We have simulated the steady state of a stoichiometric neutralisation reaction in a capillary flow reactor. The reactive flow occurs in an upright capillary tube with coaxial inlets in its base, an open top and with adiabatic sidewalls. A dilute solution of 0.100 M alkali or acid is injected vertically upwards through the central inlet. A 0.100 M solution of acid or alkali is also injected vertically upwards into the cylinder through a circular annulus concentric with, and immediately surrounding, the central inlet. Computational fluid dynamics modelling, using the finite-volume method, indicates that gravity has a pronounced effect on both the steady-state flow and on the chemical composition of this flow. Very large deviations from Hagen-Poiseuille flow, proportional to the ratio of the Reynolds number to a modified Froude number, are predicted when gravity is present, even though the densities of the two reactant-streams differ by less than 0.3%. Under terrestrial gravity, both the flow distribution and the steady-state conversion to products at the outlet depend strongly on whether alkali or acid forms the central inlet jet. This dependence becomes very small under microgravity conditions.