## 1 Introduction  
Supercritical fluid injections have many applications ranging from internal combustion engines to supercritical fluid extraction [1; 2]. It is well-known that the critical point is a singularity in thermodynamics. Fluids in supercritical conditions have distinct properties from subcritical conditions. In the supercritical state, the interface between the liquid and the gas phases no longer exists, as the liquid surface tension and the latent heat of evaporation tend towards zero. So there is no longer a distinction between liquid and gas, but it is collectively referred to as a homogeneous supercritical fluid. Its density is close to that of the liquid and its transport characteristics are close to those of the gas. When a liquid approaches the critical point, the isothermal compression coefficient, constant pressure heat and gas solubility in the liquid are sharply increased. In that condition, the phenomena such as liquid jet disintegration, atomizing and droplet evaporation (usually occurring at subcritical condition during the fuel injection and the mixture formation) no longer exist. More specifically, the injection is more like gas-gas mixing in supercritical conditions. Therefore, the mechanism of supercritical injection is very complicated and essentially different from subcritical spray. A good understanding of the destabilization mechanism of supercritical jets is demanded urgently. In recent years, many numerical studies on shear injection and mixing at supercritical conditions have been performed [3; 4; 5; 6; 7; 8]. However, there are limitations to current injection modeling techniques. For subcritical conditions a means for tracking the phase boundaries must be included, and since all traditional methods for modeling such processes are based on the solutions of the Navier-Stokes equations, an accurate knowledge of the constituent transport and material properties along with an accurate equation of state are required. This can be particularly difficult because of the dramatic changes in the physical properties of the fluid near the critical point. Molecular dynamics simulations have been proven to be a suitable method for studying the behavior of liquid in supercritical conditions. Molecular dynamics simulations are based purely on first principles. As a result, there is no need for material or transport properties as a function of pressure and temperature, and there is no need to track phase boundaries. In addition, the simulation is three-dimensional. All physical processes are spontaneous and the supercritical mixing occurs naturally without the need for tracking the phase boundary of the jet. Also, as stated by [PERSON] and [PERSON] [9], two distinctively different interfacial conditions can be classified using the Knudsen number criterion. The Knudsen number \(K\mathrm{n}\ =\ \lambda/\iota\), where \(\lambda\) is the molecular mean free path and \(\iota\) is the corresponding interface thickness calculated using linear gradient theory. Knudsen numbers greater than 0.1 characterize non-continuum molecular scales, while Knudsen numbers smaller than 0.1 correspond to continuum regimes. According to the theory of [PERSON] and [PERSON] [9], as the Knudsen number is greater than 0.1 in the test conditions in the present study, molecular dynamics simulation is suitable to investigate the processes in the present study, which are governed by molecular dynamics [10]. Various studies have been conducted on supercritical or subcritical injection. Of these studies, [PERSON] et al. [11] conducted a molecular dynamics simulation and experiment of nitrogen injection under supercritical conditions. In the study, a new model of supercritical injection was proposed and proved to be suitable for studying supercritical injection. [PERSON] [12] described in detail the method of using molecular dynamics to simulate supercritical jets. [PERSON] et al. [13] investigated the phenomenon of nanojet injection in a high-pressure environment by non-equilibrium molecular dynamics.