  Experiments of particle-laden inclined film flow [Zhou, Dupuy, Bertozzi, and
Hosoi, Phys. Rev. Lett. 94 (2005)] have displayed different settling behaviors
depending on the particle concentration $\phi$ and angle of inclination
$\theta$, in which particles accumulate on the substrate or near the advancing
contact line, or remain mixed. Zhou et al. presented a lubrication model that
captures the qualitative behavior of the high-$\phi$, high-$\theta$ regime,
characterized by a particle-rich ridge near the contact line, but cannot
explain the other observed settling behaviors. This work presents a model in
which $\phi$ varies through the film depth, unlike Zhou et al.'s model. Average
velocities for the liquid and particulate phases are computed, and the
implications for phase separation are discussed. It is found that the
equilibrium depth profile of $\phi$ is more important than gravitational
settling in the down-slope direction in determining phase separation. The
predicted settling behavior is directly compared with Zhou et al.'s
experimental data.
