Rarefaction-singular shock dynamics for conserved volume gravity driven particle-laden thin film

We employ a recently proposed model [Murisic et. al, JFM 2013] to study a finite-volume, particle-laden thin film flowing under gravity on an incline. For negatively buoyant particles with concentration above a critical value, the similarity solution is of the rarefaction-singular shock type. We investigate the structure in detail and find that the particle/fluid front advances linearly to the leading order with time to the one-third power as predicted by the Huppert solution [Huppert, Nature 1982] for clear fluid (i.e. in the absence of particles). We also explore a deviation from this law when the particle concentration is high. Both results are carried over for the buoyant particles with any concentrations. We conduct several experiments with both buoyant and negatively buoyant particles whose results qualitatively agree with the theoretics.