  We present a theory for the self-propulsion of symmetric, half spherical
Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is
generated by release (diffusive emission or dissolution) of water-soluble
surfactant molecules, which modulate the air-water interfacial tension.
Propulsion either requires asymmetric release or spontaneous symmetry breaking
by coupling to advection for a perfectly symmetrical swimmer. We study the
diffusion-advection problem for a sphere in Stokes flow analytically and
numerically both for constant concentration and constant flux boundary
conditions. We derive novel results for concentration profiles under constant
flux boundary conditions and for the Nusselt number (the dimensionless ratio of
total emitted flux and diffusive flux). Based on these results, we analyze the
Marangoni boat for small Marangoni propulsion (low Peclet number) and show that
two swimming regimes exist, a diffusive regime at low velocities and an
advection-dominated regime at high swimmer velocities. We describe both the
limit of large Marangoni propulsion (high Peclet number) and the effects from
evaporation by approximative analytical theories. The swimming velocity is
determined by force balance, and we obtain a general expression for the
Marangoni forces, which comprises both direct Marangoni forces from the surface
tension gradient and Marangoni flow forces. We unravel, whether the Marangoni
flow contribution is exerting a forward or backward force during propulsion.
Our main result is the relation between Peclet number and swimming velocity.
Spontaneous symmetry breaking and, thus, swimming occurs for a perfectly
symmetrical swimmer above a critical Peclet number, which becomes small for
large system sizes. We find a supercritical swimming bifurcation for a
symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.
