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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 [2]. Following the analysis presented by Smith [3] 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. REFERENCES
  • [1] R. Usha, S. Millet, H. Ben Hadid and F. Rousset, Shear-thinning film on a porous substrate: Stability analysis, Chem.Eng. Sci., 66, 22, pp.5614-5627
  • [2] J.P. Pascal, Linear stability of fluid flow down a porous inclined plane, J. Phys. D: Appl. Phys. Vol. 32, pp. 417- 422, (1999).
  • [3] M. K. Smith, The Mechanism for the long-wave instability in thin liquid film, J. Fluid Mech., Vol. 217, pp. 469-485, (1990).
  • [4] Anjalaiah, R. Usha, and S. Millet, Thin film flow down a porous substrate in the presence of an insoluble surfactant: Stability analysis, Phys. Fluids 25, 022101 (2013) doi: 10.1063/1.4789459
  • [5] . S. Millet, V. Botton, F. Rousset, H. BenHadid, Wave celerity on a shear-thinning fluid film flowing down an incline., Phys. Fluids , vol. 20, 031701, 2008. http://dx.doi.org/10.1063/1.2889140

Dernière modification : April 04 2013, 10:18:43.