The interstitial voidage profiles prevailing in static and flowing beds of nearly buoyant granular materials in aqueous solutions are measured directly by scanning with the use of gamma-ray tomography, the contents of a mass-flow hopper and vertical stand-pipe system. In a series of 'start-stop' flow and 'steady-state' flow experiments, horizontal line profiles, and radial profiles of interstitial voidage are produced at different heights within the conical hopper and vertical stand-pipe sections. The voidage profiles obtained within the static beds prior to the onset of discharge are compared with the profiles measured at the same heights during batch discharge of the hopper contents. Furthermore, the plane mean values of the flowing bed voidage are calculated at different heights using the cross-sectional profiles of voidage obtained under the steady discharge condition. The resulting vertical profiles of plane-mean voidage obtained with three different food analogues are found to reveal hitherto unavailable and highly significant new information about the transitions accompanying flow between the packed-bed and settling-suspension states as a function of the mixture discharge rates and the single particle properties, such as particle size, shape, and particle density. The experimental results presented here are subsequently incorporated into simple mean-field models (ignoring interparticle and wall frictional effects) which are used to calculate slip velocities of the particle phase, interstitial pore pressures due to the fluid phase, as well as the observed variation of the discharged solids concentration with the mixture discharge rate. The model predictions are compared with experimental measurements in Faderani et al. (1998, Chem. Engng Sci. 53, 575).