In a previous work (Mauret and Renaud, Chern. Engng Sci. 52, 1807-1817), we investigated the limits of applicability of a capillary model based on conduit flow. For the range of non-applicability of the capillary approach, we develop here a model based on flow around submerged objects. From the definition of the drag force related to a consistent expression for the drag coefficient of a particle (sphere or cylinder), the model describes pressure drops in high voidage beds composed of spheres and fibers, both for the linear and non-linear laminar flow regimes. Moreover, this particulate model is based on a novel definition of tortuosity which corresponds to a velocity ratio, whereas capillary tortuosity is viewed as a path length ratio. Particulate tortuosity is a decreasing function of porosity and Reynolds number, as it integrates disturbances in the flow field generated by particles. The theoretical study of the transition between the capillary and particulate models validates the observations made by analyzing experimental data. The particulate model may be useful in many fields of chemical engineering, particularly for describing pressure drops through filtering media and phases of pulp preparation and papermaking.