  Bubble-propelled catalytic colloids stand out as a uniquely efficient design
for artificial controllable micromachines, but so far lack a general
theoretical framework that explains the physics of their propulsion. Here we
develop a combined diffusive and hydrodynamic theory of bubble growth near a
spherical catalytic colloid, that allows us to explain the underlying mechanism
and the influence of environmental and material parameters. We identify two
dimensionless groups, related to colloidal activity and the background fluid,
that govern a saddle-node bifurcation of the bubble growth dynamics, and
calculate the generated flows analytically for both slip and no slip boundary
conditions on the bubble. We finish with a discussion of the assumptions and
predictions of our model in the context of existing experimental results, and
conclude that some of the observed behaviour, notably the ratchet-like gait,
stems from peculiarities of the experimental setup rather than fundamental
physics of the propulsive mechanism.
