## 4 Discussion
This can be used to explain the phenomenon where the optimum mass fraction of 12 wt % and the mass fraction of 18 wt %, show the weakest erosion capability all of the time, as shown in Figures 6 and 8. Moreover, for the experiments on the influence of the ambient pressure under constant \(\Delta P\), the density of the SC-CO\({}_{2}\) fluid at the nozzle inlet increases with increasing ambient pressure, as shown in Figure 12. This results in the increase of the optimum nano-silica mass fraction with increasing ambient pressure, and the obvious enhancement of the erosion ability of the jet with the mass fraction of 18 wt %, at comparatively high ambient pressures of 20 MPa and 25 MPa, as shown in Figure 9.  
Figure 11: The density of SC-CO\({}_{2}\) fluid versus nozzle inlet pressure (Data from REFPROP). Figure 12: The density of SC-CO\({}_{2}\) fluid versus ambient pressure under constant \(\Delta P\) (Data from REFPROP). In addition, for the experiments on the effect of fluid temperature, the density of CO\({}_{2}\) fluid decreases with the increase of fluid temperature, as shown in \[F_{v}=\frac{1}{2}\rho_{f}V_{p}\frac{\text{d}(V_{f}-V_{p})}{\text{d}x} \tag{3}\]0 As a result, the optimum nano-silica mass fraction has a decreasing trend with the increase of fluid temperature. Another interesting phenomenon that can be observed in Figures 6-10, is that the nano-silica additive can cause a reduction in the erosion capability of the SC-CO\({}_{2}\) jet, under certain conditions. For instance, the erosion ability of the jet with a nano-silica mass fraction of 18 wt % is worse than that of the pure SC-CO\({}_{2}\) jet at inlet pressures below 50 Mpa, as shown in \[F_{v}=\frac{1}{2}\rho_{f}V_{p}\frac{\text{d}(V_{f}-V_{p})}{\text{d}x} \tag{3}\]1 This is likely to be due to the existence of competition between the erosion enhancement and the additional energy dissipation. To be more specific, the viscosity of the fluid can be increased by the nano-silica additive [45]. So, excessive mass fractions of the nano-silica additive will raise the viscous dissipation of the energy of the high speed turbulent SC-CO\({}_{2}\) jet flow, thus resulting in the reduction of the erosion capability. On the other hand, impingement of the nano-silica particles, accelerated by the high speed SC-CO\({}_{2}\) jet fluid, can enhance the rock erosion ability, and the better the acceleration effect is, the greater the enhancement is. Therefore, if the enhancement of the erosion caused by the impingement of nano-silica particles, is stronger than that of the energy dissipation, the erosion capability of the SC-CO\({}_{2}\) jet will be improved by the nano-silica additive; if not, energy dissipation will be the dominated effect, resulting in a reduction of the erosion ability. This hypothesis can be used to explain the experimental phenomena where the acceleration effect is poor with a low density of SC-CO\({}_{2}\) fluid, and the high mass fraction of the nano-silica additive tends to cause a negative effect on the erosion ability. Finally, it is well known that the nozzle design, including structural parameters and nozzle types, can strongly affect the characteristics of the SC-CO\({}_{2}\) jet, such as the focussing of the jet, Mach shock, jet collimation etc. Furthermore, it greatly affects the rock erosion behaviors of the SC-CO\({}_{2}\) jet. Therefore, the impact of the nozzle design on the rock erosion characteristics of the SC-CO\({}_{2}\) jet will be emphatically studied in the near future.