Study of Fluid Flow Passing Through the Vicinity of the Critical Point

The fluid flow passing through the vicinity of the critical point in a micrometric capillary is studied in the steady state. A phenomenological analysis of the Navier-Stokes and the heat transfer equations is undertaken. The flow distribution is described by distinguishing three areas within the capillary. In the first upstream region, the mass flow rate is approximated and singularities are put into light when the fluid gets closer to the critical point. The second region is critical and corresponds to a free boundary layer where a thermomechanical coupling occurs due to fluid expansion. Convective heat transfer in this area is significant and is linked to the conductive heat of the first upstream area. In the third downstream area, the flow is connected to the free boundary layer by asymptotical matching, which enables finding the mass flow rate correction. Finally, a relationship is established between the mass flow rate and the critical point position. It is shown that the presence of the free boundary layer close to the capillary outlet provides a cap effect.