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A method is proposed for creating a non-equilibrium ensemble with a constant number of molecules, constant temperature and constant pressures with different target values in two reservoirs [referred to as NT(P(1)-P(2)) ensemble] that are connected by a finite length nanopore. This method includes two steps. The first step places a partition between the two reservoirs and then creates a static pressure field and a proper system volume by using two self-adjusting plates on which two external forces/pressures with different target values are exerted. The second step removes the partition and the two self-adjusting plates and the pressure difference between the two reservoirs is maintained by a "pump" designed to simultaneously create a periodic boundary condition between the two reservoirs and supply the necessary force (work) to a subset of molecules for a steady state flow. To examine this method, several cases using liquid argon with a truncated and shift Lennard-Jones potential under different target pressures and pump sizes were studied. Results show that the method proposed in this paper works well. In addition, the method proposed in this paper was compared with the other external force field methods. The results show that as long as the external force is applied to a restricted set of molecules away from the channel a constant pressure difference between two reservoirs is maintained. The advantage of the algorithm proposed here also sets the absolute pressures with different target levels in two reservoirs instead of it being arbitrary. Studies show that the fluid flow rate or permeability through a nanopore depends not only on the pressure difference between two reservoirs, but also on the absolute pressures in two reservoirs.

The effect of pore wall-liquid interaction on the liquid transport through a nanopore in a membrane was studied by an improved pressure-driven non-equilibrium molecular dynamics (NEMD) method. The NEMD results showed that pressures in the reservoirs were constant and were equal to the pressures externally exerted on the self-adjusting plates that drove the flow; pressures in the nanopore decreased monotonically in the stream-wise direction when the solid wall-liquid had weak or neutral interaction, but exhibited a different distribution pattern in the case of the solid wall-liquid exhibiting strong attractive interaction. The transport ability of the nanopore depended significantly on the pore wall-liquid interaction.

The entrance and exit effects on liquid transport through a nano-sized cylindrical pore under different solid wall-liquid interactions were studied by comparing molecular dynamics (MD) results of a finite length nanopore in a membrane with those of an infinite length one. The liquid transport through a finite length nanopore in a membrane was carried out by using a pressure-driven non-equilibrium molecular dynamics (NEMD) method proposed by Huang et al. [C. Huang, K. Nandakumar, P. Choi and L. W. Kostiuk, J. Chem. Phys., 2006, 124, 234701]. The fluid motion through an infinite length nanopore, which had the same cross-stream dimension as the finite length channel in the membrane, but with periodic boundary conditions in the stream-wise direction, was carried out by using the external-field driven NEMD approach [J. Koplik, J. R. Bavanar and J. F. Willemsen, Phys. Rev. Lett., 1988, 60, 1282]. The NEMD results show that the pressure and density distributions averaged over the channel in the radial direction in both finite and infinite length channels are similar, but the radial distributions of the stream-wise velocity were significantly different when the solid wall was repulsive. The entrance and exit effects lead to a decrease in flow rate at about 39% for the repulsive wall and 6% for the neutral-like wall.

Steady state pressure driven flow of liquid argon through a finite length cylindrical nanopore was investigated numerically by classical Navier-Stokes (NS) hydrodynamic models and nonequilibrium molecular dynamics (MD) simulations. In both approaches, the nanopore was nominally 2.2 nm in diameter and 6 nm long. For the MD simulations, the intermolecular properties of the walls were specified independently from the liquid. Comparisons between the approaches were made in terms of the gross feature of total flow rate through the nanopore, as well as the more refined considerations of the spatial distributions of pressure, density, and velocity. The results showed that for the NS equations to predict the same trends in total flow rate with increasing pressure difference as the MD simulation, submodels for variations in density and viscosity with pressure are needed to be included. The classical NS boundary conditions quantitatively agreed with the flow rate predictions from MD simulations only under the condition of having a neutral-like solid-liquid interaction. Under these conditions, the NS and MD models also agreed well in streamwise distributions of pressure, density, and velocity, but not in the radial direction.

Fluid transport through a nanopore in a membrane was investigated by using a novel molecular dynamics approach proposed in this study. The advantages of this method, relative to dual-control-volume grand-canonical molecular dynamics method, are that it eliminates disruptions to the system dynamics that are normally created by inserting or deleting particles from control volumes, and that it functions well for dense systems due to the number of particles being fixed in the system. Using the proposed method, we examined liquid argon transport through a nanopore by performing nonequilibrium molecular dynamics (NEMD) simulations under different back pressures. Validation of the code was performed by comparing simulation results to published experimental data obtained under equilibrium conditions. NEMD results show that constant pressure difference across the membrane was readily achieved.