Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary
Résumé
We consider a non-Newtonian fluid flow in a thin domain with thickness η ε and an oscillating top boundary of period ε. The flow is described by the 3D incompressible Navier-Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index p, with 9/5 ≤ p < +∞. We consider the limit when the thickness tends to zero and we prove that the three characteristic regimes for Newtonian fluids are still valid for non-Newtonian fluids, i.e. Stokes roughness (η ε ≈ ε), Reynolds roughness (η ε ε) and high-frequency roughness (η ε ε) regime. Moreover, we obtain different nonlinear Reynolds type equations in each case.
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