Mathematical models that predict the separation by the dense medium cyclone have been developed by researchers since the 1960's. These models have ranged from simple empirical equations to comprehensive models. A common factor shared by all these models is that they were developed from data that was focused upon a particular range of operating conditions, such as the feed medium density. This restriction limits the models ability to apply to both low-density coal separations and high-density mineral separations. For example, Wood (1990a) developed a comprehensive model focused upon the separation of coal. While this model accounts for a broad range of design and operating conditions, Tuteja (1991) found it could not be applied to high density mineral separations. Likewise, Napier-Munn (1977) developed a comprehensive model that was restricted to diamondiferous ore separations with a constant diameter cyclone. The absence of a model that spans the range of feed medium densities was recognised by Scott (1988), who proposed the pivot phenomenon as a possible solution. However, although this approach showed promise for the pilot plant data, Scott was unable to incorporate both his pilot plant and industrial data into the same model. Therefore, the objective of the present work is to develop a model that applies to both low-density coal separations and high-density mineral separations. The modelling approach taken in this thesis was to- first identify a mathematical description of the separation from the literature. The review concluded that the simplified theoretical description termed the pulp-split function (Schubert and Neesse, 1973) could be applied. This function considers particle settling and remixing due to turbulence to be the rate controlling processes. The pulp-split function has three parameters that describe the cyclone geometry and separation conditions. Of these parameters, one was held constant, with empirical equations being developed to predict the remaining two parameters (the inefficiency parameter and the cut density). As the aim of the thesis was to develop a general model applying to low and high density separations, a database of 83 data sets was compiled for the development of the model. This included 54 data sets from previous researchers and 29 data sets from an experimental program. These data covered a broad range of conditions, with feed medium densities from 1220 kg/m3 to 30 12 kg/m3 and cyclone diameters from 200 mm to 1150 mm. The separations included coal, sulphide ore, iron ore and tracer tests. In addition to developing equations to predict the pulp-split function parameters, models were also developed to predict the feed flowrate, the recovery of medium to the underflow, and the product medium densities. The product medium densities were calculated by predicting the classification of the medium, which was also modelled with the pulp-split function. The importance of viscosity upon the separation was recognised within the model. However, because ferrosilicon and magnetite medium have non-Newtonian characteristics, an estimate of the shear rate is required. This was achieved by fitting viscosity to the pulp-split function, then back-calculating the shear rate. This process suggested that the dominant shear rate is less than 60 s-1, and that the dominant separation location is within the outer half of the cyclone diameter. As viscosity is rarely measured on an industrial operation, its' inclusion into the cyclone model may provide difficulties for the models application. Therefore, to provide a simple and consistent means of estimating the viscosity, the Shi rheological model (Shi and Napier-Munn, 1996a,b) has been fitted to dense medium and can be used to predict the medium viscosity. This enables the model to be applied to the optimisation of existing operations and to the design/development of new operations. These models were validated with nineteen independent industrial data sets from coal, sulphide ore, iron ore and diamondiferous ore operations. The validation demonstrated that the predicted Ep is generally within the 95% confidence interval of the experimental data (except for the diamondiferous ore data). The cut density for mineral separations is also predicted to within the 95% confidence interval of the experimental data, while for coal separations it is predicted to within 50 kg/m3.