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Journal Articles IMA Journal of Applied Mathematics Year : 2019

Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary

Abstract

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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Dates and versions

hal-01665760 , version 1 (16-12-2017)

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María Anguiano, Francisco J. Suárez-Grau. Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary. IMA Journal of Applied Mathematics, 2019, 84 (1), pp.63-95. ⟨10.1093/imamat/hxy052⟩. ⟨hal-01665760⟩

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