  In this paper, we consider the homogenization of stationary and evolutionary
incompressible viscous non-Newtonian flows of Carreau-Yasuda type in domains
perforated with a large number of periodically distributed small holes in
$\mathbb{R}^{3}$, where the mutual distance between the holes is measured by a
small parameter $\varepsilon>0$ and the size of the holes is
$\varepsilon^{\alpha}$ with $\alpha \in (1, \frac 32)$. The Darcy's law is
recovered in the limit, thus generalizing the results from
[\url{https://doi.org/10.1016/0362-546X(94)00285-P}] and
[\url{https://doi.org/10.48550/arXiv.2310.05121}] for $\alpha=1$. Instead of
using their restriction operator to derive the estimates of the pressure
extension by duality, we use the Bogovski\u{\i} type operator in perforated
domains (constructed in [\url{https://doi.org/10.1051/cocv/2016016}]) to deduce
the uniform estimates of the pressure directly. Moreover, quantitative
convergence rates are given.
