Mathematical model for swelling in a liquid emulsion membrane system

Application of the liquid emulsion membrane (LEM) technology to the industrial scale is hindered by the challenges imposed by stability of the emulsion during the transfer of the solute (pertraction). One of the important factors which leads to the instability is swelling. Emulsion undergoes swelling due to the osmotic gradient across the membrane as well as due to the occlusion of the external phase into the membrane phase; the latter is caused by the hydrodynamic deformation of the membrane globules. In the present work, we have studied swelling of the emulsion phase in a water-in-oil-in-water type LEM system. Nitric acid is the internal aqueous phase and is encapsulated in organic membrane phase composed of DEHPA–kerosene-SPAN80. Demineralised water is used as the external phase. The effect of the composition of the system and the hydrodynamic condition on the rate of swelling has been studied. A mathematical model has been developed to describe the effects of the relevant parameters on swelling of the emulsion. The globules of the emulsion are viewed as having a core-shell structure, based on the visual evidence. The model takes into account both the osmotic and the occlusion modes of swelling and also the leakage of the internal phase. The predictions of the model are found to be in good agreement with the experiments. The model would be useful for evaluating the rate of pertraction of a solute through the membrane–strip combination used in the present study. The study would also be useful for tuning the design and the operating parameters in LEM pertraction to achieve minimum swelling of the emulsion.

Np — [S] — The model presented in this work appears be consistent with all the experimental data on both water/membrane/water system and nitric acid/ membrane/water system under various operating conditions. The model is therefore a fairly good presentation of the actual process. The work has resulted in the following understandings about the LEM system. 1. For the present experiments, core and shell model appears to be appropriate representation of the emulsion globule. 2. The occlusion coefficient is independent of the impeller speed, which is consistent with the decrease in the globule size. 3. The occlusion coefficient increases with the increase in the surfactant concentration. 4. It is observed that between the two swelling mechanisms viz. occlusion and osmotic swelling, the latter dominates the rate. The present study has allowed us to collect the information, which will be useful for estimating the rate of pertraction of a solute through the nitric acid/membrane/solution LEM system with the help of the developed model. The study will also provide data for tuning the design and the operating parameters in LEM pertraction to achieve minimum swelling of the emulsion. More importantly, it also provides an insight into the mechanisms of swelling and their relative importance.