We develop a simple, efficient, and general statistical mechanical technique for calculating the pressure tensor of an atomic fluid. The method is applied to the case of planar Poiseuille flow through a narrow slit pore, and the results indicate that our technique is accurate and relatively efficient. A second method to calculate shear stress is derived from the momentum continuity equation. This mesoscopic method again is seen to be accurate with low statistical uncertainty. Using both approaches, the viscosity is calculated as a function of position across the pore, and is seen to oscillate because of a wall-induced local structure in the fluid. We discuss these methods in relation to the well-known ambiguity of the pressure tensor.

In this work we use nonequilibrium molecular dynamics (NEMD) to simulate an atomic liquid undergoing gravity-fed flow down a narrow channel. We compare the simulation results against the predictions of classical Navier-Stokes theory for two different channel widths. For a channel width of 5.1 molecular diameters, we find that the velocity profile deviates significantly from the hydrodynamic prediction. The shape of this velocity profile is found to be independent of the applied field (pressure gradient). We find that the heat flux profile does not agree with the cubic profile predicted by Navier-Stokes hydrodynamics, but shows significant oscillations located about one molecular diameter from the walls. This result differs from the earlier work of Todd and Evans [B. D. Todd and D. J. Evans, J. Chem. Phys. 103, 9804 (1995)], in which an assumption of a purely quadratic velocity profile resulted in very weak oscillations in the heat flux. We find that in narrow channels the viscosity cannot be described by a linear, local constitutive relation. However, classical Navier-Stokes behavior is approached for a channel width of >∼10 molecular diameters.

The purpose of this paper is threefold. First, we review the existing literature on flow rates of water in carbon nanotubes. Data for the slip length which characterizes the flow rate are scattered over 5 orders of magnitude for nanotubes of diameter 0.81–10 nm. Second, we precisely compute the slip length using equilibrium molecular dynamics (EMD) simulations, from which the interfacial friction between water and carbon nanotubes can be found, and also via external field driven non-equilibrium molecular dynamics simulations (NEMD). We discuss some of the issues in simulation studies which may be reasons for the large disagreements reported. By using the EMD method friction coefficient to determine the slip length, we overcome the limitations of NEMD simulations. In NEMD simulations, for each tube we apply a range of external fields to check the linear response of the fluid to the field and reliably extrapolate the results for the slip length to values of the field corresponding to experimentally accessible pressure gradients. Finally, we comment on several issues concerning water flow rates in carbon nanotubes which may lead to some future research directions in this area.

Data for the flow rate of water in carbon nanopores is widely scattered, both in experiments and simulations. In this work, we aim at precisely quantifying the characteristic large slip length and flow rate of water flowing in a planar graphene nanochannel. First, we quantify the slip length using the intrinsic interfacial friction coefficient between water and graphene, which is found from equilibrium molecular dynamics (EMD) simulations. We then calculate the flow rate and the slip length from the streaming velocity profiles obtained using non-equilibrium molecular dynamics (NEMD) simulations and compare with the predictions from the EMD simulations. The slip length calculated from NEMD simulations is found to be extremely sensitive to the curvature of the velocity profile and it possesses large statistical errors. We therefore pose the question: Can a micrometer range slip length be reliably determined using velocity profiles obtained from NEMD simulations? Our answer is “not practical, if not impossible” based on the analysis given as the results. In the case of high slip systems such as water in carbon nanochannels, the EMD method results are more reliable, accurate, and computationally more efficient compared to the direct NEMD method for predicting the nanofluidic flow rate and hydrodynamic boundary condition.

We provide a review of the literature for non-equilibrium molecular dynamics (NEMD) simulations of homogeneous fluids. Our review focuses on techniques for simulations of shear and elongational flows in viscous fluids and covers the formulation and application of NEMD algorithms for atomic and molecular fluids. We provide a set of expositions that can be effectively used as guidelines to formulate the relevant equations of motion, periodic boundary conditions and thermostats. We also provide a survey of applications in a convenient tabular form as an aid to researchers who wish to use NEMD to study transport phenomena.

In this work we show how different use of thermostating devices and modeling of walls influence the mechanical and dynamical properties of confined nanofluids. We consider a two dimensional fluid undergoing Couette flow using nonequilibrium molecular dynamics simulations. Because the system is highly inhomogeneous, the density shows strong fluctuations across the channel. We compare the dynamics produced by applying a thermostating device directly to the fluid with that obtained when the wall is thermostated, considering also the effects of using rigid walls. This comparison involves an analysis of the chaoticity of the fluid and evaluation of mechanical properties across the channel. We look at two thermostating devices with either rigid or vibrating atomic walls and compare them with a system only thermostated by conduction through vibrating atomic walls. Sensitive changes are observed in the xy component of the pressure tensor, streaming velocity, and density across the pore and the Lyapunov localization of the fluid. We also find that the fluid slip can be significantly reduced by rigid walls. Our results suggest caution in interpreting the results of systems in which fluid atoms are thermostated and/or wall atoms are constrained to be rigid, such as, for example, water inside carbon nanotubes.