We have examined the local and global evolution of the extent of neutralisation in an upright cylindrical flow reactor with a rigid adiabatic base and sidewall but with an open top. The cylinder is initially filled with a dilute aqueous solution of a strong base or a strong acid. A dilute solution of strong acid or strong base is injected as a steady Poiseuille flow towards the centre of the base of the reactor through a large capillary tube coaxial with the cylindrical reactor. Computational fluid dynamics modelling, using the finite-volume method, indicates that each neutralisation reaction progresses at a significantly different rate under conditions of normal terrestrial gravity and microgravity. The gravitational dependence of the conversion of acid or base to salt and water is attributed to secondary flows due, largely, to buoyancy forces associated with the dependence of the local liquid density on the local chemical composition. The influence of these secondary flows on the spatial distribution of the salty product is illustrated. For the rather dilute solutions examined here we find excellent agreement between results from our weakly compressible hydrodynamic treatment and those from a more standard analysis employing the Boussinesq approximation.