Physics of rapidly expanding supercritical solutions: A first approach

TL;DR

This paper analytically investigates the formation and characteristics of expansion shocks during rapid supercritical fluid expansion, focusing on supercritical carbon dioxide, to better understand the RESS manufacturing process.

Contribution

It provides the first detailed analytic calculation of expansion shock shape and location in supercritical fluids using Whitham's method, highlighting dependence on operating conditions.

Findings

Expansion shocks occur when the equation of state becomes concave in P-V space.

Shape and position of the shock depend on pressure, temperature, and flow conditions.

Results improve understanding of rapid supercritical solution expansion in manufacturing.

Abstract

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.