  In this paper, we consider the multi-species parabolic-elliptic
Patlak-Keller-Segel system coupled with the Navier-Stokes equations near the
2-D Poiseuille flow $(\ A(1-y^2), 0\ )$ in a finite channel
$\Omega=\mathbb{T}\times\mathbb{I}$ with $ \mathbb{I}=(-1,1)$. Furthermore, the
Navier-slip boundary condition is imposed on the perturbation of velocity $u$.
We show that if the Poiseuille flow is sufficiently strong ($A$ is large
enough), the solutions to the system are global in time without any smallness
restriction on the initial cell mass.
