Modeling of flux decline during crossflow ultrafiltration of colloidal suspensions

Mass transfer during crossflow ultrafiltration is mathematically expressed using the two-dimensional convective–diffusion equation. Numerical simulations showed that mass transfer in crossflow filtration quickly reaches a steady-state for constant boundary conditions. Hence, the unsteady nature of the permeate flux decline must be caused by changes in the hydraulic boundary condition at the membrane surface due to cake formation during filtration. A step-wise pseudo steady-state model was developed to predict the flux decline due to concentration polarization during crossflow ultrafiltration. An iterative algorithm was employed to predict the amount of flux decline for each finite time interval until the true steady-state permeate flux is established. For model verification, crossflow filtration of monodisperse polystyrene latex suspensions ranging from 0.064 to 2.16 μm in diameter was studied under constant transmembrane pressure mode. Besides the crossflow filtration tests, dead-end filtration tests were also carried out to independently determine a model parameter, the specific cake resistance. Another model parameter, the effective diffusion coefficient, is defined as the sum of molecular and shear-induced hydrodynamic diffusion coefficients. The step-wise pseudo steady-state model predictions are in good agreement with experimental results of flux decline during crossflow ultrafiltration of colloidal suspensions. Experimental variations in particle size, feed concentration, and crossflow velocity were also effectively modeled.     

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.     

Finite element analysis as a tool for crossflow membrane filter simulation

Finite element analysis (FEA) is a very powerful tool in analyzing many engineering problems. In this study, FEA was used to simulate the development of concentration polarization in ultrafiltration of protein solutions. A miniature crossflow membrane filter was developed to verify the FEA models. Polysulfone membrane disks (47 mm) were used in this study. Bovine serum albumin (BSA) solutions of different concentrations were pumped across the membrane flow channel. The crossflow velocity of the feed solution was carefully controlled at the laminar region. With the flow velocities within the flow channel estimated by a perturbation solution, the protein concentration on the membrane surface and the mass transfer coefficient were accurately predicted by FEA. This simulation method may provide a useful tool in engineering analysis and design of a membrane filtration process.     

Further studies on solvent extraction with immobilized interfaces in a microporous hydrophobic membrane

Investigations on solvent extraction of acetic acid into xylene or methyl isobuty] ketone by using immobilized interfaces in microporous hydrophobic membranes have now been extended to a number of different membranes with a wide variation in pore size and porosity. Measured intrinsic membrane transfer coefficients of the solute are adequately described by the simple model of unhindered diffusion in tortuous pores developed earlier. Applied pressure difference did not influence the overall solute transfer coefficient as long as it was not close to that required for the breakthrough of aqueous phase into organic phase. Aqueous and organic boundary layer mass transfer coefficients in the flow type test cell have been determined with a known membrane and utilized to predict effectively the overall solute transfer coefficient observed with other membranes.     

Turbulent flow technique for the estimation of oxygen diffusive permeability of membranes for the oxygenation of blood and other cell suspensions

When transport-efficient membrane modules (such as those where the liquid flows outside hollow fibre membranes) or membranes with prolonged resistance to wetting are used for the oxygenation of blood or other cell suspensions, membrane contribution to the overall oxygen transfer resistance into the liquid may become significant. Thus, estimation of membrane diffusive permeability towards relevant gases (e.g., oxygen) is important to develop new membranes and to ensure reproducible commercial membrane performance.

In this paper, we report on a turbulent flow technique for the estimation of the oxygen diffusive permeability of membranes used in outside-flow oxygenators. Water is re-circulated under turbulent flow conditions in a closed-loop from a reservoir to the shell of lab-scale membrane modules. The overall oxygen transfer to water coefficient is estimated at increasing water flow rates from the time the change of dissolved oxygen tension in the stream leaving the water reservoir occurs. Oxygen diffusive permeability is estimated as the reciprocal overall transfer resistance at infinitely high water flow rates, for negligible gas-side oxygen transport resistance. The technique was used to estimate oxygen diffusive permeability of commercial Oxyphan^® polypropylene membranes for blood oxygenation and of two laboratory polypropylene membranes, the one featuring a microporous wall structure with smaller-than-standard pore size, the other featuring an outer thin, dense layer supported by a thick spongy layer. The turbulent flow technique yields oxygen diffusive permeability estimates consistent both with membrane hydraulic permeability towards gaseous nitrogen, membrane wall structure, and with values in literature obtained using a liquid reactive with oxygen, but without the complications associated with reaction and physical transport kinetic characterisation. We conclude that the turbulent flow technique is a useful tool in the development and quality control of membranes for the oxygenation of blood and other cell suspensions.     

Use of intermittent jets to enhance flux in crossflow filtration

This paper deals with the influence of a new flow unsteadiness on the permeate fluxes in crossflow filtration. A pneumatically controlled valve generates intermittent jets from the main flow, causing the formation of large vortices moving downstream along the tubular membrane. The main results of the numerical calculation of such flows are given. The experimental study was carried out by filtering a bentonite suspension through an ultrafiltration mineral membrane. Time evolutions of flux were achieved in steady and unsteady operating conditions. Results concerning the influence and limits of the nozzle to tube diameter ratio and the jet velocities are discussed. The applicability of such an unsteady flow is examined with a view to effects on energy consumption and possible viscosity effects.     

Mathematical modeling of gas separation permeators — for radial crossflow,countercurrent, and cocurrent hollow fiber membrane modules

A new approach to solve the mass transfer problem posed by the permeation process in a hollow fiber permeator is presented and analyzed. The algorithm models the separation offered for a membrane module, for given gas conditions, simulating the permeate and residue composition and the stage cut. The advantage of the ‘succession of states’ approach utilized here is the option of retroactive incorporation of more complex interactions such as permeate pressure buildup, a pressure, composition and temperature dependent permeability. The two dimensional mass transfer in a radial crossflow permeator has been qualitatively discussed in the past, but it has not been modeled in the literature. The countercurrent, cocurrent and crossflow configurations (all single dimensional mass transfer cases) for gas separation have been modeled in literature primarily by numerical integration of the differential equations over the relevant boundary conditions. Incorporation of nonlinearities such as pressure and permeability variations complicate the mathematics considerably for a single dimension, and make their solution almost impossible in two dimensions. This paper proposes an algorithm that simplifies the understanding of the problem posed, in terms of practical parameters (such as stage cut), and analyses the three flow patterns (radial crossflow, countercurrent, and cocurrent) in detail.     

Determination of the surface potential for hollow-fiber membranes by the streaming-potential method

A procedure has been proposed for measuring the surface potential of hollow-fiber membranes by the streaming-potential method under the conditions of a tangential flow of a solution. The zeta-potential and surface charge of nanofiltration hollow-fiber polyacrylonitrile membranes have been measured. The measurements have been performed for membranes with different porosities, which were obtained by partial drying of initial humid membranes. The porosity has been determined from the electrical conductivity of a membrane. An equation has been proposed for calculating the charge transfer by a solution flow in a porous layer. It has been shown that the use of the proposed equation makes it possible to obtain more correct values of the membrane surface potential.     

Chemical reaction and Soret effect on an unsteady MHD heat and mass transfer fluid flow along an infinite vertical plate with radiation and heat absorption

In the current investigation, it is anticipated to examine the influence of heat absorption and radiation on an unsteady transient MHD heat and mass transfer natural convective flow of an optically thin non-Grey Newtonian fluid through an abruptly started infinite vertical porous plate with ramped wall temperature and plate velocity in the presence of Soret and chemical reaction of the first order is solved precisely. Using the similarity variables, the governed PDE's are converted into dimensionless governing equations and they are solved numerically by employing the finite element technique. Numerical calculations and graphs are used to illustrate the important features of the solution on fluid flow velocity, heat, and mass transfer characteristics under different quantities of parametric circumstances entering into the problem. Moreover, we computed the physical variables such as the coefficient of drag force, rate of heat, and mass transfer. The findings indicate that when the thermal radiation parameter increases, the thermal boundary layer becomes thinner. To establish the veracity of our present results, we compared them to previously published research and found substantial concordance.     

Torch Design Modification Using Micro-jets to Suppress Fluid Dynamic Instabilities in Plasma Arc Cutting

Highly constricted plasma arcs are widely used for metal cutting. One important characteristic of the cutting process is the consistency of the cut edge around the perimeter of the workpiece. Cut edge properties, including surface roughness, edge shape and dross formation, are presumed to depend on the local temperature and chemical composition of the cutting arc adjacent to the cut edge. Fluid dynamic instabilities in the arc boundary leading to entrainment of the low temperature ambient gas can have a strong effect on cutting performance. This paper describes the use of micro-jets to suppress fluid dynamic instabilities in the boundary layer of a plasma cutting arc. Previously developed optical diagnostics and analysis methods are used to characterize the arc boundary layer. Multiple nozzle designs have been investigated to quantify the effects of utilizing micro-jet flow around the arc column, and some relationships between nozzle design and cut quality are presented.     

On the gas-separation properties of two-layer porous membranes

The peculiarities of the flows of binary gaseous mixtures through two-layer membranes are investigated at different orientations of the membranes with respect to the flows. The separation properties of the membranes are shown to depend on the membrane orientation and to dramatically decrease when supporting coarse layers are located before the finely disperse active layer with respect to the direction of a gaseous mixture flow through the membrane. The consecutive location of the layers with increasing average pore sizes along the flow direction appears to be more advantageous. The magnitude of the asymmetry effect significantly depends on the parameters that characterize the Knudsen and bulk diffusion and the viscous transfer of a gaseous mixture.     

Prediction of mass transfer coefficient with suction for turbulent flow in cross flow ultrafiltration

Sherwood number relations for the prediction of the mass transfer coefficient for developing concentration boundary layer have been obtained for turbulent flow regime from first principles. The common flow modules, namely, rectangular channel, tubular and radial cross flow are considered. The relationships developed include the effect of suction through the membrane. Relevant relations for the estimation of mass transfer coefficient for cross flow ultrafiltration are formulated. The proposed Sherwood relations are used in conjunction with the osmotic pressure model to predict the permeate flux in osmotic pressure governed ultrafiltration. The simulated results are compared with the experimental data obtained from the literature. A detailed parametric study has been performed to observe the effects of the operating conditions on the filtration performance in terms of the permeate quantity and quality.     

PERVAPORATION PROPERTIES OF PDMS MEMBRANES CURED WITH DIFFERENT CROSS-LINKING REAGENTS FOR ETHANOL CONCENTRATION FROM AQUEOUS SOLUTIONS

Ethanol perm-selective PDMS/PVDF composite membranes were prepared by curing polydimethylsiloxane (PDMS) with various cross-linking reagents,such as tetraethoxylsilane(TEOS),γ-aminopropyltriethoxylsilane(APTEOS), phenyltrimethoxylsilane(PTMOS) and octyltrimethoxylsilane(OTMOS) as well.The cross-linking density and surface properties of the PDMS active layer were adjusted by varying cross-linking reagents.The pervaporation performance of PDMS membranes cured with different cross-linking reagents was inves...     

Effect of anion-exchange membrane surface properties on mechanisms of overlimiting mass transfer

Four effects providing overlimiting current transfer in ion-exchange membrane systems are examined. Two of them are related to water splitting: the appearance of additional current carriers (H+ and OH- ions) and exaltation effect. Two others are due to coupled convection partially destroying the diffusion boundary layer: gravitational convection and electroconvection. Three anion-exchange membranes, which differ in surface morphology and the nature of ion-exchange sites within a surface layer, are examined. The ion transfer across these membranes in NaCl solutions is studied by voltammetry, chronopotentiometry, and pH-metry. By excluding the effects of water splitting and gravitational convection, it is shown that the main mechanism of overlimiting mass transfer in narrow membrane cells at low salt concentrations is electroconvection. The reasons explaining why water splitting suppresses electroconvection are discussed. The scenario of development of potential oscillations with growing current and time is compared with that described theoretically by Rubinstein and Zaltzman.     

Crossflow microfiltration of oily water

Two α-alumina ceramic membranes (0.2 and 0.8 μm pore sizes) and a surface-modified polyacrylonitrile membrane (0.1 μm pore size) were tested with an oily water, containing various concentrations (250–1000 ppm) of heavy crude oil droplets of 1–10 μm diameter. Significant fouling and flux decline were observed. Typical final flux values (at the end of experiments with 2 h of filtration) for membranes at 250 ppm oil in the feed are ≈30–40 kg m⁻² h⁻¹. Increased oil concentrations in the feed decreased the final flux, whereas the crossflow rate, transmembrane pressure, and temperature appeared to have relatively little effect on the final flux. In all cases, the permeate was of very high quality, containing <6 ppm total hydrocarbons. The addition of suspended solids increased the final membrane flux by one order of magnitude. It is thought that the suspended solids adsorb the oil, break up the oil layer, and act as a dynamic or secondary membrane which reduces fouling of the underlying primary membrane. Resistance models were used to characterize the type of fouling that occurs. Both the 0.2 μm and the 0.8 μm ceramic membranes appeared to exhibit internal fouling followed by external fouling, whereas external fouling characterized the behavior of the 0.1 μm polymer membrane from the beginning of filtration. Examination of the external fouling layer showed a very thin hydrophobic oil layer adsorbed to the membrane surface. This oil layer made the membrane surface hydrophobic, as demonstrated by increased water-contact angles. The oil layer proved resistant to removal by hydrodynamic (shear) methods. By extracting the oil layer with tetrachloroethylene, followed by IR analysis, its average thickness at the end of a 2 h experiment under typical conditions was determined to be 60 μm for the 0.2 μm ceramic membrane and 30 μm for the 0.1 μm polymer membrane. These measured amounts of oil associated with the membrane at the end of the experiments are in good agreement with those determined from a simple mass balance, in which it is assumed that all of the oil associated with the permeate collected is retained on or in the membrane, indicating that the tangential flow did not sweep the rejected oil layer to the filter exit.     

Mass transfer mechanism and chemical stability of strongly basic anion-exchange membranes under overlimiting current conditions

The dynamics of changes in overall and partial voltammetric characteristics with respect to chloride and hydroxide ions is studied by the method of rotating membrane disk (RMD) under the conditions of stabilized diffusion layer thickness for the original strongly basic MA-41P and homogeneous AMX membranes and also for the modified heterogeneous MA-41P-M membrane at high current densities. For unmodified anion-exchange membranes at currents exceeding the limiting value, the hydrolysis of fixed ammonium bases produces secondary and ternary amino groups which are catalytically active in the reaction of water molecule dissociation. The hydrolysis of amino groups in the membrane surface layer is the mechanism of degradation of electrochemical characteristics of strongly basic membranes. This results in the increase of transport numbers with respect to hydroxide ions and weakening of mass transfer with respect to salt ions. For the surface-modified heterogeneous anion-exchange membranes, no degradation of electrochemical characteristics is observed. The characteristics of the surface-modified MA-41P-M membrane remain stable: after long-term operation of the energized membrane, the partial currents with respect to hydroxide ions are close to zero and the mass transfer with respect to salt ions is considerably intensified. The dependences of the thickness of the hydrolyzed layer of a strongly basic anion-exchange membrane on the time of its exposure to solutions of high pH are determined. An original method is developed for determination of the hydrolyzed layer thickness for strongly-basic anion-exchange membranes, which is based on the copper ability to form stable complex compounds with weakly basic amino groups of anion-exchange membranes.     

The effect of oscillatory flow on crossflow microfiltration of beer in a tubular mineral membrane system – Membrane fouling resistance decrease and energetic considerations

We have investigated the consequences due to the changes in hydrodynamics above the membrane surface brought about by an oscillatory flow in the crossflow microfiltration (CFMF) of beer on a tubular mineral membrane. Experimental results in oscillatory flow filtration were analysed in terms of membrane resistance to filtration and energy consumption and compared with steady flow filtration. Two types of beers were used: a clarified beer composed of colloids and macromolecular material and a rough beer containing in addition yeast cells. Oscillatory flow was found to decrease membrane fouling resistance (up to 100%) in rough beer filtration in the presence of a yeast cell cake layer on the membrane surface, whereas it has no effect in clarified beer filtration in the presence of membrane clogging. The detrimental effect of transmembrane pressure on membrane resistance (at ΔP>1 bar) has been emphasized in both oscillatory and steady flows. The time-average hydraulic power dissipated by friction in the filtration module, in relation with the absolute value of the time-average flow rate in oscillatory flow, was found to be systematically higher than for steady flow filtration. However, the hydraulic energy per unit volume of permeate in the microfiltration of rough beer under oscillatory flow was close to that in steady flow at a time-average tangential velocity of 3 m/s. By considering the specific energy (per m³ of permeate) related to the kinetic energy applied to fluid in oscillatory and steady flow modes, the system by gas compression in oscillatory flow led to a reduction of specific energy ranging from 15% to 40%. Finally the ratio of hydraulic power consumed in oscillatory and steady flow was compared with a theoretical calculation based on the assumption that the oscillating flow regime is quasi-steady.     

Some hydrodynamic boundary layer influences on mass transfer coefficients

As an initial approach to the quantitative understanding of the importance of various components of intestinal' contents as factors in mass transfer resistance, studies have been performed in diffusion cells containing polydimethylsiloxane membranes under circumstances sensitive to the boundary layers. (1) The effect of temperature change on permeability was measured. Under the conditions of the study, demonstration of a clear transition from membrane control to boundary control with rising temperature proved elusive. (2) When membrane thickness was systematically decreased, a gradual transition from membrane to boundary control was demonstrated, yet practical restrictions of the experimental conditions and system limited the degree to which either membrane or diffusion layers could be manipulated into a rate controlling role. (3) The effect of solution viscosity on mass transfer was also studied. Methylcellulose and sucrose were used as polymeric and low molecular weight viscosity inducing agents respectively. It was readily shown that viscosity has a much greater influence on the flux of a permeant through decreased diffusion coefficients than through increased boundary layer thicknesses, as is predicted by diffusional theories.     

Modeling Transport Asymmetry in Bilayered Ion-Exchange Membranes Interacting with Surface-Active Organic Substances

A model is suggested for the electrical mass transfer in bilayered ion-exchange membranes, which accounts for the layers' structure. The concentration polarization in a bilayered system is analyzed and the extreme concentration variations at the boundary between layers with different selectivities are determined. It is shown that the current characteristics and the diffusion penetrability can go asymmetric following a change in the orientation of a bilayered membrane with respect to the ion flow. The asymmetry of an integral diffusion penetrability coefficient is determined quantitatively for ion-exchange membranes modified with surface-active organic substances. It is shown that the proposed approach is adequate for describing transport phenomena in anisotropic membranes with stable layer characteristics.     

Membrane formation by isothermal precipitation in polyamide-formic acid-water systems II. Precipitation dynamics

An analysis is presented, which describes the isothermal ternary diffusion process encountered in the formation of the aliphatic polyamide membranes such as Nylon-66 by direct immersion-precipitation of a polymeric solution in a nonsolvent bath. A material coordinate is employed to derive the mass transfer equations for the membrane solution. The convective mass transfer in the coagulation bath is taken into account by solving the hydrodynamic boundary layer equations. Diffusion coefficients were measured and used to deduce ternary phenomenological coefficients. The computed results are found to agree with measured precipitation times and with membrane morphologies observed by scanning electron photomicrographs. © 1995 John Wiley & Sons, Inc.