CFD modeling for flow and mass transfer in spacer-obstructed membrane feed channels

The effect of spacer geometry on fluid dynamics and mass transfer in feed channels of spiral wound membranes has been investigated. Three-dimensional computational fluid dynamics (CFD) simulations reveal significant influence of spacer geometric parameters such as filament spacing, thickness and flow attack angle on wall shear rates and mass transfer coefficients. The spacers with filaments in axial and transverse direction induce higher shear stresses at the top membrane surface when compared to the bottom; the mass transfer rates are almost equal. The distribution of mass transfer coefficients become uniform when the spacing between axial filaments is increased or transverse filament thickness is decreased. For spacers with filaments inclined to the channel axis, the flow structure depends on spacing and flow attack angle. The fluid follows a zigzag path when spacing is greater while it begins to line-up with the filaments when spacing is reduced or flow attack angle is increased. The flow when aligned with the filaments increases the wall shear stress but confines the region of higher mass transfer coefficient values to a narrower portion. The zigzag flow movement increases these values on a major portion of membrane surface which enhances the mass transfer rates.     

Effect of tin concentration on the electrical properties of ceramic membranes used as separators in electrochemical reactors

This paper deals with the study of different microporous ceramic membranes used as separators in electrochemical reactors to treat the activating solutions coming from the electroless plating of polymers. The main component of these solutions is Sn(IV) in HCl as diluting agent, then, the effect of the complex species formed between Sn⁴⁺ and Cl⁻ ions on the electrical properties of the membranes has been studied.     

Effect of convective channel-to-channel mass flow in a polymer electrolyte fuel cell

The effect of convective channel-to-channel mass flow on the local performance of a polymer electrolyte fuel cell (PEFC) air cathode is determined experimentally by using submillimeter resolved current density distribution measurements in channel and land areas. A special cell is employed, where the two parallel channels of the cathode flow field can be operated at different pressure. For isobaric operation of the channels (Δp = 0 mbar), the lateral current density distribution shows a distinct minimum in the land area between the channels as diffusive mass transport becomes limiting at a higher cell polarization. Toward higher Δp, the local cell performance in the land area improves initially as a result of an improving convective channel-to-channel mass flow. However, as the pressure difference exceeds a value of 10 mbar, no noteworthy additional benefit is observed with further increasing Δp. Under these conditions, the convective mass flow provides an abundant reactant supply in the land area and, since reactant depletion is no longer limiting, the lateral current density distribution is primarily governed by the local ohmic resistance. As a result, the current density exhibits a maximum in the land area, where the local ohmic resistance shows a minimum.     

Effect of porosity on the effective electrical conductivity of different ceramic membranes used as separators in eletrochemical reactors

Different microporous ceramic membranes have been investigated to be used as separators in electrochemical reactors. The effect of porosity on the effective electrical conductivity of the ceramic membranes has been studied. The porosity of the membranes has been modified by changing the manufacturing pressure and by the addition of starch to the alumina–kaolin matrix. In the absence of starch the pore size distribution becomes more uniform with the increase of the manufacturing pressure, and lower porosities and average pore sizes are obtained. On the other hand, the porosity and the average pore size increase with the addition of starch to the alumina–kaolin matrix, but pore size distribution is less uniform and becomes bimodal with two different characteristic pore diameters.

The effective electrical conductivity of the membranes, κ_eff, increases with the decrease of manufacturing pressure and with the increase of starch content. The following correlation between the effective electrical conductivity and the porosity has been obtained: f_c = κ_eff/κ = 0.35 ^1.04, where κ is the electrolyte electrical conductivity.     

Numerical modeling of the Joule heating effect on electrokinetic flow focusing

In electrokinetically driven microfluidic systems, the driving voltage applied during operation tends to induce a Joule heating effect in the buffer solution. This heat source alters the solution's characteristics and changes both the electrical potential field and the velocity field during the transport process. This study performs a series of numerical simulations to investigate the Joule heating effect and analyzes its influence on the electrokinetic focusing performance. The results indicate that the Joule heating effect causes the diffusion coefficient of the sample to increase, the potential distribution to change, and the flow velocity field to adopt a nonuniform profile. These variations are particularly pronounced under tighter focusing conditions and at higher applied electrical intensities. In numerical investigations, it is found that the focused bandwidth broadens because thermal diffusion effect is enhanced by Joule heating. The variation in the potential distribution induces a nonuniform flow field and causes the focused bandwidth to tighten and broaden alternately as a result of the convex and concave velocity flow profiles, respectively. The present results confirm that the Joule heating effect exerts a considerable influence on the electrokinetic focusing ratio.     

Numerical modeling of surface reaction kinetics in electrokinetically actuated microfluidic devices

We outline a comprehensive numerical procedure for modeling of species transport and surface reaction kinetics in electrokinetically actuated microfluidic devices of rectangular cross section. Our results confirm the findings of previous simplified approaches that a concentration wave is created for sufficiently long microreactors. An analytical solution, developed for the wave propagation speed, shows that, when normalizing with the fluid mean velocity, it becomes a function of three parameters comprising the channel aspect ratio, the relative adsorption capacity, and the kinetic equilibrium constant. Our studies also reveal that the reactor geometry idealized as a slit, instead of a rectangular shape, gives rise to the underestimation of the saturation time. The extent of this underestimation increases by increasing the Damkohler number or decreasing the dimensionless Debye–Hückel parameter. Moreover, increasing the values of the Damkohler number, the dimensionless Debye–Hückel parameter, the relative adsorption capacity, and the velocity scale ratio results in lower saturation times.     

Recent developments in on-line electrochemical stripping analysis--an overview of the last 12 years

This paper presents an overview of the field of electrochemical stripping analysis in flow systems covering developments in the last 12 years (since 1998). The review discusses the flow schemes utilized in stripping analysis, techniques for on-line sample pre-treatment, the main pre-concentration and stripping/detection modes, the most important flow-through cell configurations used and the different types of working electrodes. Finally, applications in inorganic and organic analysis are discussed. Special emphasis is given to different novel approaches developed over the last few years that hold some promise for the future such as the use of the lab-on-a valve (LOV) configuration, microfluidic manifolds, flow-probes for remote sensing, environmentally friendly electrode materials and hyphenation with spectroscopic techniques.     

Control of flow rate in supercritical fluid chromatography

Summary Supercritical Fluid Chromatograph was constructed using two pumps and two restrictors. With this system in conjunction with the fused silica column packed with relatively large particles (40 μm), the flow rate was controlled both for isobaric and pressure programmed operations. Application of this system to the determination of molecular weight distribution of polystyrene oligomers was presented.     

The effects of the column pressure drop on retention and efficiency in packed and open tubular supercritical fluid chromatography

The effects of the pressure drop across the column on retention and efficiency in SFC have been studied. Numerical methods are described which enable the prediction of hold-up time and pressure drop in both packed and open tubular columns. Predictions of both hold-up time and pressure drop are in good agreement with experimental data. The density gradient along the column can be calculated using the numerical methods and a procedure is described which enables the calculation of the overall capacity factors of the solutes from the density profile in the column. Significant variations of the capacity factor are observed along the column. The effect of the density gradient along the column on local diffusivity and dispersion is studied. The column efficiency in systems with significant pressure drops is affected by changes in: the linear velocity of the mobile phase; the diffusion coefficients; and the capacity factors of the solutes along the column. The overall efficiency of the chromatographic system can be calculated if, as is the case for open tubular columns, adequate plate height equations are available.     

A numerical study of the assumptions underlying the calculation of the stationary zone mass transfer coefficient in the general plate height model of chromatography in two-dimensional pillar arrays

The present study investigates the validity of one of the key assumptions underlying the general plate height model of chromatography, i.e., the presumed independency of the individual band broadening contributions. More precisely, it is investigated under which conditions the mass transfer inside the stationary zone (e.g., porous pillars) is independent from the axial transport of species outside this zone, and how strongly any such dependency would affect the validity of the general plate height model of chromatography. For this purpose, detailed calculations of the species concentration distribution inside and outside the porous pillars of a computer-mimic of a porous pillar array column have been made. These simulations revealed a clear interplay between the mass transfer inside and outside the pillars, manifesting itself as an asymmetry of the species concentration distribution inside the pillars. The latter is in disagreement with the basic assumption used to calculate the value of the C_s-term of the general plate height model. The asymmetry-effect is largest at low reduced velocities, high retention factors and high intra-pillar diffusion coefficients. Fortunately, these are conditions where the C_s-term is relatively small, which might explain why the general plate height model of chromatography (and based on the symmetry assumption) can represent the band broadening in a porous pillar array within an accuracy on the order of some 1–2%.     

Mathematical modeling of flow and kinetics in a reactor for dilute-acid hydrolysis of cellulose particles

Amathematical model to simulate the dilute-acid hydrolysis process of cellulose particles is presented. In this model, the mass is treated as a mixture of different components. A test case is considered for which transport equations for components are developed and solved together with the momentum equation for the fluid flow. To solve the model equations, a commercially available flow solver was used. All input data were taken from previously published works. For the small static mixer considered as test geometry, the result, in terms of the conversion of the cellulose particles, was reasonable. With input parameters that are relevant to a plant-size reactor, the model can be used to predict the conversion of both cellulose and hemicellulose particles.     

Numerical study of two-dimensional multi-layer spacer designs for minimum drag and maximum mass transfer

Based on the insights gained from previous published works, a series of multi-layer spacer designs for use in spiral wound membrane modules are proposed and evaluated via computational fluid dynamics simulations. The filament diameter to channel height ratio of traditional cylindrical filaments is reduced from 0.6 to 0.4 and 0.3, and one or two layers of elliptical filaments with various attack angles are introduced in the middle region of the channel. The mass transport equations are solved in conjunction with the momentum and continuity equations for a solute with Schmidt number of 600, and the hydraulic Reynolds number is varied from 50 up to 800. Spacer performance is evaluated via a basic permeate processing cost analysis. The proposed designs did not lower processing costs when operating at hydraulic Reynolds numbers above 200, but showed potential for reducing costs in the steady laminar flow regime, at hydraulic Reynolds numbers equal to or less than 200. Implications for design improvements of spacer meshes, such as extra layers of spacer filaments to direct the bulk flow towards the membrane walls, and changes to the filament profiles to reduce form drag are discussed.     

Computational fluid dynamics simulation of the adsorption separation of three components in high performance liquid chromatography

Summary The four stereoisomers of nadolol were successfully separated into three groups (SRS)-nadolol and (SSR)-nadolol, (RRS)-nadolol and (RSR)-nadolol using HPLC. The adsorption equilibrium coefficients, mass transfer coefficients of the three groups and the bed voidage were experimentally determined. The computational fluid dynamics (CFD) simulation of the separation was carried out using FEMLAB, which is application software from MATLAB. The simulation visualized the processes of dispersion and separation occurring inside the column. The curvature of the concentration profiles within the column were observed using the simulation. The simulated chromatogram correctly predicted the peak behavior of the eluted compounds except dispersion was overestimated, which is due to the limitation of the software used.     

Mathematical modeling of the graft reaction between polystyrene and polyethylene

Polystyrene (PS) and polyethylene (PE) are two major components of household plastic waste whose blends are immiscible. Recycling them together is an attractive option that requires a compatibilization process to improve the blend mechanical properties. If a PE/PS copolymer is added or formed in situ, it may act as compatibilizer. The structure and molecular properties of this copolymer are key factors to assure its effectivity as a compatibilizer. In this work, we study the graft copolymerization reaction between polystyrene and polyethylene using the catalytic system composed of AlCl₃ and styrene. We develop a model of this process which considers that PE/PS grafting and PS degradation occur simultaneously. We propose a kinetic mechanism for the whole process and apply the method of moments to solve the mass balance equations. The model is able to calculate average molecular weights as well as the amount of grafted PS. It accurately describes the available experimental data, constituting a valuable tool for simulation and optimization purposes.     

High order accurate,one-sided finite-difference approximations to concentration gradients at the boundaries,for the simulation of electrochemical reaction-diffusion problems in one-dimensional space geometry

Accurate calculation of concentration gradients at the boundaries is crucial in electrochemical kinetic simulations, owing to the frequent occurrence of gradient-dependent boundary conditions, and the importance of the gradient-dependent electric current. By using the information about higher spatial derivatives of the concentrations, contained in the time-dependent, kinetic reaction-diffusion partial differential equation(s) in one-dimensional space geometry, under appropriate assumptions it is possible to increase the accuracy orders of the conventional, one-sided n-point finite-difference formulae for the concentration gradients at the boundaries, without increasing n. In this way a new class of high order accurate gradient approximations is derived, and tested in simulations of potential-step chronoamperometric and current-step chronopotentiometric transients for the Reinert-Berg system. The new formulae possess advantages over the conventional gradient approximations. For example, they allow one to obtain a third order accuracy by using two space points only, or fourth order accuracy by using three points, and yet they yield smaller errors than the conventional four-point, or five-point formulae, respectively. Needing fewer points, for approximating the gradients with a given accuracy, simplifies also the solution of the linear algebraic equations arising from the application of implicit time integration schemes.     

微透析取样-流动注射电化学检测测定表柔比星与牛血清白蛋白体外结合参数

建立了微透析取样-流动注射电化学检测法测定表柔比星与牛血清白蛋白体外结合参数的方法。流动相为pH 3.0的0.1 mol/L H3PO4-NaH2PO4缓冲液(含3.4×10﹣5mol/L Na2EDTA),流速为0.3 mL/min。电化学检测的工作电极为玻碳电极,工作电位为0.52V。表柔比星浓度在5.0×10-5～5.0×10-7 mol/L范围内与峰电流呈良好的线性关系,其相关系数为0.9997,检出限为2.0×10-7mol/L。结合微透析取样,实现了对表柔比星与牛血清白蛋白结合参数的测定。表柔比星与牛血清白蛋白的体外结合符合Scatchard曲线,结合常数和结合位点数分别为2.41×104L/mol和4.02。     

Application of matrix solid-phase dispersion to the determination of amitrole and urazole residues in apples by capillary electrophoresis with electrochemical detection

A new method based on matrix solid-phase dispersion (MSPD) extraction was studied for the extraction of amitrole (3-amino-1,2,4-triazole), and its metabolite urazole (3,5-dihydroxy-1,2,4-triazole), in apple samples. The influence of experimental conditions on the yield of the extraction process and on the efficiency of the cleanup step was evaluated. Determination was carried out by capillary electrophoresis (CE) with electrochemical detection, demonstrating the compatibility between MSPD and CE techniques. The method has been successfully applied to different apple varieties. Recoveries in samples spiked at 1.6 and 1.7 μg g⁻¹ for amitrole and urazole were 88 and 82%, respectively. The limits of detection were 0.4 μg g⁻¹ for both compounds using electrochemical detection.     

Electrochemical copolymerization of pyrrole and 2,2-bithiophene and semiconducting characterization of the resulting copolymer films by electrochemical impedance spectroscopy and photoelectrochemistry

The electrochemical copolymerization of pyrrole and bithiophene was studied at a polymerization potential of 1.1 V for various monomer ratios. The cyclic voltammograms showed that the electrochemical properties of the resulting copolymer films changed gradually from those of polypyrrole to polybithiophene with an increase in concentration of bithiophene in the initial electrolyte. The evidence for copolymer formation is based on the analytical results of electrospray ionization mass spectroscopy, thermoanalysis, and Raman spectroscopy. The results showed that cooligomers and homooligomers were found in the electrolyte after copolymerization. The difference between the morphology of a copolymer of pyrrole and bithiophene and a polymer mixture of polypyrrole and polythiophene was demonstrated by scanning electron microscopy. Electrochemical impedance and photocurrent measurements were carried out in order to achieve information on the semiconducting properties of the homopolymers and copolymers obtained. A model of a very thin layer of polypyrrole formed immediately on the electrode surface covered by a thicker copolymer film was developed to explain the results.Dedicated to Zbigniew Galus on the occasion of his 70^th birthday.