  Graphene hosts an ultra-clean electronic system with electron-electron
collisions being the dominant source of scattering above liquid nitrogen
temperatures. In this regime, the motion of the electron fluid resembles the
flow of classical liquids and gases with high viscosity. Here we show that such
a viscous electron flow can cause the generation of a spin current
perpendicular to the direction of flow. Combining the Navier-Stokes equations
and the spin diffusion equation in the presence of the spin-vorticity coupling,
we derive an expression for the spin accumulation emerging purely as a result
of the viscous electron flow. We explore Poiseuille flow and Jeffery-Hamel flow
and show that the spin Hall angle may exceed 0.1 over a wide range of
temperatures and can be controlled by carrier density, temperature, and the
geometry of sample boundaries. Our theory points to new functionality of
graphene as a spin current source.
