong molecular interaction between the oxygen and the tissue, causing an influx of oxygen into the tissue by convective diffusion in the anomalous osmosis process. The transport of the second gas, nitrogen, dissolved in the blood plasma, is also taken into the consideration. As the patient does not inhale nitrogen during HBO treatment, but exhales it along with oxygen and carbon dioxide, the concentration of nitrogen in blood plasma drops and the nitrogen concentration gradient becomes directed from blood to tissue. On the assumption of weak interaction between the inert nitrogen and the human tissue, normal osmosis for the nitrogen transport takes place. Thus, the directions of anomalous osmotic flow caused by the oxygen concentration gradient coincide with the directions of normal osmotic flow, caused by the nitrogen concentration gradient. This leads to the conclusion that the presence of nitrogen in the human body promotes the oxygen delivery under HBO conditions, rendering the overall success of the hyperbaric oxygen treatment procedure.