This paper presents an extension of the lumped particle model in [1] to include
the effects of particle collisions. The lumped particle model is a flexible framework
for the modeling of particle laden flows, that takes into account fundamental
features, including advection, diffusion and dispersion of the particles. In this paper,
we transform a binary collision model and concepts from kinetic theory into a
collision procedure for the lumped particle framework. We apply this new collision
procedure to investigate numerically the role of particle collisions in the hindered settling
effect. The hindered settling effect is characterized by an increase in the effective
drag coefficient C_{D} that influences each particle in the flow. This coefficient is given by
C_{D} =(1−φ)^{−n}C^{∗}_{D}, where φ is the volume fraction of particles, C^{∗}_{D }is the drag coefficient
for a single particle, and n ≃ 4.67 for creeping flow. We obtain an approximation for
CD/C^{∗}_{D }by calculating the effective work done by collisions, and comparing that to the
work done by the drag force. In our numerical experiments, we observe a minimal
value of n = 3.0. Moreover, by allowing high energy dissipation, an approximation
for the classical value for creeping flow, n = 4.7, is reproduced. We also obtain high
values for n, up to n=6.5, which is consistent with recent physical experiments on the
sedimentation of sand grains.