## 3 Results and Discussion
### Nitrogen Jet Profile  
After verifying that the molecular dynamics results are consistent with the SRK equation, we continued the simulation of the jet. The result of the molecular dynamics simulation of the supercritical nitrogen jet was visualized, as shown in Figure 4. The thermodynamic conditions of the jet for images (a)-(e) correspond to conditions I-V shown in Table 2 with the environment T = 201.6 K, P = 4.08 MPa and \(\rho\) = 73.5 kg/m\({}^{3}\) for all five conditions. The original jet molecules are shown in red while the ambient gas is shown in blue. From the series of jet images, we can obtain the characteristics of the supercritical jet. For Figure 4a, the jet is still in a subcritical condition while the environment is supercritical, the diameter of the jet first remains unchanged for a short distance and then slightly increases. We can see the clear vapor-liquid boundaries (no jet molecules dispersed in the ambient gas) and the perturbation of the shear layer is also clear. As the reduced temperature increases, there are more and more molecules detached from the jet, as shown in Figure 4b,c. For Figure 4d, which is a typical supercritical jet, there is no clear vapor-liquid interface but a thick mixing layer forms, and the mixing layer expands along the direction of the streams, with a certain cone angle. All these phenomena are very similar to those observed in a macroscale supercritical jet, as reported by [PERSON] et al. (2016). Figure 4: Image of jet at different conditions; the thermodynamic conditions of jet for images (a)–(e) correspond to conditions I-V shown in Table 2.  
Figure 3: The equation of state of nitrogen obtained using molecular dynamics compared with the SRK equation of state. (a) T = 132 K, (b) T = 300 K. (MD means the equation of state obtained by molecular dynamics with error bar; SRK means the modified Soave-Redich-Kwong equation of state; IDG means the ideal gas equation of state). This phenomenon can be described as a mixing layer regress (MDL) model [1] for supercritical injection, as illustrated in Figure 5, which is the axial sectional view, compared with the subcritical condition. Although theoretically there is no difference between the gas-liquid two-phase in a supercritical fluid, since the initial temperature of the jet is lower than the critical temperature, the jet does not immediately reach the supercritical state after it is injected into the supercritical environment, but under the action of heat transfer, the jet gradually transformed into a supercritical state. Therefore, the transcritical/supercritical liquid jet structure consists of a liquid core and a thick vapor-liquid mixing layer surrounding the liquid core and an external high-density gas. The mixing layer is a transitional layer from the liquid state transition to the gaseous state, in which there is a large density gradient. No droplets but scattered nitrogen vapor molecules exit the system. After the diameter of the liquid core is reduced to zero, the jet completely disintegrates. For the subcritical condition, however, the liquid has a continuous liquid core and the boundary layer is also clear compared with the supercritical condition. According to References [27; 28; 29], the density profile should be determined prior to the instability analysis. Figure 6 shows the density profiles of supercritical and subcritical jets. The density profile on the axial section, which is located at a position 5 nm downstream of the nozzle, was obtained statically from MD simulation results. It can be seen that the density profiles of supercritical and subcritical jets are generally the same, although it is well-known that the sharpest changes in the physical properties are observed in the vicinity of the critical point. However, there are still some minor distinctions between the density profiles of supercritical and subcritical jets. It is shown in Figure 6 that for both conditions the ambient density is the same.