CFD simulations of net-type turbulence promoters in a narrow channel

The most common spacers or turbulence promoters for membrane processes are net-like materials which enhance mass transfer as well as provide passage for feed solutions. The enhanced membrane performance of spacer-filled channels is determined by the fluid flow patterns induced by the spacer filaments. Insight into the effect of spacer characteristics can be obtained by computational fluid dynamics. In this research, the commercial finite volume package FLUENT was used to visualise the flow pattern in a rectangular membrane channel. Three transverse filament arrangements were simulated. The results show that both high shear stress regions and eddies are present in the channel due to the spacer cylinders. The mass transfer enhancement on the wall/membrane surface is directly related to the high shear stress value, velocity fluctuation, and eddy formation. The peak shear stress and velocity fluctuation are repeated after each spacer cylinder, while the eddies are generally found before and after each cylinder. The CFD simulation also suggests that reducing the transverse filament distance will reduce the distance between shear stress peaks and consequently introduce larger shear stress regions near the wall region and increase the number of eddies, which will benefit membrane mass transfer. However, the penalty for this is that energy losses will also be significantly increased. The selection of optimum spacer geometry design involves a trade-off between these competing effects.     

A numerical and experimental study of mass transfer in spacer-filled channels: Effects of spacer geometrical characteristics and Schmidt number

A systematic study is presented on the effect of both Reynolds (Re) and Schmidt (Sc) numbers on Sherwood (Sh) number, for narrow channels with spacers, closely simulating conditions of feed-side channels in spiral-wound modules. Results of direct numerical simulations performed for the three-dimensional geometries resulting from non-woven cylindrical filament (net-type) spacers show the significant influence of spacer geometry on local Sh distributions. These distributions exhibit a tendency to be displaced towards lower values for more sparse spacer geometries, and towards higher values as the angle between crossing filaments is increased. Additionally, the distribution of the local time-averaged mass transfer coefficients is generally similar to the corresponding distribution of shear stresses at the channel walls, with a tendency to exhibit closer similarity with increasing Sc, as one would expect. To validate the results of numerical simulation, a significant amount of mass transfer data is reported for nine different prototype spacer geometries, plus a common commercial spacer, and three Sc numbers in each case. Correlations of average Sh are obtained for each geometry, in terms of Re and Sc numbers; the exponent of Sh dependence on Sc is near 0.4, as is also obtained from the numerical simulations. Moreover, in agreement with the numerical results, the experimental data reveal a similar trend in the dependence of the average Sh number on spacer geometrical characteristics, namely decreasing with increasing ratio L/D (of cell side L over filament diameter D) and increasing with the filaments crossing angle β. A mass transfer correlation is also proposed for the square-cell commercial spacer commonly used in RO/NF modules.     

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.     

Mass transfer examination in electrodialysis using limiting current measurements

The impact of electrodialysis module characteristics on mass transfer was examined using the limiting current method. The current-voltage curves of different electrodialysis modules were measured and limiting currents were determined using the derivative method. The mass transfer coefficients were calculated and the parameters of their dependence on linear flow velocity were estimated. From these the impact of spacer thickness, spacer net type, membrane type, and module geometry were evaluated. It was found that the impact of spacer thickness was almost negligible within the examined range, but a decrease in the mass transfer coefficient could be expected in the case of thicker spacers. By contrast, the spacer net type and type of membrane were found to be very important parameters able to significantly influence the mass transfer. By modifying the module geometry, the mass transfer coefficient could also be altered and, only in this case, the exponential parameter of the dependence was changing. The parameters thus determined may be used to calculate the limiting current in a wide range of operational conditions and may help predict the performance of different electrodialysis module types.     

Axial and radial diffusion coefficients in a liquid chromatography column and bed heterogeneity

The axial and transverse diffusion coefficients of a band of iodine in a chromatographic column were measured optically as a function of time. It was found that the axial diffusion coefficient remains constant even when the edges of the sample band get close to the wall. By contrast, the radial diffusion coefficient decreases progressively with increasing time when the edges of the sample band leave the core region and begin to diffuse inside the wall region. The local axial and transverse diffusion coefficients of the band decrease from the column center toward the wall. Hence, the increase in local height equivalent to a theoretical plate observed in the region close to the wall must be explained by increasing mass transfer resistances and degree of heterogeneity of the bed.     

Enhanced performance for pressure-driven membrane processes: the argument for fluid instabilities

The performance of pressure-driven membrane processes may be significantly improved when unsteady fluid instabilities are superimposed on crossflow. The role of fluid mechanics, in particular unsteady secondary flows resulting from surface roughness, flow pulsations and centrifugal instabilities, coupled to solute mass transfer is discussed with respect to depolarization and defouling of membranes. Various possible mechanisms including wall shear rate and repeated renewal of the mass boundary layer are analyzed. The secondary flow pattern in a spiral crossflow filter has been visualized and shows a uniform velocity field with a steep gradient adjacent to the membrane surface. Unsteady flows of this type have been used with ultrafiltration and microfiltration membranes to show the efficacy of secondary flows. Significant dissipation with repeated renewal of the mass transfer boundary layer due to secondary flows is used to explain the multiple increase in membrane permeation rates.     

The effect of shell side hydrodynamics on the performance of axial flow hollow fibre modules

Fluid flow and mass transfer experiments have been performed on axial flow hollow fibre modules of varying packing density (32 to 76%). Shell-side pressure drop was found to be proportional to (flowrate)ⁿ, where n varied from about 1.1 at high packing density to 1.5 at low packing density, for shellside Reynolds numbers < 350. Assuming an Ergun-type pressure drop relationship it was found that for packing densities < about 50% the inertial (turbulent) losses exceeded the viscous (laminar) losses. Inspection of cross-sections taken from the middle of modules revealed non-uniform fibre packing with regions of high and low packing density. The cross-sections also change along the length of the module. It is inferred that, in addition to axial flow along fibres, there is also a degree of stream splitting which provides transverse flow across fibres as fluid continuously seeks preferential paths through regions of lower packing density. The presence of transverse flow would explain the higher than expected velocity exponent. Mass transfer experiments involving the removal of oxygen from water flowing through the shell to a sweep gas in the fibre lumens produced higher than expected shell-side mass transfer coefficients. The results are correlated within ± 15% by Sh = (0.53 − 0.58φ)Re^0.53Sc^0.33. The exponent on Re is consistent with entry region conditions, caused by repeated stream splitting and transverse flow. Compared with mass transfer predicted for axial flow through a uniformly packed shell the experimental results are up to 2× higher, with the most significant enhancement at the lower packing densities. The implication of this work is that module design requires a more sophisticated approach than the traditional assumption of laminar flow through parallel axial ducts.     

Elasticity and flow properties of actin gels

Actin gels formed by polymerizing monomeric actin have been studied by use of small amplitude oscillatory deformations and steady shear flow. The length of actin filaments within the gel was varied by copolymerization in the presence of the filament-capping protein gelsolin. The results for short filaments are in qualitative agreement with a model for semi-dilute solutions of inter-penetrating rods. Long filaments give rise to additional motions, believed to be flexing of rods. Steady shear viscosities, at high shear rates, are independent of initial filament length. Results are explained as due to breaking of filaments in shear flows.     

Shear-Induced Order in Nematic Polymers

Several nematic side-chain polysiloxanes with the same backbone and the same mesogens but containing various ratios of two spacers having different lengths were prepared. Within this series of homo- and copolymers, the phase behavior changes continuously from purely nematic for the homopolymer containing only the shorter of the two spacers to nematic plus smectic for the homopolymer containing only the longer spacer. The flow behavior determined by in situ deuterium NMR spectroscopy under shear and the anisotropy of the coil conformation measured by small angle neutron scattering exhibit a continuous change as well.     

Mass transfer and fluid flow visualization in packed and fluidized beds by the adsorption method

Mass transfer coefficient (j _D ) between fluid and column wall in liquid packed and fluidized beds of spherical inert particle has been studied experimentally using adsorption method. Experiments were conducted in column 40 mm in diameter for packed and fluidized beds. In all runs mass transfer rates were determined in presence of spherical glass particles 2.06 mm in diameter. This paper introduced adsorption method as very suitable method for studies of mass transfer and for fluid flow visualization. The adsorption method is based on the dynamic adsorption of an organic dye onto a surface covered with a thin layer of a porous adsorbent. Local and average mass transfer coefficients were determinated from the surface color intensity of the foils of silica gel. Correlation j _D = f(Re) was derived using mass transfer coefficients data. The article is published in the original.     

大型液相色谱分离甘露醇和山梨醇的热力学及动力学参数辨识

本文研究了液相色谱分离过程的吸附平衡常数、传质系数参数的估值模型，用色谱技术和以惰性物示踪的扰动应答实验技术测定甘露醇和山梨醇在钙型吸附剂上的吸附相平衡常数和总传质系数以及床层中的轴向扩展系数，结果表明：吸附平衡常数和吸附剂的选择性随温度的升高而下降；液固相间的总传质系数随温度的升高而增大；轴向扩散系数随流速的增大而增大，参数灵敏度分析的结果表明，相平衡关系，尤其是吸附选择性，对色谱分离的影响有较     

Improved spacer design and cost reduction in an electrodialysis system

In electrodialysis using thin membranes and spacers, the compactness of the membrane cell-pairs leads to a small potential drop, and hence to energy saving. The spacer design itself has a great effect on the cost of the plants, since spacers act as turbulence promoters. A careful design, to increase the mass transfer coefficients, can reduce the membrane surface area required for a given application. Limiting current measurements, cell-pair resistance and pressure losses are presented for several thin spacers, for different flow-velocity values and feed water concentrations. It was possible to find an advantageous geometry of the separating mesh leading to substantial savings on investment and operation costs.     

Modélisation théorique d'écoulements pulses de fluides non newtoniens en conduites viscoélastiques poreuses et anisotropes

A theoretical study concerning the pulsatile flow of an inelastic fluid through anisotropic porous viscoelastic pipes is presented. The objective is to investigate the effects of porosity, conicity in pause, anisotropy and viscoelasticity of pipe wall material for a generalized Casson fluid. An implicit difference method is used to solve the equations, and to determine the axial and radial velocity profiles, the pressure, the flow rate and the flow rate filtration distributions, the transverse rotation and the wall axial and radial displacement. This study, considered as a step in the modelling of flow in blood vessels, may also contribute to other important fields such as water desalination or gel filtration.     

Analysis of rheology and wall depletion of microfibrillated cellulose suspension using optical coherence tomography

A rheometric method based on velocity profiling by optical coherence tomography (OCT) was used in the analysis of rheological and boundary layer flow properties of a 0.5% microfibrillated cellulose (MFC) suspension. The suspension showed typical shear thinning behaviour of MFC in the interior part of the tube, but the measured shear viscosities followed interestingly two successive power laws with an identical flow index (exponent) and a different consistency index. This kind of viscous behaviour, which has not been reported earlier for MFC, is likely related to a sudden structural change of the suspension. The near-wall flow showed existence of a slip layer of 2–12 μm thickness depending on the flow rate. Both the velocity profile measurement and the amplitude data obtained with OCT indicated that the slip layer was related to a concentration gradient appearing near the tube wall. Close to the wall the fluid appeared nearly Newtonian with high shear rates, and the viscosity approached almost that of pure water with decreasing distance from the wall. The flow rates given by a simple model that included the measured yield stress, viscous behavior, and slip behavior, was found to give the measured flow rates with a good accuracy.     

Mesoscale Simulation for Polymer Migration in Confined Uniform Shear Flow

The structure and dynamics of confined single polymer chain in a dilute solution, either in equilibrium or at different shear rates in the uniform shear flow fields, were investigated by means of dissipative particle dynamics simulations. The no-slip boundary condition without density fluctuation near the wall was taken into account to mimic the environment of a nanochannel. The dependences of the radius of gyration, especially in three different directions, and the density profile of the chain mass center ...     

Dewetting of liquid filaments in wedge-shaped grooves

The dewetting of liquid filaments in linear grooves of a triangular cross section is studied experimentally and theoretically. Homogeneous filaments of glassy polystyrene (PS) are prepared in triangular grooves in a nonequilibrium state. At elevated temperatures, the molten PS restores its material contact angle with the substrate. Liquid filaments with a convex liquid-vapor interface decay into isolated droplets with a characteristic spacing depending on the wedge geometry, wettability, and filament width. This instability is driven by the interplay of local filament width and Laplace pressure and constitutes a wide class of 1D instabilities that also include the Rayleigh-Plateau instability as a special case. Our results show an accurately exponential buildup of the instability, suggesting that fluctuations have a minor influence in our system.     

Biosorption of Chromium(III) by Biomass of Seaweed Sargassum sp. in a Fixed-Bed Column

This work aimed at modeling chromium biosorption using the biomass of seaweed Sargassum sp. in a fixed-bed column. The mathematical model used was obtained from the mass balance of the component in the liquid phase and in the biosorbent material. The effects of both axial dispersion in the column and the resistance to mass transfer in the solid were considered for the solution of the partial differential equations of the model, using the Galerkin method on finite elements. To represent the equilibrium data of the batch system the Langmuir isotherm were used. The chromium ion adsorption capacity of the seaweed Sargassum sp., at a temperature of 30°C and pH 3.5, was 2.61 mmol/g. The model performance was evaluated from experimental data obtained at 30°C for flow rates of 2, 6 and 8 mL/min. The parameters of the model, mass transfer and axial dispersion coefficients, were adjusted from these experimental data. The model proved adequate to describe chromium biosorption dynamics in fixed-bed columns.     

Convective mass transport in cross-corrugated membrane exchangers

Cross-corrugated triangular ducts provide high mass transfer capabilities in membrane related gas separations. The mixing effect would intensify the convective mass transfer coefficients on membrane surfaces. By modeling transport of water vapor in dry air, in this study, periodic fully developed fluid flow and mass transfer in a cross-corrugated triangular duct is numerically studied. To model the transitional flow in the topology, a validated low Reynolds number k–ω (LKW) turbulence model is employed to account for the turbulence in the flow. The vapor mass fractions, velocity, and turbulent kinetic energy and specific dissipation rate contours are obtained in the three-dimensional complex domain. The friction factors and the segment mean Sherwood numbers are calculated and correlated with Reynolds numbers, for uniform mass fraction boundary conditions. It is found that the transitional flow is represented by a turbulence center, which intensifies and migrates from the upper wall corrugation to the lower wall corrugation with increasing Reynolds numbers.     

Influence of spacer and terminal group lengths on the smectic ordering of cholesterol-containing dimer liquid crystals

The smectic properties of four series of dimer liquid crystals containing cholesteryl and biphenylyl groups were investigated by polarization microscopy, DSC and X-ray diffraction. Compounds that contain the strongly dipolar cyanobiphenylyl group exhibit a smectic layer spacing that is about 1.7 times the length of the molecule. Three series of alkoxybiphenylylcontaining dimers exhibit two other smectic modifications. For short spacers, a smectic layer spacing is observed that is about the same length as the molecule and for long spacers the smectic layer spacing is about half the length of the molecule. In the latter cases the entropy change at the SmA-N* transition is clearly larger than for the compounds with the other smectic modifications. One or two compounds in each alkoxybiphenylyl-containing series, that have similar spacer length and terminal group length and have an odd number of flexible units in the spacer, exhibit only a chiral nematic phase, and no smectic phase.     

Transport dynamics in open microfluidic grooves

In microscopic rectangular grooves various liquid wetting morphologies can be found, depending on the wettability and details of the geometry. When these morphologies are combined with a method to vary the apparent contact angle reversibly, transitions between droplike objects and elongated liquid filaments can be induced. Liquid can thus be transported on demand along the grooves. The dynamics of liquid filaments advancing into grooves as well as receding from grooves has been studied, varying the contact angle using the electrowetting effect. The dynamics of the receding filament is purely capillarity driven and depends only on the contact angle, the viscosity of the liquid, and the geometry of the groove. The length and the dynamics of the advancing filaments, on the other hand, are strongly dependent on the ionic content of the liquid and the applied ac voltage.