This paper examines the relationship between liquid flow rate and liquid holdup in packed beds of particles. The experiments were carried out on a model system consisting of spherical glass beads, but with particle sizes and flow rates consistent with those found in heap leaching. These flow rates are thus very low (superficial flow rates as low as 27 mm/h) and the system is unsaturated, with drops and rivulets being the dominant flow features. This paper shows that this system exhibits quite strong hysteresis, with the holdup depending not only on the current flow rate, but also the flow history. A novel set of measurements is used to demonstrate that the hysteresis is predominantly caused by a change in the number of rivulets within the system as the flow rate is increased, rather than being caused by a change in the shape of the rivulet. This is achieved by scaling both the liquid flux and the liquid holdup by the residual holdup and demonstrating that, when these scaled values are plotted against one another, both arms of the hysteresis collapse onto a single line. A theoretically based model is then derived that accurately describes the behaviour of these systems. (C) 2012 Elsevier Ltd. All rights reserved.