Modélisation du transport des solutés neutres à travers des membranes de nanofiltration

L'exclusion engendrée par la présence de membranes de nanofiltration est due à la superposition de plusieurs mécanismes. Aussi, il est important de pouvoir distinguer ces différents modes de transports afin de les comprendre et de proposer des modèles adéquats. Cette étude s'attachera uniquement à la compréhension du transport de solutés neutres à travers des membranes de ce type. Trois sucres, le glucose, le saccharose et le raffinose, ont été utilisés pour caractériser deux membranes organiques fournies par la société Osmonics. Ce travail montre qu'un modèle simple, basé sur la diffusion, tenant compte des conditions hydrodynamiques du module, est en accord avec les résultats obtenus au laboratoire mais également trouvés dans la littérature. Une bonne adéquation entre le modèle et l'expérience est ainsi obtenue, à la fois sur des modules plans et tubulaires, pour des écoulements laminaires et turbulents.Although nanofiltration appeared at the end of the 1970s under various names, it was only really recognized as a useful separation process in the 1980s. Nanofiltration membranes are porous media with a mean pore diameter around 1 nanometer. These membranes do not obey the traditional solution-diffusion model given for reverse osmosis or the convection-diffusion model used to describe ultrafiltration. Although the technique has benefited from a fast technological development, the transport mechanisms are still misunderstood and for a particular separation the choice of a nanofiltration membrane remains empirical.The main objective of this work was to understand and to model the transport of neutral solutes through nanofiltration membranes. Neutral solutes were chosen to emphasise geometrical exclusions, to avoid any electrical interactions and to identify the preponderant transport mechanisms through these materials. The experiments were carried out with a laboratory filtration apparatus. The membranes were laid out in a parallel plane osmotic cell, which makes tangential filtration possible. The geometry of the filtration cell involved the choice of two organic membranes supplied as flat sheets: a BQ01 and a MX07 membrane. The filtration area was 86 cm2. The pressure varied from 7 to 30 bars. The temperature was maintained at 20°C whereas tangential velocity in the cell was fixed at 0.45 m×s-1 (the Reynolds number was 3350). As the solutions used were slightly concentrated, the pH remained close to neutral pH. Three sugars were chosen as solutes: glucose, saccharose and raffinose. These molecules have two advantages: they are electrically neutral and they have molecular weights close to the membranes' MWCO, as provided by the manufacturer.First, saccharose was studied on the two membranes with two different concentrations. These experiments showed that the separation of neutral solutes by nanofiltration membranes is due only to a sieving effect. In subsequent experiments a single concentration was used to characterize the retentions of both glucose and raffinose. The results of the filtrations carried out on the three sugars validated the molecular weight cut-off specified by the manufacturer: the MWCO of the BQ01 membrane was estimated to be 1000 Da, and that for the MX07 membrane was 200 estimated as 200 Da.Schematically, the solute transport can be divided into three stages: in the feed, at the feed/membrane interface, and within the membrane material. In the feed, one notes an increase in solute concentration if one approaches the membrane from upstream. This phenomenon, which is general to any selective transport, is called concentration polarization and is described by film theory. This theory stipulates the creation of an antagonistic diffusive flow, from the membrane towards the feed, seeking to restore the concentration balance within the feed solution. The modification of the concentration at the feed/membrane interface leads to the definition of two retention coefficients: a measured value, the observed retention (Robs), and a calculated value, the intrinsic retention (Rm). Steric exclusion based on the size difference between the pore and the solute is set up at the interface. Uncharged solutes can be visualised as rigid spheres and the membranes can be regarded as a bundle of cylindrical, parallel, rigid and right capillaries. Since the elements are rigid and the solutes are subjected to the same geometrical constraints at the entry and at the exit of a pore, the partition coefficients are identical at those two ends. Finally, lying between reverse osmosis and ultrafiltration, transport through nanofiltration membranes is often expressed as the sum of convective and diffusive phenomena. However, the experimental results show that the observed retentions are stable or increase when pressure increases. These observations also highlight the fact that the values of infinite retention are always compatible with values close to 1. These observations corroborate the idea that diffusion is the predominant transport mechanism of neutral species through the studied materials (BQ01, MX07). The transport equation of neutral solutes can then be simplified to its diffusive component. The expression of the intrinsic retention is obtained by using Fick's law, the definition of the retention coefficients and the definition of the partition coefficients:Rm= 1-(1 / 1+Jvα)The geometrical and physicochemical characteristics of the solutes and of the membranes merge into the α parameter.The results found with the theoretical relation were confronted with experimental data derived from film theory (in order to take into account concentration polarization). The simple one-parameter model was successful in correlating the results obtained in this work. The model was also tested with data coming from Combe et al. (1997), who studied filtrations of glucose, saccharose and raffinose in a laminar flow system by ceramic nanofiltration membranes laid out in the shape of tubular module. The results obtained show that the simple model also successfully correlates with the performances of these membranes.With the data obtained in our laboratory as well with the data found in literature, this study shows that a simple one-parameter model, based on the diffusional transport of the solutes within the membrane material, predicts the rejection of neutral solutes by nanofiltration membranes. The simple one-parameter model is able to simulate any filtration carried out by these membranes for different circulation conditions, for diverse geometrical shapes and for various materials

Absorption et désorption du dioxyde de souffre par des gouttes d'eau de fort diamètre en chute.

Cet article concerne l’absorption et la désorption du SO2 par des gouttes d’eau de diamètre supérieur à 1mm en chute libre dans un mélange air-SO2 à faible et moyenne concentrations. Dans ce cas, le transfert résulte du couplage des résistances interne et externe à la goutte. Dans la phase liquide, un modèle local basé sur la vitesse de frottement inter faciale et le diamètre de la goutte permet le calcul du coefficient de transfert interne kl. Le coefficient de transfert externe kg dans la phase gazeuse est déterminé à l’aide d’une expression plus classiqueAfin de valider le modèle, des investigations expérimentales sont menées en absorption et en désorption sur une colonne de 2.3 m de hauteur dans laquelle le temps de séjour des gouttes est de l’ordre de la seconde. Le présent modèle simule fort bien l’ensemble de ces expériences réalisées pour différents diamètres de goutte [2.04 ; 4.31] mm et différentes concentrations [100 ; 2000] ppm. Le modèle proposé est aussi comparé avec succès à des résultats expérimentaux de la littérature à faible et moyenne concentrations pour des temps de contact beaucoup plus grands.Son domaine d’application couvre donc désormais l’absorption et la désorption du SO2 pour des concentrations comprises entre quelques ppm et quelque %.Mass transfer in dispersed media is of interest to fields such as nuclear engineering, process engineering and environmental engineering. It occurs when two phases, not under chemical equilibrium, are in contact. Knowledge of mass transfer mechanisms in the case of gas absorption from and/or into droplets is necessary to understand the scavenging of trace gases in clouds, rain and wet scrubbers. Our studies focus on absorption and desorption phenomena involving free falling water droplets in a mixture of air and gas. For example, acid rain is formed when a drop of rain falls through an atmosphere contaminated with gaseous acid precursors. A similar phenomenon occurs in specific atmospheric scrubbers, where pollution is trapped at the source. In all cases, the transfer of trace gases from the air into the falling droplets is controlled by molecular diffusion and by convection outside and inside the drops.For droplets, falling inside a soluble gas medium, the main transfer resistance is located in the gas phase. A survey of published studies shows that a number of good numerical models exist, as well as experimental correlations for predictions of the mass transfer coefficient in the gas film. For the liquid phase controlled resistance, Saboni (1991) proposed a model based on local scales, interfacial liquid friction velocity and drop diameter. The model was validated experimentally by Amokrane et al. (1994). The experimental study and model validation in the case of sulfur dioxide absorption by water droplets falling through air with a high gas concentration (few %) has been described previously in detail by Amokrane et al. (1994).The purpose of the present article was to extend our previous model to predict SO2 absorption and desorption by droplets (1-5 mm) falling in air with a low gas concentration. In the liquid phase, a model based on local scales, interfacial liquid friction velocity and droplet size diameter was used. In the continuous gas phase a more classical model was applied. To support the model, two types of experiments were carried out. The first type was adapted to measure the absorption of gas by droplets of known diameter. A second set of experiments gave the desorption rate from droplets with an initial concentration of sulfur dioxide falling through SO2 -free air. Absorption occurred during the fall through a 2.3 m long column for various gas concentrations and for various droplet diameters. A sketch of the experimental equipment is presented schematically in Figure 1. It consists of a cylindrical column 2.3 m in height and 0.104 m in diameter. Before each experiment, a gas mixture with the desired SO2 concentration in air, ranging between 100 and 2000 ppm, was introduced into the column. The SO2 concentration was set at the desired value by regulating the volumetric flow rates of sulfur dioxide and air with calibrated rotameters. The gas concentration in the column was measured continuously by a chemical cell analyzer. The air temperature and humidity were continually measured at the top, in the middle and at the bottom of the column. They ranged from 18°C to 20°C and from 40% to 50%, respectively. Droplets were generated using a specific injector consisting of a demineralized water tank at the base of which identical thin needles were placed. In the case of the smallest droplets, seven needles, 300 µm in diameter, were used. For the largest droplets, one needle of about 1 mm was used. The artificial rain was started by exerting an overpressure in the tank and it was stopped by exerting a depression. This device allowed the generation of almost identical water drops at a controlled rate. Droplets fell with zero initial velocity. Their diameters were determined by collecting a known number of droplets and weighing them on a precision balance. The droplets were collected in a special glass cup placed at the bottom of the rain shaft. This collector initially contained a known volume of kerosene. The presence of this organic compound allowed the creation of a film to prevent additional absorption of SO2 during the experiment and natural desorption of sulfur after the experiment. An experiment consisted of dropping 10 to 20 mL of rain. This amount is enough to precisely measure the sulfur concentration.For reversible desorption, experimentation was undertaken directly in a lab atmosphere. For these experiments, the 4.31 mm diameter droplets free fall occurred over 16.3 m. Three intermediate levels were also examined with falling times varying from 0.7 to 2.4 s. The ambient temperature was measured in the surrounding area of both the injector and the collector and the maximum variation was 2°C. Various initial sulfurous acid concentrations were obtained as a result of various contact times of demineralized water with air-SO2 mixtures. Initial concentrations ranged from 0.5 10-3 mol·L-1 to 1.8 10-3 mol·L-1. In this case, the collector initially contained a known volume of hydrogen peroxide to immediately convert sulfurous acid into sulfuric acid. This avoided additional desorption of sulfurous acid during and after the experiments. In this case, the presence of the organic film was not necessary.The results achieved with the theoretical model were compared to the experimental results. The present model was successful in correlating the experimental results carried out for various droplet diameters ranging between 2.04 and 4.31 mm, and gas concentrations ranging between 100 and 2000 ppm. The model also compared successfully with experimental results from the literature in the case of much longer contact times. The applicability of the model thus covers the absorption and desorption of SO2 for concentrations ranging between ppm to a few %

Mass transfer into a spherical bubble

A numerical study has been conducted to investigate the mass transfer inside a spherical bubble at low to moderate Reynolds numbers. The Navier–Stokes and diffusion–convection equations were solved numerically by a finite difference method. The effect of the bubble Schmidt number (over the range 0.1<Scd<5) and of the internal Reynolds number (over the range 0.1<Red<13) on mass transfer is investigated. The results show that the mass transfer is strongly dependent on the Reynolds number and the Schmidt number. From the numerical results, a predictive equation for the Sherwood number in terms of the Schmidt number and the Reynolds number is derived

Assessing the Intrinsic Radiation Efficiency of Tissue Implanted UHF Antennas

Dielectric loss occurring in tissues in close proximity to UHF implanted antennas is an important factor in the performance of medical implant communication systems. Common practice in numerical analysis and testing is to utilize radiation efficiency measures external to the tissue phantom employed. This approach means that radiation efficiency is also dependent on the phantom used and antenna positioning, making it difficult to understand antenna performance and minimize near-field tissue losses. Therefore, an alternative methodology for determining the intrinsic radiation performance of implanted antennas that focuses on assessing structural and near field tissue losses is presented. The new method is independent of the tissue phantom employed and can be used for quantitative comparison of designs across different studies. The intrinsic radiation efficiency of an implant antenna is determined by assessing the power flow within the tissue phantom at a distance of at least λg/2 from the radiating structure. Simulated results are presented for canonical antennas at 403 MHz and 2400 MHz in homogeneous muscle and fat phantoms. These illustrate the dominance of propagating path losses in high-water content tissues such as muscle, whereas nearfield dielectric losses may be more important in low-water tissues such as fat due to the extended reactive near-field