  A water monolayer squeezed between two solid planes experiences strong
out-of-plane confinement effects while expanding freely within the plane. As a
consequence, the transport of such two-dimensional water combines hydrodynamic
and nanofluidic features, intimately linked with each other. In this paper, we
propose and explicitly solve a non-linear hydrodynamic equation describing
two-dimensional water flow with viscosity parameters deduced from molecular
dynamic simulations. We demonstrate that the very ability of two-dimensional
water to flow in short channels is governed by the second (dilatational)
viscosity coefficient, leading to flow compression and velocity saturation in
the high-pressure limit. The viscosity parameter values depend strongly on
whether graphene or hexoganal boron nitride layers are used to confine 2D water
that offers an interesting opportunity to obtain various nanofluids out of the
same water molecules just by using alternate materials to fabricate the 2D
channels.
