Impeller-stirred mixing is one of the most important processes employed throughout the chemical, metallurgical and allied industries. The research reported in this thesis is focused on impeller stirred mixing associated with the refining of lead bullion. The aim of this process is to sequentially remove contained impurities such as copper, antimony, silver and bismuth. This occurs in hemispherical vessels, called kettles, where reagents are initially added to the lead bath to form surface dross that contains both the required impurity and a large amount of lead oxide. This dross is then continuously mixed back into the bath to remove the lead oxide and capture more of the required impurity. A key requirement for this process is to obtain and remove dross that contains a high concentration of the impurity. Although this process has been in operation for many years, there is very little known on how the fluid dynamics associated with the mixing process affects final dross content. The aim of this research is to fully investigate the lead refining process using scientific analysis methods that help understand the mixing process and provide design tools which can be used to optimise process conditions. The three methods of analysis used are: (1) Direct readings from a real kettle, (2) Physical modelling (using water), and finally (3) Computational Fluid Dynamics (CFD). The use of physical modelling, exploiting the techniques of similitude, to predict vortex was also validated. An Acoustic Doppler Velocimeter (ADV) probe was used for the velocity measurement at various locations inside the water model and this gave valuable insight about the flow phenomena occurring inside the refining kettle. A particular important finding was that when fluid is stirred above certain rotational speed the vortex depth becomes independent of the Reynolds number of the operation. With regards CFD technology, the Volume of Fluid (VOF) method was used to capture the free surface and the Lagrangian Particle Tracking (LPT) and Algebraic Slip Model (ASM) to simulate the dross phase. Appropriate methods were also used to represent the moving impeller region. Validation of simulation results against experimental data was very encouraging. Computed vortex depth showed the similar trend as observed during the experiments on the physical model. A design strategy was developed that integrates results from both physical and computational modelling to allow optimal process conditions to be predicted at the kettle design stage. The use of this integrated physical and computational modelling methodology successfully helped eliminate surface swirl by introducing baffles to the kettle. The design and introduction of these flow controllers was also validated to ensure that it optimised the dross mixing process and final impurity content in the dross.