In the past 5 years, membrane ultrafiltration has gained increasing prominence as a simple and convenient process for concentrating, purifying, and fractionating solutions of moderate-to-high molecular weight solutes and colloids, and for purifying water and other solvents containing such solutes. The emergence of this new molecular separation technique for both laboratory and industrial applications is almost entirely attributable to the development of a family of uniquely structured polymeric membranes which display extraordinarily high hydraulic permeabilities coupled with the capacity to retain even quite small solute molecules.

Solute polarization and cake formation in membrane ultrafiltration: causes, consequences, and control techniques

There is growing concern about the transfer of methane originating from water bodies to the atmosphere. Methane from sediments can reach the atmosphere directly via bubbles or indirectly via vertical turbulent transport. This work quantifies methane gas bubble dissolution using a combination of bubble modeling and acoustic observations of rising bubbles to determine what fraction of the methane transported by bubbles will reach the atmosphere. The bubble model predicts the evolving bubble size, gas composition, and rise distance and is suitable for almost all aquatic environments. The model was validated using methane and argon bubble dissolution measurements obtained from the literature for deep, oxic, saline water with excellent results. Methane bubbles from within the hydrate stability zone (typically below ∼500 m water depth in the ocean) are believed to form an outer hydrate rim. To explain the subsequent slow dissolution, a model calibration was performed using bubble dissolution data from the literature measured within the hydrate stability zone. The calibrated model explains the impressively tall flares (>1300 m) observed in the hydrate stability zone of the Black Sea. This study suggests that only a small amount of methane reaches the surface at active seep sites in the Black Sea, and this only from very shallow water areas (<100 m). Clearly, the Black Sea and the ocean are rather effective barriers against the transfer of bubble methane to the atmosphere, although substantial amounts of methane may reach the surface in shallow lakes and reservoirs.

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Fate of rising methane bubbles in stratified waters: How much methane reaches the atmosphere?

The internal circulation and the shape of water drops falling at terminal velocity in air of 20°C at sea level pressure, and nearly water saturated, were studied by means of a wind tunnel. Drops with an equivalent radius a0 smaller than 140 um had within the experimental error no detectable deformation from spherical shape. Drops of sizes 140 μm ≤ a0 ≤ 500 μm were slightly deformed into an oblate spheroid. The deviation of these drops from spherical shape was found to be in fair agreement with that theoretically predicted by Imai (1950) and others. The deformation of drops of sizes 0.5 mm < a0 < 4.5 mm was found to be linearly related to the drop size. Such a linear relationship is predicted by the semi-empirical calculations of Savic (1953).



By means of a tracer technique it was established that water drops falling at terminal velocity in air have a well developed internal circulation. The flow pattern inside a drop was found to be consistent with the flow pattern of the air around the drop and that predicted theoretically by Hadamard (1911) and by Hamielec and Johnson (1962). The surface velocity at the equator of a drop was found to be about 1/100 of the drop's terminal velocity. The experimentally determined internal velocities were compared with those predicted theoretically by McDonald (1954) from boundary layer theory and by Hadamard (1911) based on Stokes flow.

A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air

The synthesis of cost optimal heat exchanger networks. An industrial review of the state of the art

Combustion of droplets of liquid fuels: A review

The absorption rates of carbon dioxide, ethylene, and butene from single rising bubble of equivalent diameter 04–20 cm in water have been measured using an apparatus in which the bubble volume change with time of rise can be measured The apparatus uses techniques previously reported but also is suitable for studies of mass transfer without and with chemical reaction at higher pressures (up to 4 atmospheres) The results have been compared with theoretical equations for rate of gas solution at the frontal surface of the bubble based upon potential flow theory and Higbie theory



The data are assessed together with those of others to show that they can be correlated well by



This equation is valid for bubbles of equivalent diameter 06 < d < 40 cm and within the range



500 < NRe < 20,000



On a mesure les vitesses d'absorption de l'anhydride carbonique, de l'ethylene et du butene a partir d'une simple bulle de diametre equivalent a 04–20 centimetres qui s'elevait dans l'eau; on a utilise a cette fin un appareil ou l'on pouvait mesurer le changement de volume de la bulle avec le temps d'elevation et qui permettait, tout en utilisant des methodes deja connueg, d'etudier le transfert de masse avec ou sans reaction chimique a des pressions plus elevees (allant jusqu'a 4 atmospheres) On a compare les resultats obtenus avec ceux des equations theoriques utilisees pour mesurer la vitesse d'une solution d'un gaz a la surface frontale d'une bulle en se basant sur les theories de l'ecoulement potentiel et de Higbie On a evalue les resultats en meme temps que ceux que d'autres ont obtenus pour demontrer qu'on peut les decrire et etablir une correlation entre eux au moyen de l'equation



NSk=113 Npe(de/045+02de)1/2



laquelle est valide pour des bulles de diametres equivalents a 06 < d, < 40 centimetres et dans l'echelle correspondante a



500 < NRe < 20,000

Mass transfer from a single rising bubble

Numerical solution of the Navier‐Stokes equation for flow past spheres: Part II. Viscous flow around circulating spheres of low viscosity

A model has been developed for the preparation of mass transfer by forced convection inside drops for mass transfer with and without simultaneous first-order chemical reaction.



Solutions of the forced convection equation have been obtained using finite difference methods for Reynolds number and viscosity ratio ranges of 0 ≤ Re ≤ 90 and 0 ≤ μ1/μo ≤ ∞, respectively. The effect of circulation rate inside the drop on the mass transfer rate has also been studied.



The model is believed to be generally applicable as evidenced by a comparison with existing analytical models. Thus the results for physical mass transfer approached the Kronig and Brink solution when the viscosity ratio tended towards zero in the Stokes' flow regime. However, as the viscosity ratio increased, the results approached the Newman solution. The model also agreed with those of Johns and Beckmann for physical mass transfer. Similarly, the results for mass transfer with first-order chemical reaction agreed with Dankwerts' generalization of the Kronig and Brink and the Newman models.



On a mis au point un modele pour predire le transfert de masse par convection forcee a l'interieur de gouttes de liquifies, en presence ou en absence d'une reaction chimique simultanee de premier ordre. On a obtenu des solutions de l'equation de convection forcee en utilisant des methodes finies de difference pour des nombres de Reynolds et des rapports de viscosite respectifs de 0 ≤ Re ≤ 90 et 0 ≤ μ1/μo ≤ ∞. On a aussi etudie l'effet produit par la vitesse de circulation a l'interieur des gouttes sur la vitesse du transfert de masse. On croit que le modele a des applications generates comme l'atteste une comparaison avec les modeles analytiques actuels. Aussi, les resultats dans le cas du transfert physique de masse se sont approches de la solution de Kronig et Brink, lorsque le rapport des viscosites tendait vers zero dans le regime d'ecoulement de Stokes; cependant, lorsque le dit rapport augmentait, les resultats se sont averes voisins de ceux de la solution de Newman. Le modele concorde avec ceux de Johns et Beckmann, en ce qui a trait au transfert physique de masse; de meme, les resultats de transfert de masse dans une reaction chimique de premier ordre s'accordent avec la generalisation Dankwert de Kronig et Brink et les donnees des modeles de Newman.

A theoretical study of mass transfer with chemical reaction in drops

Reaction accompanied mass transfer from fluid and solid spheres has been studied for creeping flow and a first order reaction.



The results are presented graphically as Sherwood number plotted against Peclet number, with a dimensionless reaction rate factor as a parameter. At high values of the Peclet number the results approach the curves for physical mass transfer, while at low Peclet numbers the results may be predicted by the equations for reaction accompanied diffusions.



The results were obtained by Yuge's method and by finite-difference numerical methods. The latter methods had limited ranges of applicability.



On etudie le transfert de masse accompagne d'une reaction du premier ordre pour des spheres solides et fluids en ecoulement tres lent.



Les resultats sont presentes graphiquement, soit: le nombre de Sherwood vs le nombre de Peclet avec, comme parametre, un facteur sans dimension de taux de reaction On peut predire les resultats pour des valeurs faibles de Pe a l'aide d'equations de diffusion accompagnees de reaction alors que pour les nombres de Pe eleves les resultats sont plus semblables a ceux de transfert de masse seul.



Les resultats ont ete obtenus a l'aide des methodes de Yuge et des differences finies bien que ces dernieres ne s'appliquent pas dans toutes les regions.

Reaction accompanied mass transfer from fluid and solid spheres at low reynolds numbers

Rates of mass transfer from water drops into cyclohexanol and from drops of cyclohexanol, isobutanol, and o-toluidine into water were measured. These experimental data were augmented by published results, to cover, at drop Reynolds numbers less than 10, a Peelet number range of 0.01 to 5,000,000 for non-circulating spheres and 700 to 24,000,000 for circulating spheres. Transfer rates, expressed as Sherwood numbers, were in substantial agreement with those predicted from a theoretical model. The contribution of natural convection, inherent in the measurements, but omitted in the model, was approximately accounted for. Data for circulating spheres verified the hypothesis that internal motion affects the external transfer rate. This effect depends on the ratio of continuous to disperse phase viscosity of the system; a four to six-fold enhancement of mass transfer due to internal circulation was found for water drops falling in cyclohexanol.



Les auteurs ont mesure les taux de transfert de masse a partir de gouttes d'eau dans le cyclohexanol et a partir de gouttes de cyclohexanol, d'isobutanol et de o-toluidine dans l'eau. On a ajoute aux resultats experimentaux en puisant a meme des resultats publies pour balayer, a des nombres de Reynold inferieurs a 10 pour les gouttes, un champ correspondant a un nombre de Peclet allant de 0.01 a 5,000,000 pour des spheres ne comportant pas de circulation, et de 700 a 24,000,000 pour des spheres avec circulation. Les taux de transfert, exprimes sous forme de nombres de Sherwood, s'accordent assez bien avec ceux que l'on a predits a partir d'un modele theorique. On a tenu compte, de facon approximative, de l'effet de convection naturelle inherent aux methodes de mesure mais omis dans le modele. Les resultats pour les spheres comportant une circulation interne verifient l'hypothese que cette circulation affecte le taux de transfert a l'exterieur. L'effet note depend du rapport de la viscosite de la phase continue a celle de la phase dispersee; on a trouve un accroissement, par un facteur allant de 4 a 6, du transfert de masse attribuable a la circulation interne pour des gouttes d'eau tombant dans le cyclohexanol.

A. I. Johnson

Papers

Mass transfer from a single rising bubble

Numerical solution of the Navier‐Stokes equation for flow past spheres: Part II. Viscous flow around circulating spheres of low viscosity

A theoretical study of mass transfer with chemical reaction in drops

Reaction accompanied mass transfer from fluid and solid spheres at low reynolds numbers

Mass transfer from fluid and solid spheres at low Reynolds numbers: Part II