A Theory for Shock Dynamics in Particle-Laden Thin Films

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...

Shock Dynamics in Particle-Laden Thin Films

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

Our study focuses on gravity-driven, particle-laden flows which are pertinent to a wide range of industrial and geophysical settings in which transport of suspensions occur. In the present study we employ a previously derived model [1] which uses the lubrication approximation to describe particle-laden films on an incline. The model consists of a coupled system of hyperbolic conservation laws f...

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 ...

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) ...