Isothermal and non-isothermal water transport in porous membranes. I. The power balance

A quantitative study of water transport through porous, unselective membranes of various types is presented. Effects produced by hydraulic pressure are compared with those due to a transmembrane temperature gradient. p]The quantities directly determined for five types of porous partitions of different structure are: hydraulic permeability, thermoosmotic permeability, activation energies of both these transport processes and thermal pressure. Experiments have been systematically conducted at temperatures from +20°C to +60°C. From the experimental data, thermohydraulic conductivity, thermal conductivity, heat of transport, ratio of conductive to convective heat fluxes and thermodynamic efficiency of the transport process have been calculated. Each of these quantities is expressed in terms of specific physical properties of system's components. p]These findings provide deeper insight in the fundamental physico-chemical aspects of thermodialysis, and open at the same time promising perspectives of practical applications for this process of direct transformation of thermal into mechanical (and electrochemical) energy.     

Transport of gaseous mixtures through membranes

Thermoosmosis of ternary mixtures of oxygen, nitrogen, and carbon dioxide across a porous unglazed membrane has been studied, The thermoosmotic pressure difference, ΔP, created by a temperature difference, ΔT, has been measured at various mean temperatures and pressures. Experimental data have been interpreted in the light of non-equilibrium thermodynamics of irreversible processes and the dusty gas model of Mason. Heats of transport for the mixtures, Q^★, have been estimated from the measured values of pressure difference and temperature difference. It is found that the heat of transport of mixtures is independent of the mean temperature and temperature difference as was found in earlier studies on multicomponent mixtures.     

Temperature polarization effects in thermo-osmosis

Water transport induced by heat flow across cellophane and cellulose acetate membranes has been extensively studied in recent years. In comparing the results obtained by the various authors, remarkable differences emerge among the apparent behaviour of otherwise similar membranes. Discrepancies are so large that in some cases the very existence of this transport phenomenon has been questioned.In this paper, an effect is discussed which appears significantly to affect heat-and-mass-transfer-coupled phenomena. A temperature polarization concept is used as an analogy to concentration polarization in reverse osmosis. This appears to account for most of the discrepancies in the published data. However, there remain differences in the experimental results which cannot be explained solely on the basis of “temperature polarization”. Thus, it appears necessary to perform further experimental investigations on thermo-osmosis through these membranes under well controlled thermal conditions. In this regard, a standard procedure is suggested which should allow determination of true thermo-osmotic transport coefficients, by accounting for thermal polarization effects.A physical interpretation of mass transfer across membranes induced by heat flow is also introduced. This will be further developed in subsequent papers.     

Simultaneous electroosmotic and permeation flows through a Nafion membrane. 1. Aqueous electrolyte solutions

The volume flow through a Nafion membrane originated by the simultaneous action of an electric potential difference and a pressure difference has been measured using aqueous KCl solutions under different experimental conditions. The behavior has been analyzed when both gradients act in the same and in the opposite sense. The results indicate that the simultaneous action of the pressure and potential differences originates a total flow different from the sum of the electroosmotic and permeation flows due to each force acting separately. The application of irreversible thermodynamics, which includes second-order terms, allowed the determination of the phenomenological coefficients. Moreover, from these values, the equivalent pore radius was estimated on the assumption that the membrane is a porous medium filled with an internal solution.     

On the theory of permeation and thermoosmosis

It is shown that by due consideration of the mechanical equilibrium inside the membrane, formulas for membrane processes derived previously (1966) and subject to certain restrictions become perfectly general. These formulas relate membrane properties, such as mechanical and thermoosmotic permeabilities, to transport coefficients which are valid for the interior of the membrane (treated as a binary continuous system) such as diffusion coefficient and thermal diffusion factor. The method used in this general treatment is that of Thermodynamics of Irreversible Processes. As an example, the interrelation between the (mechanical) permeability and the diffusion coefficient is given explicitly.     

Thermoelastic Behaviour of Amorphous Polymers Above and Through the Glass Transition Interval I. Polystyrene

The thermoelastic behaviour of an unfractionated polystyrene was studied in the temperature interval 353–453 K in the regimes of isobaric cooling and of isothermal quasi-adiabatic loading, respectively. The main experimental results can be summarized as follows. 1. In the temperature interval far above the glass transition temperature T_g, both the temperature and volume relaxations of the polystyrene melt after sudden pressure jumps were completely reversible and proved to be simple exponential functions of the time. Therefore, by a straightforward application of Eqs (1) and (2) to the relevant thermoelastic data obtained in a single experimental run one can arrive at the reasonable values of the specific volume, specific heat capacity, thermal diffusivity and heat conductivity of the polymer in the equilibrium melt state. 2. In the temperature interval close to T_g, both the temperature and volume relations of the supercooled polystyrene melt in compression/expansion cycles became markedly asymmetric and non-exponential. The low values of the exponent β in the fractional-exponent Eq. (5) for the volume relaxation suggest a broad spectrum of relaxation times indicating the high degree of coupling between different mechanisms of the molecular motions involved. This revised version was published online in July 2006 with corrections to the Cover Date.     

Salt splitting with radiation grafted PVDF anion-exchange membrane

A radiation grafted poly(vinylidene fluoride) anion-exchange membrane has been formulated and its behaviour is analysed through the splitting of sodium sulphate by electrohydrolysis. Experiments carried out in a two-compartment membrane electrolysis cell, investigated the influence of flow rate, current density and salt concentration on the performance of the membrane. The different flow conditions had a small influence on current efficiencies, while productivity was significantly greater at higher current densities.The new PVDF material gave acceptable selectivity, low electrical resistance and good chemical, thermal and mechanical stability. A comparison with experiments using cation-exchange membranes demonstrated an inferior performance of the anion-exchange PVDF membrane, in terms of current efficiency and transport properties, despite the lower energy requirements.     

Thermo-osmosis of sorbable gases in porous media : Part II. Cascades

The theoretical basis of mixture separation by thermo-osmosis has been developed for two different experimental arrangements. In the first of these two vessels are connected only by a membrane across which a temperature gradient is maintained. Expressions were obtained for the separation factor of binary mixtures in terms of heats of transport, for pressure and composition changes across the membrane, and for determining the heat of transport of each component. In the second arrangement the vessels are connected via the membrane and also by a capillary of appropriate geometry, so that in the steady state there is a constant circulation of each component of the mixture. Expressions have again been derived for the steady state separation factor, and pressure and composition differences for binary mixtures.     

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.     

An investigation of the yield and postyield behavior and corresponding structure of poly(methyl methacrylate)

The mechanical behavior of glassy polymers is time and temperature dependent as evidenced by their viscoelastic and viscoplastic response to loading. The behavior is also known to depend strongly on the prior history of the material, changing with time and temperature without chemical intervention. In this investigation, we examine the effects of this process of physical aging on the yield and postyield behavior and corresponding evolution in the structural state of glassy polymers. This has been achieved through a systematic program of uniaxial, isothermal, constant strain–rate tests on poly(methyl methacrylate) (PMMA) specimens of different thermal histories and by performing positron annihilation lifetime spectroscopy (PALS) measurements prior to and after mechanical deformation. PALS is an indicator of the free volume content, probing size and density of free volume sites and can be considered to be a measurement of structural state. The results of the mechanical tests show that aging acts to increase both the initial yield stress and the amount of strain softening which occurs subsequent to yield. Moreover, the amount of strain softening was found to be independent of strain rate indicating that softening is related to an evolution in structure as opposed to deformation kinetics. Furthermore, after sufficient inelastic straining, the initial thermal history is completely erased as evidenced by identical values of flow stress following strain softening, for both annealed and quenched polymer. Strong confirmation of the structural state or free volume related nature of the strain softening process is obtained by our companion PALS measurements. PALS detects an increase in the size of free volume sites following inelastic deformation and finds the initially annealed and quenched specimens to posses the same post-deformation distribution. The size of sites is found to evolve steadily with inelastic strain until it attains a steady-state value. This evolution of free volume with strain follows the observed softening of the flow stress to a steady-state value. These results provide experimental evidence that an increase in free volume with inelastic straining accompanies the strain softening phenomenon in glassy polymers and that strain softening is indeed a de-aging process. Based on our experimental results a mechanistically based constitutive model has been formulated to describe the effects of thermal history on the yield and postyield deformation behavior of glassy polymers up to moderate strains. The model is found to successfully capture the effects of physical aging, strain softening, strain rate, and temperature on the inelastic behavior of glassy polymers when compared with experimental results. © 1993 John Wiley & Sons, Inc.     

Simultaneous electroosmotic and permeation flows through a Nafion membrane 2. Methanol-water electrolyte solutions

The volume flow of methanol-water potassium chloride solutions through a Nafion membrane originated by the simultaneous action of electric potential and pressure gradients has been measured at different percentages of methanol. Measurements were conducted when both gradients act in the same and in the opposite directions under different experimental conditions. The results indicate that the simultaneous action of the pressure and potential differences originates a total flow different from the sum of the individual electroosmotic and permeation flows due to each force acting separately. The application of the irreversible thermodynamics theory, which includes second-order terms, allowed the study of the influence of the composition of the solutions on the determination of the different phenomenological coefficients.     

On the flow characteristics of highly concentrated oil-in-water emulsions

The laminar flow characteristics of oil-in-water emulsions with oil concentrations greater than 59% by volume have been investigated experimentally. Up to an oil concentration of 65% by volume, the emulsions exhibited power-law non-newtonian behaviour. At a higher oil concentration, of 72.21% by volume, a dramatic change in the flow behaviour of the emulsion was observed. The flow curve, i.e. shear stress vs. shear rate plot on a log-log scale, clearly exhibited the presence of a yield-stress.The rheological data on the emulsions were used to correlate the laminar pipeline transport data on the same emulsions. For power-law emulsions, values of the drop in pipeline pressure could be accurately predicted from simple rheological measurements. For a yield-stress emulsion, the experimental pipeline data deviated from the predicted values especially at low values of shear stress.     

Effect of a resistance-free tank on the resistance to gas transport in high vacuum tube

The expression for the time lag in a cylindrical tube, into which a gas at very low flow rate enters at one end while the other end is connected to a resistance-free accumulation tank, has been derived assuming that the gas transport in the tube is a diffusive process. Assuming a constant diffusion coefficient of the gas in the tube allowed obtaining an analytical expression for the time lag using the concept of linear asymptotes and Laplace transformation of the governing partial differential equation. The obtained expression indicates that if the pressure response is monitored in the tube, the presence of the tank at the end of the tube would lead to a negative time lag in the tube. The time lag becomes more negative as the distance from the tank increases and the volume of the tank increases while the cross-sectional area of the tube decreases.

The comparison of the model with the experimental data obtained in tests with nitrogen in which the pressure response to a step increase in feed pressure of membrane was monitored in the tube at two different distances from the membrane cell, indicates that the error due to resistance to gas transport in the tube on the experimental time lag of tested medium is even greater than that predicted by the model. This is because of the assumption of constant diffusion coefficient in the tube, which does not allow predicting the experimentally observed increase in the slope of the asymptote with the distance from the membrane cell.     

Dielectric analysis of multi-layer structure of nanofiltration membrane in electrolyte solutions: Ion penetrability, selectivity, and influence of pH

A mathematical framework for analysing electrokinetic flow in microchannel networks is outlined. The model is based on conservation of volume and total charge at network junctions, but in contrast to earlier theories also incorporates conservation of ion charge there. The model is applied to mixed pressure-driven/electro-osmotic flows of binary electrolytes through homogeneous microchannels as well as a 4:1:4 contraction-expansion series network. Under conditions of specified volumetric flow rate and ion currents, non-linear steady-state phenomena may arise: when the direction of the net co-ion flux is opposite to the direction of the net volumetric flow, two different fully developed, steady-state flow solutions may be obtained. Model predictions are compared with two-dimensional computational fluid dynamics (CFD) simulations. For systems where two steady states are realisable, the ultimate steady behaviour is shown to depend in part upon the initial state of the system.     

Advanced kinetic tools for the evaluation of decomposition reactions

Summary An advanced kinetic study on the thermal behaviour of pyrotechnic ignition mixtures has been carried out by differential scanning calorimetry using different B/KNO3 mixtures (50:50, 30:70, 20:80) as a model reaction. The experimental conditions applied (isochoric conditions/closed crucibles and isobaric conditions/open crucibles) as well as the composition of the mixtures noticeably influences the relative thermal stabilities of the energetic materials. The kinetic study focused on the prediction of the thermal stability of the different mixtures both in extended temperature ranges and under temperature conditions at which ordinary investigation would be very difficult. Using advanced numerical tools [1], thermal ageing and influence of the complex thermal environment on the heat accumulation conditions were computed. This can be done for any surrounding temperature profile such as isothermal, non-isothermal, stepwise, modulated, shock, adiabatic conditions and additionally for temperature profiles reflecting real atmospheric temperature changes (yearly temperature profiles of different climates with daily minimal and maximal fluctuations). Applications of accurate decomposition kinetics enabled the determination of the time to maximum rate under adiabatic conditions (TMR_ad) with a precision given by the confidence interval of the predictions. This analysis can then be applied for the examination of the effects of the surrounding temperature for safe storage or transportation conditions (e.g. determination of the safe transport or storage temperatures).     

Some properties of electrolyte solutions in nanoconfinement revealed by the measurement of transient filtration potential after pressure switch off

We have demonstrated that with a composite nanoporous ceramic membrane in a batch membrane cell it is technically feasible to switch off the trans-membrane hydrostatic pressure difference within tens of milliseconds. That enabled us to resolve practically the whole time evolution of transient filtration potential. Measurements of the latter have been complemented by measurements of steady-state salt rejection by the composite membrane and by measurements of the streaming potential and hydraulic permeability of membrane supports available separately. A theory has been developed in terms of network thermodynamics for the electrical response of a bilayer membrane to a pressure perturbation. In combination with the results of salt rejection measurements, from the time transients of filtration potential we could determine the ion transport numbers within the nanoporous layer. Besides that, from the dependence of steady-state salt rejection on the trans-membrane volume flow, we have determined the diffusion permeability of and the salt reflection coefficient in the nanoporous layer. This has enabled us to estimate the contributions of Donnan and non-Donnan mechanisms to the rejection of ions by the nanoporous membrane used in this study. It has been unexpectedly found that the Donnan exclusion played only a secondary role. Our hypothesis is that the non-Donnan exclusion of ions from the nanopores might be caused by changes in water properties in nanoconfinement. Proceeding from the results of steady-state filtration experiments with the membrane and the support, we also concluded that the nanoporous layer was imperfection-free and had a quite narrow pore size distribution, which made it a suitable object for fundamental studies of ion transfer mechanisms in nanopores.     

Dependence of thermal diffusion effects in liquids on the physical properties of the dispersing phase

A generalization of the radiation-pressure theory of thermal diffusion in liquids explains the genesis of the forces acting in a condensed phase when heat flows through it. The analytical expressions obtained make it possible to connect such forces originated by the radiation pressure of thermal waves with the transport of matter taking place in solutions or suspensions of particles and also with the ultimate result of this transport, that is, the steady-state concentrations of the dispersed phase in the hot and in the cold regions of the nonisothermal solution. The form in which the theoretical results are laid down lends itself to direct and unambiguous experimental verification. The confrontation with a few data found in the literature lends support to the theory.     

Solute transfer in on-line analytical flow-through dialyzers

Mass transfer in infinite parallel-plate dialyzers with co-flow between sample and detector streams is discussed for three different theoretical models. Analytical solutions with coupled diffusion and membrane transfer equations were obtained for plug flow in both channels. The finite-difference approximation method was used to obtain numerical solutions for a laminar-flow regime. Results obtained with a mixing-cup model under steady-state conditions were also included. With the dimensions typical for analytical dialyzers, there were only small differences between the laminar-flow and plug-flow models. The mixing-cup model predicted higher fluxes through the membrane than the other two models, particularly when the channel heights were increased. The theoretical results were compared with experimental results for dialysis of zinc(II) ions and the flow dependence agreed reasonably well with theory provided that the hydrostatic pressures were equal on both sides, and that stresses which could result in membrane bulging were kept low.     

Selective permeation of CO2 through poly 2-(N,N-dimethyl)aminoethyl methacrylate membrane prepared by plasma-graft polymerization technique

A membrane having an amine moiety was prepared by plasma-grafting 2-(N,N-dimethyl)aminoethyl methacrylate (DAMA) onto a microporous polyethylene substrate. Permselectivity of the membrane for CO₂ over N₂ was achieved in both dry and water swollen conditions. When the CO₂ partial pressure in the feed gas was 0.047 atm, the selectivity of CO₂ over N₂ reached 130 for the highly swollen water containing membrane. This value was found to agree with that obtained with a mobile carrier membrane (supported liquid membrane) using DAMA as the carrier. The effects of several experimental conditions such as degree of grafting, feed partial pressure and temperature on the membrane performance were studied. It was suggested that the membrane acted as a fixed carrier membrane for CO₂ facilitated transport in under the dry condition and acted as a fixed reaction site membrane in the water swollen condition. The carrier transport mechanism is discussed for dry and aqueous membranes.     

Rapid aqueous sample extraction of VOCs: effect of physical parameters

Rapid aqueous sample extraction (RASE) devices were constructed and characterized using m-xylene as a test analyte. Extraction of m-xylene from aqueous samples was studied under many different conditions, independently varying extractor volume, extraction gas flow rate, temperature, pressure, sample volume, and sample concentration. Gas samples were analyzed as controls to determine the non-extraction (transport) component of the analyte pulse width. The extraction of analyte from water to the gas phase took proportionately longer (compared to transport) for RASE apparatus that had a volume greater than 10 ml. An order of magnitude change in RASE volume resulted in larger than an order of magnitude change in extraction time and total analyte pulse width. The flow rate of the extraction gas had a much larger effect on a RASE apparatus with a volume greater than 10 ml. For these large extractors, both extraction time and total analyte pulse width decreased by a factor of 4 for a flow increase from 40 to 120 ml min(-1). There was little change at higher flow rates, or for extractors with smaller volumes. Temperatures below 40 degrees C resulted in large increases in the pulse duration due to broadening during transport. The temperature effect on extraction time was only a factor of 2 over a range from 25 to 85 degrees C. Pressure also had only a relatively small effect, increasing extraction time and total pulse width by a factor of 2 over a range from 12 to 34 PSI. There was no observed change in either extraction time or total pulse width when the sample volume injected varied from 10 to 1000 mul, or over a concentration range from 170 to 17 000 mug l(-1). RASE apparatus were capable of complete extraction of analyte from water in less than 5 s under optimized conditions.