title: Instabilities of a liquid film flowing down an inclined porous plane.
abstract: The problem of a film flowing down an inclined porous layer is considered. The fully developed basic flow is driven by gravitation. A careful linear instability analysis is carried out. We use Darcy's law to describe the porous layer and solve the coupling equations of the fluid and the porous medium rather than the decoupled equations of the one-sided model used in previous works. The eigenvalue problem is solved by means of a Chebyshev collocation method. We compare the instability of the two-sided model with the results of the one-sided model. The result reveals a porous mode instability which is completely neglected in previous works. For a falling film on an inclined porous plane there are three instability modes, i.e., the surface mode, the shear mode, and the porous mode. We also study the influences of the depth ratio d, the Darcy number delta, and the Beavers-Joseph coefficient alphaBJ on the instability of the system.
authors.affiliation: Key Laboratory of Microgravity,National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Rong
authors.initials: R
authors.lastname: Liu
authors.forename: Qiusheng
authors.initials: Q
authors.lastname: Liu
mesh_terms: D003198:Computer Simulation; D017276:Friction; D006112:Gravitation; D008567:Membranes, Artificial; D008956:Models, Chemical; D016062:Porosity; D012212:Rheology / Q000379:methods*; D012996:Solutions / Q000737:chemistry*
chemical_list: D008567:Membranes, Artificial; D012996:Solutions