The objective of this work was to implement a kinetic model for mineral flotation into the framework of an existing computational fluid dynamics (CFD) code. The open source CFD framework of OpenFOAM was selected for this task, as it allows for the greatest freedom in terms of model implementation. In the course of this work several examples of dispersed two-phase flow were studied. Although, these simulations of bubbly flows are not directly related to the work on flotation, they serve to illustrate the chosen simulation method and, in the case of the stirred tank, lay some ground work for the later application of the flotation model. Two sorts of bubble columns have been simulated and validated with data from various sources. First, a bubble column following Becker et al. was validated against data gathered from in-house experiments. Then, the Deen bubble column was validated using simulation and measurement data from published literature. The investigated stirred tank featured a cylindrical vessel with baffles and a Rushton impeller. This widely used configuration is rather well suited for validation, as there is a large body of literature available. The simulations of both the bubble column cases and the stirred tank fit well to the validation data. The flotation model has been implemented following the example of OpenFOAM's own implementation making use of the concept of object orientation. This leads to a modular and easily extendible design of the flotation model. Finally, the implemented flotation model has been applied to two cases. The first application is an aerated, generic stirred tank, representing mechanical flotation cells. This test case features a well defined geometry and has been extensively studied in several aspects. The second application is a scaled-up version of an industrial flotation apparatus produced by the industrial partner. This apparatus represents a continously operating flotation device in contrast to the first case, which represents a batch process. The simulations demonstrate the feasibility of a combined simulation of the two-phase flow and the flotation kinetics within a flotation apparatus. However, the simulations also reveal an issue related to the different time scales of the flow dynamics and the kinetic process.