Acta Mechanica

, Volume 230, Issue 6, pp 2201–2220 | Cite as

The mechanism of long-wave instability in a shear-thinning film flow on a porous substrate

  • S. MilletEmail author
  • R. Usha
  • V. Botton
  • F. Rousset
Original Paper


A linear stability analysis of a thin shear-thinning film with a deformable top surface flowing down an inclined porous substrate modelled as a smooth substrate with velocity slip at the wall is examined, and the physical mechanism for the long-wave instability is analysed. Through a phenomenological model, the influence of slip velocity and the shear-thinning rheology on the wave speed of long surface waves on a non-Newtonian shear-thinning film down a substrate with velocity slip is predicted. The viscosity disturbance plays a significant role in the destabilization of the flow system. Indeed, slip at the bottom that accounts for the characteristics of the porous/rough substrate does not affect the physical mechanism of the instability. However, it is shown that slip at the bottom enhances the inertia effects which in turn destabilizes the flow system at smaller Reynolds numbers.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratoire de Mécanique des Fluides et d’Acoustique UMR CNRS 5509, École Centrale de Lyon, INSA-Lyon, Université Lyon 1Université de LyonLyonFrance
  2. 2.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia
  3. 3.INSA Euro-MéditerranéeUniversité Euro-Méditerranéenne de FèsFesMorocco
  4. 4.UMR5008, CETHIL, INSA-Lyon, CNRSUniversité de LyonVilleurbanneFrance

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