Francisco J. Suárez-Grau — Page 2

arXiv2018

Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions

We consider the Stokes system in a thin porous medium $Ω_\varepsilon$ of thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $\varepsilon$. On the boundary of the cylinders we prescribe non-homogeneous slip boundary conditions depending on a parameter $γ$. The aim is to give the asymptotic behavior of the velocity and the pressure of the fluid as $\varepsilon$ goes to zero. Using an adaptation of the unfolding method, we give, following the values of $γ$, different limit systems.

math.AP↗

arXiv2017

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

We consider a non-Newtonian fluid flow in a thin domain with thickness $η_\varepsilon$ and an oscillating top boundary of period $\varepsilon$. 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 $9/5\leq p<+\infty$. 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 ($η_\varepsilon\approx \varepsilon$), Reynolds roughness ($η_\varepsilon\ll \varepsilon$) and high-frequency roughness ($η_\varepsilon\gg \varepsilon$) regime. Moreover, we obtain different nonlinear Reynolds type equations in each case.

math.AP↗