The impact of mass transfer and interfacial expansion rate on droplet size in membrane emulsification processes

In membrane emulsification, especially under conditions where droplets are forming with a narrow droplet size distribution, it is conjectured that the interfacial phenomena are determining the emulsification result. The process parameters of continuous phase flow and dispersed phase flux were analysed from the perspective of how they could be affecting the interfacial tension of the growing droplet. This work first reviews the applicability of current droplet formation models (force balance and spontaneous transformation based (STB)), describes the interfacial transport of surfactant molecules to an expanding oil-water interface, and models the flow of dispersed phase through a pore using MATLAB. The data from these calculations are then applied in a model to predict the final size of the droplets, which includes dynamic effects of mass transfer and expansion rate. The droplet detachment mechanism in membrane emulsification was modelled from the point of view of Gibbs free energy. An interactive finite element program called the surface evolver was used to test the model. A program was written and run in the surface evolver, which allows the user to track the droplet shape as it grows, to identify the point of instability due to free energy, and thus predict the maximum stable volume (MSV) attached to the pore. The final droplet size was found by applying a pressure pinch constraint (PPC), which is based on the division of the surface into two volumes, a droplet and a segment, which remains attached to the pore mouth. The relative size of these two volumes is such that the resulting radii of curvature of the droplet will maintain an equal Laplace pressure across the surface of both volumes. Predicted droplet sizes were compared to experimental data from the literature. It was found that changes in surfactant coverage caused by mass transfer coupled to the expansion rate of the oil-water interface have a significant and predictable effect on the final droplet size in membrane emulsification. The extent of the influence of the dispersed phase flux on dynamic interfacial tension was quantified using a dimensionless parameter, the mass transfer expansion ratio (MER). The MER can be used to predict the effect of increasing the depletion of surfactant on the relative final droplet size in membrane emulsification. This new insight into the role mass transfer and surface expansion play in membrane emulsification allows us to now predict a priori the final droplet size that would form for a particular set of conditions, and can lead to better process design methods in the future

PIV and CFD measurements of internal velocity in a forming drop in a liquid-liquid system

A PIV method has been used to determine the internal motion in an oil drop during formation and to validate a numerical simulation of the drop formation process. The PIV system included a microscope attached to the camera, which gave a focal depth of 50 µm and a possibility to measure the velocity in the centre cross section of the drop. Oil was forced through a capillary with a diameter of 200 µm into a channel with a cross-flowing continuous phase that induced a shear at the interface of the forming drop, which resulted in a rotational motion inside the drop. The angular velocity in the drop reached a maximum after 1/4 of the drop formation time and approached a steady state before drop detachment when a neck was formed above the capillary opening. The velocity of oil out of the capillary was also investigated. A clear dependence on the pressure inside the forming drop was obtained

CFD modelling of drop formation in a liquid-liquid system

The formation of an oil drop from a single capillary in a continuous phase flowing perpendicular to the capillary opening has been studied numerically. The shear stress at the interface of the forming drop, the angular velocity inside the drop and the pressure field around the drop have been determined in a cross section of the drop formation area. The results show a maximum pressure in the continuous phase near the stagnation point and a maximum shear stress in both phases nearer the top of the forming drop. The lowest pressures were found behind the top of the drop, where the surrounding flow starts to separate from the interface of the drop. The shear stress outside the drop causes a drag which, together with the drag originated from the pressure field around the drop, promotes drop detachment

Membrane emulsification modelling: how can we get from characterisation to design?

There has been an increasing interest in a new technique for making emulsions known as membrane emulsification, which uses a microporous membrane operated in cross-flow. The continuous phase is pumped along the membrane and sweeps away dispersed phase droplets forming from pore openings as shown in Fig. 1. The effects ofprocess parameters in membrane emulsification have been studied, especially on a quantitative level. However, the physical mechanisms of droplet formation are still under investigation to better elucidate the roles of operating parameters, and finally model the process. This work reviews current developments and deficiencies in the modelling membrane emulsification processes

Ultrafiltration

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Effects of pore spacing on drop size during cross-flow membrane emulsification—A numerical study

The design and pore distribution of the membrane are important factors in cross-flow membrane emulsification. To determine the effects of hydrodynamics and drop interaction on drop size, drop formation has been studied numerically using computational fluid dynamics (CFD). Oil with a viscosity of 7.0 mPa s was used as the dispersed phase and water was used as the continuous phase. The conditions studied were pore spacing of 10, 15 and 20 times the pore diameter (20 μm) at a highly dispersed phase velocity of 0.18 m/s, and 10 times the pore diameter at a low velocity of 0.019 m/s. In the case of short pore separation and a low dispersed phase velocity, the drop formation process was uniform, resulting in an emulsion with a narrow drop size distribution, and a dispersed phase flux of 500 L/m2 h. At the higher dispersed phase velocity, the shortest pore separation gave a polydispersed emulsion, whereas pore separations of 15 and 20 times the pore diameter gave nearly monodispersed emulsions, and the flux of the dispersed phase reached 3400 L/m2 h

A model for drop size prediction during cross-flow emulsification

The formation of drops is a topic of great interest in a wide variety of engineering applications, such as membrane emulsification. In order to develop an improved force balance model that is capable of predicting the final size of the detached drop, the formation of drops into a cross-flowing continuous phase has been studied with computational fluid dynamics (CFD). The force balance developed takes into account the drop deformation that occurs as the drop approaches detachment. The results given by the model have been compared with CFD simulations, and the drop diameters agree within 10%, except at low wall shear stresses. The model has also been compared with experimental results on drop formation using various membranes, cross-flow velocities and surfactants. The difference between the model and experimental results is mainly due to the adsorption of surfactants onto the drop interface and the shape of the membrane pores

Application of the PIV technique to measurements around and inside a forming drop in a liquid–liquid system

A particle image velocimetry (PIV) method has been developed to measure the velocity field inside and around a forming drop with a final diameter of 1 mm. The system, including a microscope, was used to image silicon oil drops forming in a continuous phase of water and glycerol. Fluorescent particles with a diameter of 1 μm were used as seeding particles. The oil was forced through a 200 μm diameter glass capillary into a laminar cross-flow in a rectangular channel. The velocity field was computed with a double-frame cross-correlation function down to a spatial resolution of 21 × 21 μm. The method can be used to calculate the shear stress induced at the interface by the cross-flow of the continuous phase and the main forces involved in the drop formation process