Bulk Ionic Dissociation is Crucial for Understanding Chemically-Propelled Swimmers

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., H2O2 −⇀↽ H + HO – 2. We find, using a continuum theory, that taking the dynamics of these bulk reactions into account has a strong influence on the propulsive behavior of colloids driven by surface chemical reactions (swimmers) in aqueous solution. 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 standard electrophoretic swimmers, 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 even for micron-sized swimmers under typical experimental conditions, and find that the limiting behavior fails entirely for nanoscale swimmers.