Header menu link for other important links
Thin Newtonian film flow down a porous inclined plane: Stability analysis
Published in American Institute of Physics Inc.
Volume: 20
Issue: 2
The flow of a thin Newtonian fluid layer on a porous inclined plane is considered. Applying the long-wave theory, a nonlinear evolution equation for the thickness of the film is obtained. It is assumed that the flow through the porous medium is governed by Darcy's law. The critical conditions for the onset of instability of a fluid layer flowing down an inclined porous wall, when the characteristic length scale of the pore space is much smaller than the depth of the fluid layer above, are obtained. The results of the linear stability analysis reveal that the film flow system on a porous inclined plane is more unstable than that on a rigid inclined plane and that increasing the permeability of the porous medium enhances the destabilizing effect. A weakly nonlinear stability analysis by the method of multiple scales shows that there is a range of wave numbers with a supercritical bifurcation, and a range of larger wave numbers with a subcritical bifurcation. Numerical solution of the evolution equation in a periodic domain indicates the existence of permanent finite-amplitude waves of different kinds in the supercritical stable region. The long-time waveforms are either time-independent waves of permanent form that propagate or time-dependent modes that oscillate slightly in the amplitude. The presence of the porous substrate promotes this oscillatory behavior. The results show that the shape and amplitude of the waves are influenced by the permeability of the porous medium. © 2008 American Institute of Physics.
About the journal
JournalData powered by TypesetPhysics of Fluids
PublisherData powered by TypesetAmerican Institute of Physics Inc.
Open AccessNo
Concepts (8)
  •  related image
    Linear stability analysis
  •  related image
    Mechanical permeability
  •  related image
    Porous materials
  •  related image
    Wall flow
  •  related image
  •  related image
    Subcritical bifurcation
  •  related image
    Supercritical bifurcation
  •  related image
    Newtonian flow