## 4 Conclusions  
In this work, the microscopic definition of solid/fluid boundary is investigated using classical MD simulation with metallic solid and monoatomic fluid. It is demonstrated that the average density and pressure of the nanochannel vary depending on where the solid/fluid boundary is defined. The variation in property estimation is more severe in smaller channels. This size effect can be approximately evaluated by the dimensionless number \(2\sigma_{\text{sf}}/H_{\text{cc}}\). The local thermodynamic equilibrium is tested near the solid/fluid boundary. It is found that the local equilibrium collapses near the edge of thermal oscillations of the nucleus, creating a statistically depleted region. This region is not occupied by both solid and fluid nucleus. This implies that the solid/fluid boundary is located within the depletion region. Solid/fluid boundary is determined with a sub-atomic precision through the microscopic heat flux equation and non-equilibrium MD simulation. The results show that the microscopic heat flux equation is met in a nearly identical solid/fluid boundary regardless of the channel size. The determined location of solid/fluid boundary for the different materials shows small deviations when it is normalized by \(\sigma_{\text{sf}}\). Therefore, it is implied that the LJ diameter of solid/fluid, \(\sigma_{\text{sf}}\), plays a key role in the microscopic solid/fluid boundary. The temperature effect on the solid/fluid boundary is further studied for Ar/He interface. It is shown that the solid/fluid boundary of LJ atom can be theoretically estimated by ignoring the thermal vibration. This theoretical estimation shows a good agreement with the extrapolation of the solid/fluid boundary estimated by MD simulation. The results in this study are expected to contribute to understanding nanoscale fluid transport by improving the accuracy and consistency of property calculation. Moreover, it is expected that the definition of solid/fluid boundary improves the continuum-based models for nanoscale heat and mass transport. Future works are required for molecules with complex geometry such as a water molecule. Also, the solid/fluid boundary at the charged surface must be further studied; the solid/fluid boundary could be very different to the non-charged surface as the charged surface creates the Electrical Double Layer (EDL). It is necessary to study how much this new definition of boundary improves the continuum-based model. Also, a quantum mechanical approach may need to elucidate the role of electrons in the solid/fluid boundary.  
The following are available online at [[http://www.mdpi.com/2076-3417/9/12/2439/s1](http://www.mdpi.com/2076-3417/9/12/2439/s1)]([http://www.mdpi.com/2076-3417/9/12/2439/s1](http://www.mdpi.com/2076-3417/9/12/2439/s1)), Figure S1: The thermal conductivity calculated by the [PERSON]'s law of conductance with a various solid/fluid boundary for (a) Ag(001)/Ar interface and (b) Ag(111)/Ar interface. The errors are estimated as the summation of the standard error of the heat flux equation and the uncertainty of temperature gradient of the linear least square fitting. The black dash line represents the thermal conductivity calculated by Green-Kubo Method with a homogeneous LJ argon system, which contains 12,195 argon atoms with the approximately same thermodynamic state with the bulk region of nanoconfinement, Figure S2: Density distributions of the Ag(001)/Ar nanoconfinement: (a) two-dimensional contour, (b) one-dimensional profile for convex (\(\alpha-\alpha^{\prime}\)) and concave (\(\beta-\beta^{\prime}\)) corrugation. (c) semi-three-dimensional density profile of the adsorbed fluid near the Ag surface.  
B.K. designed and supervised the research. Y.N. performed the simulations and analyzed data. All authors wrote the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1A2C1004661).  
**Conflicts of Interest:** The authors declare no conflict of interest.