Shock Solutions for Particle-Laden Thin Films
نویسندگان
چکیده
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) is the particle volume fraction. We study flows in one dimension under the constant flux boundary condition, which corresponds to the classical Riemann problem, and we find the system can have either double-shock or singular shock solutions. We present the details of both solutions and examine the effects of the particle settling model and of the microscopic length scale b at the contact line.
منابع مشابه
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...
متن کاملA 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...
متن کاملHyperbolic 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...
متن کاملRarefaction-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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM Journal of Applied Mathematics
دوره 68 شماره
صفحات -
تاریخ انتشار 2008