Shock Solutions for High Concentration Particle-Laden Thin Films

Shock Solutions for Particle-Laden Thin Films

We derive a lubrication model describing gravity-driven thin film flow of a suspension of heavy particles in viscous fluid. The main features of this continuum model are an effective mixture viscosity and a particle settling velocity, both depending on particle concentration. The resulting equations form a 2 × 2 system of conservation laws in the film thickness h(x, t) and in φh, where φ(x, t) ...

Shock Dynamics in Particle-Laden Thin Films

A Theory for Shock Dynamics in Particle-Laden Thin Films

We present a theory to explain the emergence of a particle-rich ridge observed experimentally in thin film particle-laden flow on an incline. We derive a lubrication theory for this system which is qualitatively compared to preliminary experimental data. The ridge formation arises from the creation of two shocks due to the differential transport rates of fluid and particles. This parallels rece...

Theory for shock dynamics in particle-laden thin films.

We present a theory to explain the emergence of a particle-rich ridge observed experimentally in a thin film particle-laden flow on an incline. We derive a lubrication theory for this system which is qualitatively compared to preliminary experimental data. The ridge formation arises from the creation of two shocks due to the differential transport rates of fluid and particles. This parallels re...

Linear stability of particle-laden thin films

Recent experiments [Zhou, Dupuy, Bertozzi, and Hosoi, Phys. Rev. Lett., 94 (2005)] of particle-laden film flow on an incline demonstrate new behavior distinct from the well-known clear fluid case, including the formation of a particle-rich ridge which can stabilize the advancing contact line with respect to “fingering” perturbations. We consider a model similar to that of Zhou et al. with the a...