Karakterisering en modellering van dispersiesystemen met variabele viscositeit

Multiphase systems are widespread in both natural and industrial processes. They may consist of combinations of liquid, gas or solid phases, that interact with each other through the exchange of momentum, heat and mass. Due to the improved accessibility and continued progress in computational hardware and software, numerical modelling of complex flows has become a powerful tool and an integral part of engineering practice. In most existing studies, researchers tend to focus on a single dominant phenomenon or apply simplifying assumptions. This is particularly the case for breakage and coalescence phenomena, which are of great importance because they alter the overall interfacial area available for mass transfer. Many of these models lack generality, as they rely on several empirical parameters and fitting constants that require calibration. Since they are typically validated for a single geometry and often fail when applied at larger scales, numerous models have been proposed but no broadly accepted consensus has emerged. The overarching goal of this thesis was to characterize and model systems with variable viscosity of the dispersed phase. To achieve this, a comprehensive engineering model based on computational fluid dynamics (CFD) was developed and validated. The model advanced the application of the Euler-Lagrange (EL) framework towards multiphase flow, while including detailed description of the coalescence and breakup of the dispersed phase at various levels of viscosity, as well as additional interconnected phenomena. A key requirement for the model was that it should be as general as possible. This was achieved by minimizing the number of adjustable parameters and validating the model across multiple geometries, scales and process conditions. The developed models were to be validated against a wide range of experimental data. Therefore, in parallel to the model development, a dense set of experimental data was measured. Three model systems (stirred vessels) were used for validation of the simulations. Two geometries (commercially available stirred-tank bioreactors) were employed for gas-liquid (GL) systém - 3.5 L Minifors and 250 mL AMBR vessel. Liquid-liquid (LL) systems were represented by an EasyMax vessel (commercial stirred-tank reactor) with a volume of 300 mL. GL systems are commonly used to carry out biochemical reactions. Such process must be carried out to ensure sufficient mass transfer without causing damage to the living cells or microorganisms. Accordingly, in case of gas bubbles, we compared the bubble size distribution as well as the volumetric mass transfer coefficient at various impeller speeds and fixed gas feed rate. For droplets, the validation was performed primarily in terms of the mean droplet size, measured across a wide range of process conditions. Initially, the EL framework was implemented for GL systems. There, 'pseudo' single-phase EL simulations were conducted for the Minifors vessel. In these simulations, the effect of the daughter distribution function (DDF) on the resulting bubble size distribution (BSD) was examined. For all conditions, the simulations matched the experimental data reasonably well. Subsequently, a general characterization of the system was performed in terms of the volumetric mass transfer coefficient (kLa) and the maximum hydrodynamic stress (τVS) to which the cells could be exposed. To improve the accuracy of the GL simulations, the framework was extended by coupling with the volume of fluid (VOF) method. This allowed to directly model the free surface and consider and evaluate its contribution to the overall mass transfer, which is often overlooked. The model was validated not only in a Minifors vessel but also in a smaller AMBR vessel to broaden its applicability. Again, for both geometries the simulations showed strong agreement with the experimental values - notably, the mean error of the mean bubble size was further lowered from 14 to 8 %. Additionally, we evaluated the influence of individual forces acting on bubbles and their influence on void fraction, interfacial area and kLa. In the next step, the EL-VOF model, fully validated for gas bubbles dispersed in a liquid, was adapted in order to be applicable also for droplets dispersed in water. This required further adjustments to the description of the controlling mechanisms in the breakage and coalescence kernels in order to accurately predict the mean droplet size under various process conditions. The utilization of the VOF method was shown to be crucial as it correctly predicted the deformation of the free surface and the region within the vessel available for droplet recirculation. The model showed agreement with experimental measurements, enabling reliable predictions of the mean drop size as a function of stirring speed and dispersed phase viscosity with an average error of just 13 %. Moreover, the simulations were able to successfully capture the influence of dispersed phase concentration. As an extension of the LL system, the process of spherical crystallization (SC), during which the dispersed phase viscosity increases over time, was studied. Owing to the system's complexity, only experimental investigations were performed to assess the influence of critical process parameters. To elucidate the mechanism of SC and its requirements for successful production of spherical particles, several compounds were employed to investigate the impact of process parameters. It was confirmed that the process is, to some extent, case-specific. Nevertheless, common trends were observed. Due to the miscibility of the solvent and antisolvent, a certain amount of an appropriate surfaktant or polymer was required to stabilize the transient emulsion. Depending on the nature of the solute, the stabilizer may be dissolved either in the solvent or in the antisolvent, with a more robust process achieved when the stabilizer was dissolved in the antisolvent. However, an excessive amount of stabilizer led to adverse effects, which needed to be compensated for by an increased temperature difference between the injection and the antisolvent. Droplet loading (the initial concentration of the crystallizing substance) was identified as another key parameter with a minimum value required for the successful formation of spherical particles. In conclusion, this doctoral research achieved a significant advancement in the mathematical modelling of dispersion systems of variable viscosity in stirred vessels. The final model combined the EL approach with the VOF method to describe free surface deformation. The model was applied for bubbles and droplets in liquid and validated across a wide range of operating conditions, showing promising results. Throughout the validation, the primary differences between the systems and the critical features required for accurate predictions were carefully and systematically investigated and identified. Finally, the experimental results obtained for spherical crystallization may serve as a basis for developing a future model that extends the current EL-VOF framework, which has been validated for GL and LL systems.