Reduced model for particle laden flow

The flow of thin liquid films on solid surfaces is a significant phenomenon in nature and in industrial processes where uniformity and completeness of wetting are paramount in importance. It is well known that when a clear viscous fluid flows down an inclined surface under gravity, after some time, the initially straight contact line becomes unstable with respect to transverse perturbations. Clear fluid is easier to use in experiments, but industrial processes usually involve particulates in the form of either suspensions or dry granular flows. In this work, we study the flow of a thin film down an inclined plane. The particle-fluid mixture is modeled as a single fluid with effective density and viscosity, depending on the concentration of the particles. Since the flow is slow and the fluid layer is very thin, inertial effects are ignored and a lubrication approximation is applied to simplify the analysis. It is assumed that there is no variation in the transverse direction before the onset of instability, and the fluid properties and velocity are depth averaged to remove the height-dependence. The settling velocity of the particles is hindered by the presence of neighboring particles; this phenomenon is captured by the hindered velocity function that decreases with increasing concentration. The normal component of the settling velocity is neglected in this work and the resulting model is a system of two equations accounting for the film thickness and particle concentration changes as the mixture flows down the plane. Numerical simulations are performed and it is found that the mixtures with higher concentration flow more slowly. Compared to the clear viscous fluid, particle laden flow results in a bump that is much bigger and the size of the bump

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2004

Author dc:creator

• Zhou, Junjie, 1979-

Advisor dc:contributor.advisor

• Anette Hosoi.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/17955

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/17955