Nanoflow hydrodynamics

We show by nonequilibrium molecular dynamics simulations that the Navier-Stokes equation does not correctly describe water flow in a nanoscale geometry. It is argued that this failure reflects the fact that the coupling between the intrinsic rotational and translational degrees of freedom becomes important for nanoflows. The coupling is correctly accounted for by the extended Navier-Stokes equations that include the intrinsic angular momentum as an independent hydrodynamic degree of freedom.

Prediction of fluid velocity slip at solid surfaces

The observed flow enhancement in highly confining geometries is believed to be caused by fluid velocity slip at the solid wall surface. Here we present a simple and highly accurate method to predict this slip using equilibrium molecular dynamics. Unlike previous equilibrium molecular dynamics methods, it allows us to directly compute the intrinsic wall-fluid friction coefficient rather than an empirical friction coefficient that includes all sources of friction for planar shear flow. The slip length predicted by our method is in excellent agreement with the slip length obtained from direct nonequilibrium molecular dynamics simulations.

Viscosity kernel of molecular fluids: butane and polymer melts

The wave-vector dependent shear viscosities for butane and freely jointed chains have been determined. The transverse momentum density and stress autocorrelation functions have been determined by equilibrium molecular dynamics in both atomic and molecular hydrodynamic formalisms. The density, temperature, and chain length dependencies of the reciprocal and real-space viscosity kernels are presented. We find that the density has a major effect on the shape of the kernel. The temperature range and chain lengths considered here have by contrast less impact on the overall normalized shape. Functional forms that fit the wave-vector-dependent kernel data over a large density and wave-vector range have also been tested. Finally, a structural normalization of the kernels in physical space is considered. Overall, the real-space viscosity kernel has a width of roughly 3-6 atomic diameters, which means that generalized hydrodynamics must be applied in predicting the flow properties of molecular fluids on length scales where the strain rate varies sufficiently in the order of these dimensions (e.g., nanofluidic flows).

An extended analysis of the viscosity kernel for monatomic and diatomic fluids

We present an extended analysis of the wavevector dependent shear viscosity of monatomic and diatomic (liquid chlorine) fluids over a wide range of wavevectors and for a variety of state points. The analysis is based on equilibrium molecular dynamics simulations, which involve the evaluation of transverse momentum density and shear stress autocorrelation functions. For liquid chlorine we present the results in both atomic and molecular formalisms. We find that the viscosity kernel of chlorine in the atomic representation is statistically indistinguishable from that in the molecular representation. The results further suggest that the real space viscosity kernels of monatomic and diatomic fluids depend sensitively on the density, the potential energy function and the choice of fitting function in reciprocal space. It is also shown that the reciprocal space shear viscosity data can be fitted to two different simple functional forms over the entire density, temperature and wavevector range: a function composed of n-Gaussian terms and a Lorentzian-type function. Overall, the real space viscosity kernel has a width of 3-6 atomic diameters, which means that the generalized hydrodynamic constitutive relation is required for fluids with strain rates that vary nonlinearly over distances of the order of atomic dimensions.

Viscous properties of isotropic fluids composed of linear molecules: departure from the classical Navier-Stokes theory in nano-confined geometries

In this paper we present equilibrium molecular-dynamics results for the shear, rotational, and spin viscosities for fluids composed of linear molecules. The density dependence of the shear viscosity follows a stretched exponential function, whereas the rotational viscosity and the spin viscosities show approximately power-law dependencies. The frequency-dependent shear and spin viscosities are also studied. It is found that viscoelastic behavior is first manifested in the shear viscosity and that the real part of the spin viscosities features a maximum for nonzero frequency. The calculated transport coefficients are used together with the extended Navier-Stokes equations to investigate the effect of the coupling between the intrinsic angular momentum and linear momentum for highly confined fluids. Both steady and oscillatory flows are studied. It is shown, for example, that the fluid flow rate for Poiseuille flow is reduced by up to 10% in a 2 nm channel for a buta-triene fluid at density 236 kg m(-3) and temperature 306 K. The coupling effect may, therefore, become very important for nanofluidic applications.

Dynamical properties of a confined diatomic fluid undergoing zero mean oscillatory flow: effect of molecular rotation

In this paper we investigate the spatiotemporal dynamics of a diatomic fluid undergoing zero mean oscillatory flow in a slit pore. The study is based on nonequilibrium molecular dynamics simulations together with two limiting solutions to the Navier-Stokes equations which include the effect of molecular rotation. By examining the viscoelastic properties of the system we can estimate the extent of the Newtonian regime, and a direct comparison between the molecular dynamics data and the solutions to the Navier-Stokes equations is then possible. It is found that the agreement is excellent, and that the vortex viscosity can be estimated by fitting the data obtained in the molecular dynamics simulations to the solutions to the Navier-Stokes equations. The quantitative effect of the coupling between the linear momentum and the spin angular momentum on flow is also investigated. We find that the maximum flow can be reduced up to 3-4 % due to the coupling.

Nonlocal shear stress for homogeneous fluids

It has been suggested that for fluids in which the rate of strain varies appreciably over length scales of the order of the intermolecular interaction range, the viscosity must be treated as a nonlocal property of the fluid. The shear stress can then be postulated to be a convolution of this nonlocal viscosity kernel with the strain rate over all space. In this Letter, we confirm that this postulate is correct by a combination of analytical and numerical methods for an atomic fluid out of equilibrium. Furthermore, we show that a gradient expansion of the nonlocal constitutive equation gives a reasonable approximation to the shear stress in the small wave vector limit.

Parameterization of the nonlocal viscosity kernel for an atomic fluid

In this paper we present results for the wave-vector dependent shear viscosity for a model atomic fluid with short ranged repulsive interactions computed by molecular dynamics simulations. It is shown that the data can be fitted to two different simple functional forms over a large density range, namely, a function composed of two Gaussian terms and a Lorentzian type function with a variable wave-vector exponent. The parameters of both functional forms are found to obey simple density dependencies. While the first functional form has the advantage that the inverse Fourier transform can be found analytically, the Lorentzian type function fits the wave-vector dependence better over the range of wave vectors and densities studied here. The results show that the real space viscosity kernel has a width of 2 to 3 atomic diameters. This means that the generalized hydrodynamic constitutive relation is required if the strain rate varies significantly over this distance, a situation commonly encountered for nanofluidic flows.

Molecular-dynamics simulation of model polymer nanocomposite rheology and comparison with experiment

The shear-rate dependence of viscosity is studied for model polymer melts containing various concentrations of spherical filler particles by molecular-dynamics simulations, and the results are compared with the experimental results for calcium-carbonate-filled polypropylene. Although there are some significant differences in scale between the simulated model polymer composite and the system used in the experiments, some important qualitative similarities in shear behavior are observed. The trends in the steady-state shear viscosities of the simulated polymer-filler system agree with those seen in the experimental results; shear viscosities, zero-shear viscosities, and the rate of shear thinning are all seen to increase with filler content in both the experimental and simulated systems. We observe a significant difference between the filler volume fraction dependence of the zero-shear viscosity of the simulated system and that of the experimental system that can be attributed to a large difference in the ratio of the filler particle radius to the radius of gyration of the polymer molecules. In the simulated system, the filler particles are so small that they only have a weak effect on the viscosity of the composite at low filler volume fraction, but in the experimental system, the viscosity of the composite increases rapidly with increasing filler volume fraction. Our results indicate that there exists a value of the ratio of the filler particle radius to the polymer radius of gyration such that the zero-shear-rate viscosity of the composite becomes approximately independent of the filler particle volume fraction.

Structural and dynamical properties for confined polymers undergoing planar Poiseuille flow

The authors present the results from nonequilibrium molecular dynamics simulations for the structural and dynamical properties of highly confined linear polymer fluids undergoing planar Poiseuille flow. They study systems confined within pores of several atomic diameters in width and investigate the dependence of the density profiles, the mean squared radius of gyration, the mean squared end-to-end distance, streaming velocity, strain rate, shear stress, and streaming angular velocity as functions of average fluid density and chain length. Their simulation results show that, sufficiently far from the walls, the radius of gyration for molecules under shear in the middle of the pore follows the power law Rg=ANbnu, where Nb is the number of bonds and the exponent has a value of 0.5 which resembles the value for a homogeneous equilibrium fluid. Under the conditions simulated, the authors find the onset of flat velocity profiles but with very little wall slippage. These flat profiles are most likely due to the restricted layering of the fluid into just one or two molecular layers for narrow pore widths compared to chain length, rather than typical plug-flow conditions. The angular velocity is shown to be proportional to half the strain rate in the pore interior when the chain length is sufficiently small compared to the pore width, consistent with the behavior for homogeneous fluids in the linear regime.

Local linear viscoelasticity of confined fluids

In this paper the authors propose a novel method to study the local linear viscoelasticity of fluids confined between two walls. The method is based on the linear constitutive equation and provides details about the real and imaginary parts of the local complex viscosity. They apply the method to a simple atomic fluid undergoing zero mean oscillatory flow using nonequilibrium molecular dynamics simulations. The method shows that the viscoelastic properties of the fluid exhibit dramatic spatial changes near the wall-fluid boundary due to the high density in this region. It is also shown that the real part of the viscosity converges to the frequency dependent local shear viscosity sufficiently far away from the wall. This also provides valuable information about the transport properties in the fluid, in general. The viscosity is compared with predictions from the local average density model. The two methods disagree in that the local average density model predicts larger viscosity variations near the wall-fluid boundary than what is observed through the method presented here.

Viscosity of a binary mixture: approach to the hydrodynamic limit

We have used equilibrium and nonequilibrium molecular dynamics simulations to study the solute self-diffusion coefficient and the shear rate dependence of the solution viscosity in solutions of model nanocolloidal particles that range in mass ratio from mu=1 up to mu=50 and size ratio from s=1 up to s=4.03 at various concentrations. The zero shear rate viscosities and the initial rates of shear thinning were determined from data in the shear rate region in which the suspension is strongly shear thinning while the solvent remains Newtonian or is weakly shear thinning. The rate of shear thinning increased dramatically with solute volume fraction, regardless of whether the increase was due to increasing solute size or increasing the solute concentration. In a series of simulations in which the mass ratio was varied while keeping the size ratio fixed at s=1, we found that the approach of the viscosities and self-diffusion coefficients to their limiting mass ratio independent values was well described by a rather simple exponential dependence on mass ratio. The concentration dependence of the limiting infinite mass ratio values of the self-diffusion coefficients and zero shear rate viscosities were determined, and used to compute the hydrodynamic radius RH of the solute particles by various methods. The values of RH that were obtained by the different methods were reasonably consistent with each other, and indicated that the radius at which the slip boundary condition holds is slightly smaller than the cross-interaction radius between the solute and solvent particles.

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.

Generalized Fourier law for heat flow in a fluid with a strong, nonuniform strain rate

We derive the leading terms of a generalized Fourier law for heat conduction in fluids under strong, nonuniform shear by expanding the heat flux vector as a Taylor series about the equilibrium state in powers of the temperature gradient, the velocity gradient (the first spatial derivative of the streaming velocity or the strain rate tensor), and, in an extension of previous work, the second spatial derivative of the streaming velocity (a third rank tensor). This results in a general macroscopic constitutive equation, independent of any microscopic model, and valid for all flow geometries. Assuming that the fluid is isotropic at equilibrium, we find a term representing heat flow due to a gradient in the square of the strain rate. This shows that it is possible for a nonuniform velocity gradient to generate a heat flow in the absence of a temperature gradient. We also find terms corresponding to heat flow parallel to the streamlines that are not present in uniform shear flow.