The task of implementing safer and more efficient processing and transport techniques in the handling of nuclear wastes made up of liquid-solid mixtures provides a challenging and interesting area of research. The radioactive nature of nuclear waste means that it is difficult to perform experimental studies of its transport. In contrast, the use of modelling and simulation techniques can help to elucidate the physics that underpin such flows and provide valuable insights into common problems associated with their transport, as well as assisting in the focusing of experimental research. Two phase solid-liquid wasteforms are commonplace within the nuclear reprocessing industry. Currently, there is waste, e.g., in the form of a solid-liquid slurry in cooling ponds and liquid flows containing suspensions of solid particles feature heavily in the treatment and disposal of this waste. With nuclear waste in the form of solid-liquid sludges it is important to understand the nature of the flow, with particular interest in the settling characteristics of the particulate waste material. Knowledge of the propensity of pipe flows to form solid beds is important in avoiding unwanted blockages in pipelines and pumping systems. In cases where the formation of a solid bed is unavoidable, it is similarly important to know how the modified cross-sectional area of the pipe, due to the presence of a bed, will affect particle behaviour through the creation of secondary flows effects that are also common to square duct flows. A greater understanding of particle deposition in square ducts and pipes of circular cross-section is also of significant and broad industrial relevance, with flows containing particulates prevalent throughout the nuclear, pharmaceutical, chemical, mining and agricultural industries. A greater understanding of particle behaviour in square ducts and circular pipes with variable bed height is the focus of this current work. The more computationally expensive but accurate technique of large eddy simulation (LES) is compared against the current industrial standard technique of Reynolds-averaged Navier-Stokes (RANS) modelling to ascertain how each can be best utilised to understand and predict the mobilisation and transport of nuclear waste sludges. Both approaches are coupled with a Lagrangian particle tracking (LPT) technique and have been applied to examine particle dispersion and deposition behaviour across a range of Reynolds numbers in square duct flows. Single-phase predictions are found to be in good agreement with the available experimental data. LES and RANS results are in agreement over particle deposition rate, although disagree on the final locations of deposited particles. The RANS based work is further extended to consider particle deposition in circular pipes with variable bed height ( B h ). Average particle distance from the nearest wall for spherical particles with sizes ranging from 5–500 μm is monitored in pipes of circular cross-section with bed heights = 0, 0.25 and 0.5 of the pipe diameter. The particle deposition rate is compared over particle sizes and for all values of B h , with the implications for sludge transport in practical situations commented upon. The presence of an increasing B h is found to increase particle deposition for smaller particles. The presence of a bed is found to have little, if any, effect on larger, gravity dominated, particles.