B. D. Todd

How fast does water flow in carbon nanotubes

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.

Homogeneous non-equilibrium molecular dynamics simulations of viscous flow: techniques and applications

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.

Thermostating highly confined fluids

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.

Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.

Viscoelastic properties of dendrimers in the melt from nonequlibrium molecular dynamics

The viscoelastic properties of dendrimers of generation 1-4 are studied using nonequilibrium molecular dynamics. Flow properties of dendrimer melts under shear are compared to systems composed of linear chain polymers of the same molecular weight, and the influence of molecular architecture is discussed. Rheological material properties, such as the shear viscosity and normal stress coefficients, are calculated and compared for both systems. We also calculate and compare the microscopic properties of both linear chain and dendrimer molecules, such as their molecular alignment, order parameters and rotational velocities. We find that the highly symmetric shape of dendrimers and their highly constrained geometry allows for substantial differences in their material properties compared to traditional linear polymers of equivalent molecular weight.

A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows.

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.

Internal structure of dendrimers in the melt under shear: A molecular dynamics study

The molecular structure of fluids composed of dendrimers of different generations is studied using nonequilibrium molecular dynamics (NEMD). NEMD results for dendrimer melts undergoing planar Couette flow are reported and analyzed with particular attention paid to the shear-induced changes in the internal structure of dendrimers. The radii of gyration, pair distribution functions and the fractal dimensionality of the dendrimers are determined at different strain rates. The location of the terminal groups is analyzed and found to be uniformly distributed throughout the space occupied by the molecules. The fractal dimension as a function of strain rate displays crossover behavior analogous to the Newtonian/non-Newtonian transition of shear viscosity.

The stability of nonequilibrium molecular dynamics simulations of elongational flows

We show that nonequilibrium molecular dynamics simulations of elongational flows are inherently unstable over long periods of time. This instability leads to a catastrophic nonequilibrium phase transition that destroy the true structure of the fluid. We identify the source of this instability as a lack of momentum conservation, resulting from numerical round-off errors. We show that this error grows exponentially in the direction of compression, and present two numerical recipes that involve only minor perturbations to the particle trajectories to guarantee momentum conservation.

Comparison of planar shear flow and planar elongational flow for systems of small molecules

We use nonequilibrium molecular dynamics to simulate steady state planar shear flow and planar elongational flow of fluids of small molecules at constant volume and temperature. The systems studied are Lennard–Jones diatomic molecules (chlorine), and a series of linear Lennard–Jones molecules with one, two, and four sites. In our simulations of planar elongational flow, we employ Kraynik–Reinelt periodic boundary conditions, which allow us to obtain precise values of the steady state planar elongational viscosity. We validate our application of Kraynik–Reinelt periodic boundary conditions by comparing the zero strain rate shear and elongational viscosities. The results show that the elongational viscosity is proportional to the shear viscosity in the zero strain rate limit, as expected. The viscosity, pressure, and internal energy of the atomic Lennard–Jones fluid show exactly the same behavior for the two types of flow when both sets of results are plotted against the second scalar invariant of the strai...

Viscosity of confined inhomogeneous nonequilibrium fluids

We use the nonlocal linear hydrodynamic constitutive model, proposed by Evans and Morriss [Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)], for computing an effective spatially dependent shear viscosity of inhomogeneous nonequilibrium fluids. The model is applied to a simple atomic fluid undergoing planar Poiseuille flow in a confined channel of several atomic diameters width. We compare the spatially dependent viscosity with a local generalization of Newtons law of viscosity and the Navier-Stokes viscosity, both of which are known to suffer extreme inaccuracies for highly inhomogeneous systems. The nonlocal constitutive model calculates effective position dependent viscosities that are free from the notorious singularities experienced by applying the commonly used local constitutive model. It is simple, general, and has widespread applicability in nanofluidics where experimental measurement of position dependent transport coefficients is currently inaccessible. In principle the method can be used to predict approximate flow profiles of any arbitrary inhomogeneous system. We demonstrate this by predicting the flow profile for a simple fluid undergoing planar Couette flow in a confined channel of several atomic diameters width.