  Water is a polar solvent and hence supports the bulk dissociation of itself
and its solutes into ions, and the re-association of these ions into neutral
molecules in a dynamic equilibrium, e.g., ${\rm H_2O_2}\leftrightharpoons {\rm
H^+~+~HO_2^-}$. Using continuum theory, we study the influence of these
reactions on the self-propulsion of colloids driven by surface chemical
reactions (chemical swimmers) in aqueous solution. The association-dissociation
reactions are here shown to have a strong influence on the swimmers' behaviour,
and must therefore be included in future modelling. In particular, such bulk
reactions permit charged swimmers to propel electrophoretically even if all
species involved in the surface reactions are neutral. The bulk reactions also
significantly modify the predicted speed of chemical swimmers propelled by
ionic currents, by up to an order of magnitude. For swimmers whose surface
reactions produce both anions and cations (ionic self-diffusiophoresis), the
bulk reactions produce an additional reactive screening length, analogous to
the Debye length in electrostatics. This in turn leads to an inverse
relationship between swimmer radius and swimming speed, which could provide an
alternative explanation for recent experimental observations on Pt-polystyrene
Janus swimmers [S. Ebbens et al., Phys. Rev. E 85, 020401 (2012)]. We also use
our continuum theory to investigate the effect of the Debye screening length
itself, going beyond the infinitely thin limit approximation used by previous
analytical theories. We identify significant departures from this limiting
behavior for micron-sized swimmers under typical experimental conditions, and
find that the limiting behavior fails entirely for nanoscale swimmers.
