Eliezer Rubin

A theoretical model for bubble formation at an orifice submerged in an inviscid liquid

A new theoretical model for calculating bubble formation at an orifice submerged in an inviscid liquid is presented. Simplified equations of motion for the gas—liquid interface were developed, and together with thermodynamic equations for the gas in the bubble and the chamber below the orifice plate, the instantaneous shape of the bubble during its formation was calculated. In contrast with previous models, the present model is able to determine the instant of detachment as the moment at which the neck of the bubble closes. The present model gives also a more detailed treatment of the flow through the orifice, and is suitable for low as well as high chamber volumes. Calculated results are presented for a wide range of orifice radii (0.0175–0.48 cm), gas flow rates (0.4–100 cm3/sec) and chamber volume (1–5000 cm3), including examples of calculated bubble shapes. The present model is restricted to single bubble formation, but it is able to calculate the critical flow rates and critical chamber volumes which limit this region.

Ion Fractionation by Foam

Abstract Ionic charge and size of the species present govern the selectivity of surface adsorption of counterions in foam fractionation processes. A theory based on the Gouy-Chapman model of the diffuse double layer, with the restriction that the closest approach to the surface is determined by the finite size of the hydrated ions, enables one to predict the distribution factor of each species between a solution of mixed electrolytes and a surface layer, and to calculate the selective adsorption coefficient between two ions. Good agreement was found between the theoretical prediction and experimental data.

Equilibrium shapes and quasi-static formation of bubbles at submerged orifice

Abstract A detailed analysis of the effect of chamber volume, orifice radius, orifice submergence and contact angle on quasi-static formation of bubbles is presented. It is shown, that many aspects of slow bubble formation, involving phenomena leading to various modes of the bubble release, as well as the maximum orifice diameter which sustains a bubble at equilibrium, can be explained on the basis of information on equilibrium shapes and conditions. Scaling rules enabling adoption of results for water to other liquids are also presented.

Foam separation: Surface hydrolysis effects

Abstract Surface hydrolysis enhances the inevitable pH changes in foam separation of anionic surfactants. pH changes, particularly if appreciable, may cause under certain conditions the formation of precipitates and affect foam properties and extent of separation. A theoretical and experimental study of the relation between bulk liquid and collapsed foam pH is presented. The theoretical derivations, based on an assumed constant selectivity coefficient for H + and Na + at the surface, result in a useful expression relating bulk liquid and collapsed foam pH difference to concentrations and experimental conditions. Results of foam separation experiments and available surface hydrolysis data based on surface tension measurements are in good agreement with theory.

Mixing effects in dead end hydrogenation of oils: Sulfite oxidation model

Most industrial hydrogenators are of the dead end type where the gas is bubbled at the bottom of the apparatus, builds up a certain pressure on top of the oil, and is not recirculated. The hydrogen needed by the reaction comes partly from the fraction of the bubbles that is absorbed and partly from the gas space. It was found that sodium sulfite oxidation follows the same mixing pattern, i.e., the highest rate of oxidation always occurred in the upper half of the liquid and correlated strongly with the Reynolds number of the turbine. it is shown that for Reynolds numbers above 600 the optimum impeller position is about two thirds the liquid height measured from the bottom of the vessel. Information is given regarding the variations in selectivity, isomerization and hydrogenation of oils when the speed, relative location and dimensions of the turbine are varied.

Foam Fractionation in a Stripping Column

Abstract Experiments with stripping foam fractionation columns indicate that within the range of variables studied, stripping lengths of 10 to 150 cm have negligible effect on separation. These experimental results cannot be explained adequately by the transfer unit approach. A physical model is proposed wherein the stripping length consists of two mixing regions and a countercurrent flow region in between. Negligible solute transfer is assumed in the countercurrent flow region. This model is applied to explain the experimental data.

Chromatographic Separation by Foam

Abstract The development of a unique chromatographic separation method based on liquid foams is described. The sorption bed is liquid foam moving in a tall vertical column in plug flow manner. The foam is eluted from the top counter-currently to its motion. The mechanism of separation of mixtures is based on adsorption to bubble surface and/or utilizing the foam producing surfactant as a selective carrier. It is shown how this technique can be used for pulse as well as for continuous chromatographic separations. Results of some systematic studies on the effect of two independent variables, foam velocity and elution rate, on separation of mixtures of organic dyes is presented and discussed.

Foam Chromatography: Recent Developments

Foam chromatography is a continuous Chromatographic separation technique in which liquid foam, moving in plug-flow upwards in a vertical column, is used as a sorbent. The eluent is a solution (below the CMC) of the foam-stabilizing surfactant. In this paper we present the results of a study of the parameters that control the operation of a foam chromatography system. The capacity of the system for complete separation of binary mixtures is determined by foam velocity, elution rate, the distance between the injection point of solutes and the bottom of the foam-column (“damper zone”)‚ and to a lesser extent by the distance between the injection points of eluent and solutes (“elution zone”). The interpretation of these results gives a better understanding of the mechanism of separation, and may lead to an efficient design of foam chromatography systems.