> C. Ruyer-Quil
Mechanisms of long-wave instabilities in shear-thinning films on porous substrates
Severine Millet, R. Usha, Valery Botton and Francois Rousset
The physical mechanisms for the long-wave instability are considered in the case of a gravity-driven Carreau fluid film flowing down an inclined porous medium. The porous medium is
assumed to be saturated with the same fluid. The study is based on the assumption that the characteristic length of the pore space is very much smaller than the thickness of
the film above; this reduces the boundary condition at the interface between the porous substrate and the fluid layer to a simple Maxwell - type slip condition .
Following the analysis presented by Smith  for a Newtonian fluid film on a rigid inclined substrate, the physical mechanisms involved in the long wave growth process are
investigated. This is done by analyzing separately the contributions of permeability and shear-thinning rheology to the different mechanisms.
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