This paper summarises some recent improvements in our theoretical unde
rstanding of liquid-metal ion sources. (a) Some years ago it was shown
how the standard formula for pressure difference across a charged con
ducting liquid surface could be derived directly from the laws of ther
modynamics. This is now proved equivalent to the minimisation of an un
familiar form of generalised free energy. (b) A simpler derivation of
Mair's formula for LMIS current/voltage characteristics can be obtaine
d by applying Newton's Second Law to the motion of the liquid cone as
a whole. (c) Results of modelling the effect of viscous drag on LMIS c
urrent/voltage characteristics, by incorporating a negative base-press
ure into the Forbes-Ljepojevic LMIS modelling program, are reported: t
rends obtained are in qualitative agreement with experiment. (d) Initi
al results are reported from research that aims to develop a full time
-dependent treatment of LMIS electrohydrodynamics. It seems that, unde
r the combined influence of gravitational and electrostatic forces, th
e surface of a conducting liquid can develop into a highly disorganise
d state.