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.

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.

We present the results of nonequilibrium molecular dynamics simulations of a model decane fluid performed at constant pressure and compare them with results previously obtained from simulations performed at constant volume. The strain rate dependence of the viscosity at constant pressure is found to differ from that obtained previously at constant volume. The shear thickening at high strain rates observed in constant volume simulations vanishes when the simulations are performed at constant pressure. We also investigate the question of how our low strain rate data for decane can be accurately extrapolated to zero strain rate. We find a well defined first Newtonian region in which the viscosity is independent of strain rate to within errors. The value of the viscosity that we obtain in this region agrees well with the zero strain rate viscosity calculated from the Green–Kubo formula at equilibrium.

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.

We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.