This thesis examines the static equilibrium shapes and stability of various capillary
surfaces. The equilibrium shapes are accurately approximated using asymptotic
series solutions in the micro-gravity limit. The stability of two of these
capillary surfaces is then examined using an energy functional method and these
results corroborated using a linear stability analysis. Finally, a method of improving
the stability of a vertical liquid bridge is examined numerically and
experimentally. The problems considered in this thesis are motivated by a stent
problem described in the rst chapter but, in fact, capillary phenomena are
ubiquitous in science, nature and industry and the work here has wide reaching
applications