Hyperbolic systems of conservation laws in gravity-driven,particle-laden thin-film flows

Our study focuses on gravity-driven, particle-laden flows that are pertinent to a wide range of industrial and geophysical settings in which transport of suspensions occurs. In the present study we employ a previously derived model by Murisic et al. (Physica D, 240, 2011) that uses the lubrication approximation to describe particle-laden films on an incline. The model consists of a coupled system of hyperbolic conservation laws for the interface position and the particle concentration. While it has been shown that the model compares well quantitatively with experiments, it lacks analysis. The objectives of this paper focus on the study of the Riemann problem for this system of conservation laws and how the results relate to experiments. We investigate the governing system analytically and numerically; the equations exhibit rich mathematical structures, including double-shock wave solutions, rarefaction waves, and singular shocks.