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Pré-Publication, Document De Travail Année : 2023

Effective models for generalized Newtonian fluids through a thin porous media following the Carreau law

Résumé

We consider the flow of a generalized Newtonian fluid through a thin porous medium of thickness ε, perforated by periodically distributed solid cylinders of size ε. We assume that the fluid is described by the 3D incompressible Stokes system, with a non-linear viscosity following the Carreau law of flow index 1 < r < +∞, and scaled by a factor εγ , where γ ∈ R. Generalizing (Anguiano et al., Q. J. Mech. Math., 75(1), 2022, 1-27), where the particular case r < 2 and γ = 1 was addressed, we perform a new and complete study on the asymptotic behaviour of the fluid as ε goes to zero. Depending on γ and the flow index r, using homogenization techniques, we derive and rigorously justify different effective linear and non-linear lower-dimensional Darcy’s laws. Finally, using a finite element method, we study numerically the influence of the rheological parameters of the fluid and of the shape of the solid obstacles on the behaviour of the effective systems.
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Dates et versions

hal-03885537 , version 1 (05-12-2022)
hal-03885537 , version 2 (21-03-2023)

Identifiants

  • HAL Id : hal-03885537 , version 2

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María Anguiano, Matthieu Bonnivard, Francisco J. Suárez-Grau. Effective models for generalized Newtonian fluids through a thin porous media following the Carreau law. 2023. ⟨hal-03885537v2⟩
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