The study of the settling behaviour of particles in viscoplastic fluids is closely related to the study of rheology. In this paper, a thorough examination of the flow behaviour of viscoplastic fluids, in the form of aqueous polyacrylamide solutions, has been presented. The results of this study suggest that the experimental fluids exhibit time-dependent flow characteristics, where the apparent viscosity of the solutions depends highly on their shear history. This time dependency has been attributed towards the processes of destruction and rejuvenation in the 'structural network' of the fluids (due to the presence of hydrogen bonding between polyacrylamide and water molecules), as they are subjected to changing rates of shear. A new fluid model was thus developed to capture this flow behaviour. This model, termed as 'semi-viscoplastic', features temporary yield stress characteristics that tend to dissipate once the structural network of the fluid is destroyed due to the application of shear. The time dependency of the fluid viscous parameters becomes apparent in the settling sphere experiment, where it has been demonstrated that a sphere that is following the flow path of another sphere tends to attain a fall velocity that is significantly higher than the preceding sphere. Based on this finding, a new generalised correlation has been developed, through which predictions of the fall velocity of spherical particles settling through viscoplastic fluids, of various shear history, can be made. (c) 2010 Elsevier Ltd. All rights reserved.