  We consider the case when a supercritical fluid emerges at sonic speed from a
small orifice in a high pressure chamber. The subsequent expansion causes a
pressure drop and the fluid then enters a regime where its equation of state in
$P-V$ space becomes concave towards the origin. This is the signal for an
expansion shock to occur in a non-ideal fluid. This paper provides the details
of an analytic calculation of the shape and location of this expansion shock
using Whitham's front-tracking method. Dependence of the shape of the front on
various operating conditions was calculated for the particular case of
supercritical carbon dioxide. The results shed light on the rapid expansion of
supercritical solutions (RESS), a process which is used in many manufacturing
technologies.
