First law of thermodynamics on the boundary for flow through a carbon nanotube

The definition of boundary at the nanoscale has been a matter of dispute for years. Addressing this issue, the nonequilibrium molecular dynamics (NEMD) simulations in this work investigate the flow characteristics of a simple liquid in a single-walled carbon nanotube (SWCNT), and equilibrium molecular dynamics simulations support the range of the NEMD results. The inconsistencies in defining the flow boundary at the nanoscale are understood through the first law of thermodynamics: Local thermodynamic properties (the effects of the density distribution, pressure, viscosity, and temperature) define the boundary. We have selected different boundary positions in the CNT to demonstrate the probability of density distribution that also indicates the coexistence of multiple thermodynamic states. Altering the interaction parameters, we produce convergence between the NEMD result and the no-slip Hagen-Poiseuille assumptions. Meanwhile, the results indicate that the boundary position varies between the innermost solid wall and peak density position of the CNT as a function of the input energy or work done in the system. Finally, we reveal that the ratio between the potential energy barrier and the kinetic energy is proportional to the shift of the boundary position away from the innermost solid wall.