  The observed stability of nanobubbles contradicts the well-known result in
classical nucleation theory, that the critical radius is both microscopic and
thermodynamically unstable. Here nanoscopic stability is shown to be the
combined result of two non-classical mechanisms. It is shown that the surface
tension decreases with increasing supersaturation, and that this gives a
nanoscopic critical radius. Whilst neither a free spherical bubble nor a
hemispherical bubble mobile on an hydrophobic surface are stable, it is shown
that an immobilized hemispherical bubble with a pinned contact rim is stable
and that the total entropy is a maximum at the critical radius.
