  We study the solution $u_\varepsilon$ to the Navier-Stokes equations in
$\mathbb R^3$ perforated by small particles centered at $(\varepsilon \mathbb
Z)^3$ with no-slip boundary conditions at the particles. We study the behavior
of $u_\varepsilon$ for small $\varepsilon$, depending on the diameter
$\varepsilon^\alpha$, $\alpha > 1$, of the particles and the viscosity
$\varepsilon^\gamma$, $\gamma > 0$, of the fluid. We prove quantitative
convergence results for $u_\varepsilon$ in all regimes when the local Reynolds
number at the particles is negligible. Then, the particles approximately exert
a linear friction force on the fluid. The obtained effective macroscopic
equations depend on the order of magnitude of the collective friction. We
obtain a) the Euler-Brinkman equations in the critical regime, b) the Euler
equations in the subcritical regime and c) Darcy's law in the supercritical
regime.
