It has been suggested on the basis of certain chemical observations that the winter-time stratospheric polar vortex might act as a chemical processor, or flow reactor, through which large amounts of air - of the order of one vortex mass per month or three vortex masses per winter - flow downwards and then outwards to middle latitudes in the lower stratosphere. If such a flow were to exist, then most of the air involved would become chemically `activated', or primed for ozone destruction, while passing through the low temperatures of the vortex where fast heterogeneous reactions can take place on polar-stratospheric-cloud particles. There could be serious implications for our understanding of ozone-hole chemistry and for midlatitude ozone loss, both in the Northern and in the Southern Hemisphere. This paper will briefly assess current fluid-dynamical thinking about flow through the vortex. It is concluded that the vortex typically cannot sustain an average throughput much greater than about a sixth of a vortex mass per month, or half a vortex mass per winter, unless a large and hitherto unknown mean circumferential force acts persistently on the vortex in an eastward or `spin-up' sense, prograde with the Earth's rotation. By contrast, the `sub-vortex' below pressure-altitudes of about 70 hPa (more precisely, on isentropic surfaces below potential temperatures of about 400 K) is capable of relatively large mass throughout depending, however, on tropospheric weather beneath, concerning which observational data are sparse.