Effective models for generalized Newtonian fluids through a thin porous medium following the Carreau law
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918250863919104 |
|---|---|
| author | Anguiano, Maria Bonnivard, Matthieu Suarez-Grau, Francisco Javier |
| author_facet | Anguiano, Maria Bonnivard, Matthieu Suarez-Grau, Francisco Javier |
| contents | 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 $1<r<+\infty$, and scaled by a factor $ε^γ$, where $γ\in \mathbb{R}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01844 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effective models for generalized Newtonian fluids through a thin porous medium following the Carreau law Anguiano, Maria Bonnivard, Matthieu Suarez-Grau, Francisco Javier Analysis of PDEs Mathematical Physics 76A05, 76M50, 76A20, 76S05, 35B27, 35Q35 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 $1<r<+\infty$, and scaled by a factor $ε^γ$, where $γ\in \mathbb{R}$. 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. |
| title | Effective models for generalized Newtonian fluids through a thin porous medium following the Carreau law |
| topic | Analysis of PDEs Mathematical Physics 76A05, 76M50, 76A20, 76S05, 35B27, 35Q35 |
| url | https://arxiv.org/abs/2312.01844 |