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Pré-Publication, Document De Travail Année : 2022

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

Résumé

We consider the flow of generalized Newtonian fluid through a thin porous media Ωε of thickness ε which is perforated by periodically distribute solid cylinders of size ε. Generalizing (Anguiano et al., Q. J. Mech. Math., 75(1), 2022, 1-27) we do a new and complete study on the fluid described by the 3D incompressible Stokes system with non-linear viscosity, following the Carreau law of flow index 1 < r < +∞, which is scaled by a factor ε^γ , where γ ∈ R. Depending of γ and the flow index r, using homogenization techniques, we derive different effective linear and non-linear lower-dimensional Darcy's laws.
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Dates et versions

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

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  • HAL Id : hal-03885537 , version 1

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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. 2022. ⟨hal-03885537v1⟩
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