  We show both numerically and analytically that a chemically patterned active
pore can act as a micro/nano-pump for fluids, even if it is fore-aft symmetric.
This is possible due to a spontaneous symmetry breaking which occurs when
advection rather than diffusion is the dominant mechanism of solute transport.
We further demonstrate that, for pumping and tuning the flow rate, a
combination of geometrical and chemical inhomogeneities is required. For
certain parameter values, the flow is unsteady, and persistent oscillations
with a tunable frequency appear. Finally, we find that the flow may lose its
axial symmetry and hence promotes mixing in the low Reynolds number regime.
