Mass transfer modeling in slow-release dissolution and in reactive extraction using experimental verification

Abstract

In this thesis, models related to mass transfer operations were studied in two cases. One study case was the dissolution of potassium chloride (KCl) particles in water, and another study case was the reactive solvent extraction of metal ions from aqueous solution into an organic droplet. In these study cases, the common point was that mass transport takes place over a phase boundary. However, the system structure and the hydrodynamic behavior of the interfaces are different. These differences are reflected in the mass transfer models. In the dissolution of KCl particles, the system is a suspension, and the measured parameters are averages. The phase interface is rigid between the particle and solution. In solvent extraction, the system consists of a single droplet surrounded by a large continuous phase. The interface between the droplet and the continuous phase is dynamic.

The dissolution rate of the KCl particles was controlled by using a suitable coating. Two coating materials were used: native starch and lignin. Native starch is water soluble and has a tendency to form hydrogels. Conversely, lignin is insoluble in neutral water. In addition, experiments with two uncoated KCl particles were performed. Four models were evaluated to find a suitable model to predict the dissolution: (1) a reaction kinetic model, (2) a gel model, (3) an active surface model, and (4) an active surface model assuming diffusion layer thickness is equal to particle radius. Model (1) was able to give acceptable predictions for all particles. For starch-coated particles, dissolution was explained by the gel model (2). For the lignin-coated particles, the active surface model (4) was found to be suitable.

Mass transfer in reactive solvent extraction was studied using single droplet experiments. Cu ions were extracted from the aqueous solution into a droplet where the organic solvent contained an extractant. A new image analysis method was developed to measure droplet concentration, size, and velocity. Using the new analysis method, models of mass transfer were formulated for the droplet formation, droplet rise, and droplet coalescence stages.

For droplet formation, a new empirical model was formulated taking into account the molecular diffusion coefficient, the empirical eddy diffusivity, and an empirical surface mobility parameter. A numerical model was constructed to simulate droplet formation, and the model showed that in this system, the velocity profile in the droplet during formation was non-circulating. The new model was able to better predict the mass transfer during formation when compared with findings from the literature. For mass transfer during the droplet rise, an existing empirical method was modified by using a numerical model where conservation of momentum and the mass transport equation were used to calculate mass transfer between the continuous phase and the droplet. The model predicts mass transfer coefficients and extraction reaction kinetic constants. It was recognized, that in this system, the mass transfer resistance was located at the phase interface.

The effect of droplet coalescence on the mass transfer was studied experimentally by letting two droplets coalesce in a controlled manner. The coalescence process was recorded on video. Based on concentration analysis, it was recognized that mass transfer is not affected by droplet coalescence. In addition, a droplet coalescence process is not affected by mass transfer. A numerical model of a droplet coalescence process was built and validated with experimental results.