Slip and stress from low shear rate nonequilibrium molecular dynamics: The transient-time correlation function technique

We derive the transient-time correlation function (TTCF) expression for the computation of phase variables of inhomogenous confined atomistic fluids undergoing boundary-driven planar shear (Couette) flow at constant pressure. Using nonequilibrium molecular dynamics simulations, we then apply the TTCF formalism to the computation of the shear stress and the slip velocity for atomistic fluids at realistic low shear rates, in systems under constant pressure and constant volume. We show that, compared to direct averaging of multiple trajectories, the TTCF method dramatically improves the accuracy of the results at low shear rates and that it is suitable to investigate the tribology and rheology of atomistically detailed confined fluids at realistic flow rates.

Hydrodynamic slip of alkali chloride solutions in uncharged graphene nanochannels

Using non-equilibrium molecular dynamics simulations, we demonstrate the effect of concentration and alkali cation types (K⁺, Na⁺, and Li⁺) on the hydrodynamic slip of aqueous alkali chloride solutions in an uncharged graphene nanochannel. We modeled the graphene-electrolyte interactions using the potential of Williams et al. [J. Phys. Chem. Lett. 8, 703 (2017)], which uses optimized graphene-ion Lennard-Jones interaction parameters to effectively account for surface and solvent polarizability effects on the adsorption of ions in an aqueous solution to a graphene surface. In our study, the hydrodynamic slip exhibits a decreasing trend for alkali chloride solutions with increasing salt concentration. The NaCl solution shows the highest reduction in the slip length followed by KCl and LiCl solutions, and the reduction in the slip length is very much dependent on the salt type. We also compared the slip length with that calculated using a standard unoptimized interatomic potential obtained from the Lorentz-Berthelot mixing rule for the ion-carbon interactions, which is not adjusted to account for the surface and solvent polarizability at the graphene surface. In contrast to the optimized model, the slip length of alkali chloride solutions in the unoptimized model shows only a nominal change with salt concentration and is also independent of the nature of salts. Our study shows that adoption of the computationally inexpensive optimized potential of Williams et al. for the graphene-ion interactions has a significant influence on the calculation of slip lengths for electrolyte solutions in graphene-based nanofluidic devices.

Electropumping of nanofluidic water by linear and angular momentum coupling: theoretical foundations and molecular dynamics simulations

In this article we review the relatively new phenomenon of electropumping in nanofluidic systems, in which nonzero net flow results when polar molecules are rotated by external electric fields. The flow is a consequence of coupling of the spin angular momentum of molecules with their linear streaming momentum. By devising confining surfaces that are asymmetric - specifically one surface is more hydrophobic compared to the other - unidirectional flow results and so pumping can be achieved without the use of pressure gradients. We first cover the historical background to this phenomenon and follow that with a detailed theoretical description of the governing hydrodynamics. Following that we summarise work that has applied this phenomenon to pump water confined to planar nanochannels, semi-functionalised single carbon nanotubes and concentric carbon nanotubes. We also report on the energy efficiency of this pumping technique by comparisons with traditional flows of planar Couette and Poiseuille flow, with the surprising conclusion that electropumping at the nanoscale is some 4 orders of magnitude more efficient than pumping by Poiseuille flow.

Efficiency of Electropumping in Nanochannels

Electropumping has been shown to be an effective means of inducing a net positive flow in fluids confined within planar nanochannels and carbon nanotubes. In this Letter, we investigate the efficiency of electropumping relative to Couette and Poiseuille flows. We apply a spatially uniform rotating electric field to a fluid confined in a functionalized nanochannel that couples the water's permanent dipole moment resulting in a net positive flow. We then induce a net positive flow in nanochannels for Couette and Poiseuille flows, matching volume flow rates to allow a direct comparison of average power dissipation per unit volume between all flow types. We show that while electropumping is less efficient than Couette flow, it is 4 orders of magnitude more efficient than Poiseuille flow. This suggests that, rather than being a mere novelty, electropumping is a far more energetically efficient means of transporting water compared to conventional pressure driven pumping.

Inducing a Net Positive Flow of Water in Functionalized Concentric Carbon Nanotubes Using Rotating Electric Fields

Electropumping has shown great potential as an effective means of inducing a net positive flow of water in confined channels. In this paper we present the first nonequilibrium molecular dynamics study and continuum based numerical solutions that demonstrate an effective net positive flow between concentric carbon nanotubes (CNT) using electropumping. We apply a spatially uniform rotating electric field that couples to the water's permanent dipole moment. Taking advantage of the coupling between the spin angular momentum and the linear momentum we break the symmetry of the channel radius by functionalizing the inner CNT's outer surface with carboxyl groups to induce a net positive flow. We also show that our results for concentric nanotubes are consistent with our previous work where we demonstrated that an increase in functionalization beyond an optimal point in a single walled carbon nanotube resulted in a decrease in positive net flow. We then numerically solve the coupled hydrodynamic momentum equations to show that the nonequilibrium molecular dynamics results are consistent with the continuum theory.

Compositional relaxation on the approach to the glass transition in a model trehalose solution

Molecular dynamics simulation was used to study the temperature dependence of the mutual diffusion coefficient D_{m} and the intermediate scattering function of equilibrium and metastable aqueous solutions of the cryoprotectant molecule trehalose at very low (2.2 and 9wt.%) and very high (80 and 95wt.%) concentrations. The simulations were conducted over a range of temperatures approaching the glass transition temperature T_{g} for each concentration. Similar to a recent observation made on a glass-forming model polydisperse colloidal suspension [Hannam et al., Phys. Rev. E 96, 022609 (2017)2470-004510.1103/PhysRevE.96.022609], we confirmed by a set of independent computations that D_{m} is responsible for the long-time decay of the intermediate scattering function. We observed that D_{m} decreased on the approach to the glass transition temperature, resulting in an extremely slow long-time decay in the intermediate scattering function that culminated in the arrest of compositional fluctuations and a plateau in the intermediate scattering function at T_{g}. In both cases, crystallization requires a change in the composition of the solution, which is a process controlled by D_{m}. This transport coefficient can either increase or decrease as solidification is approached, because it depends on a product of thermodynamic and mobility factors. Our observations show that in both cases, for the glass-forming liquids, it is observed to decrease, while for a previously studied monodisperse colloidal suspension which crystallizes easily, it increases. The similarity in the behavior of these two very different glass-forming systems (the polydisperse colloidal suspension and the sugar solution) shows the importance of the mutual diffusion coefficient to our understanding of vitrification and suggests a possible distinction between between glass-forming and crystallizing solutions.

Measuring heat flux beyond Fourier's law

We use nonequilibrium molecular dynamics to explore the effect of shear flow on heat flux. By simulating a simple fluid in a channel bounded by tethered atoms, the heat flux is computed for two systems: a temperature driven one with no flow and a wall driven, Couette flow system. The results for the temperature driven system give Fourier's law thermal conductivity, which is shown to agree well with experiments. Through comparison of the two systems, we quantify the additional components of the heat flux parallel and normal to the walls due to shear flow. To compute the heat flux in the flow direction, the Irving-Kirkwood equations are integrated over a volume, giving the so-called volume average form, and they are also manipulated to get expressions for the surface averaged and method of planes forms. The method of planes and volume average forms are shown to give equivalent results for the heat flux when using small volumes. The heat flux in the flow direction is obtained consistently over a range of simulations, and it is shown to vary linearly with strain rate, as predicted by theory. The additional strain rate dependent component of the heat flux normal to the wall is obtained by fitting the strain rate dependence of the heat flux to the expected form. As a result, the additional terms in the thermal conductivity tensor quantified in this work should be experimentally testable.

Dramatic slowing of compositional relaxations in the approach to the glass transition for a bimodal colloidal suspension

Molecular dynamics simulation was used to study a model colloidal suspension with two species of slightly different sized colloidal particles in an explicit solvent. In this work we calculated the four interdiffusion coefficients for the ternary system, which were then used to calculate the decay coefficients D_{±} of the two independent diffusive modes. We found that the slower D_{-} decay mode, which is associated with the system's ability to undergo compositional changes, was responsible for the long-time decay in the intermediate scattering function. We also found that a decrease in D_{-} to negligible values at a packing fraction of Φ_{g}=0.592 resulted in an extreme slow-down in the long-time decay of the intermediate scattering function often associated with the glass transition. Above Φ_{g}, the system formed a long-lived metastable state that did not relax to its equilibrium crystal state within the simulation time window. We concluded that the inhibition of crystallization was caused by the inability of the quenched fluid to undergo the compositional changes needed for the formation of the equilibrium crystal.

Dynamics of a model colloidal suspension from dilute to freezing

Molecular dynamics simulation was used to study a model colloidal suspension at a range of packing fractions from the dilute limit up to the freezing point. This study builds on previous work by the authors which modeled the colloidal particles with a hard core surrounded by a Weeks-Chandler-Anderson potential with modified interaction parameters, and included an explicit solvent. In this work, we study dynamical properties of the model by first calculating the velocity autocorrelation function, the self-diffusion coefficient, and the mutual diffusion coefficient. We also perform detailed calculations of the colloidal particle intermediate scattering function to study the change in dynamics leading up to the freezing point, and to determine whether the current model can be used to interpret light scattering experiments. We then perform a multiexponential analysis on the intermediate scattering function results and find that the data are fitted well by the sum of two exponentials, which is in line with previous analysis of experimental colloidal suspensions. The amplitudes and decay coefficients of the two modes are determined over a large range of wave vectors at packing fractions leading up to the freezing point. We found that the maximum wave vector at which macroscopic diffusive behavior was observed decreased as the packing fraction increased, and a simple extrapolation shows the maximum wave vector going to zero at the melting point. Lastly, the ratio of the two decay coefficients is compared to the scaling law proposed by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)PRLTAO0031-900710.1103/PhysRevLett.77.771]. It was found that the ratio was not constant, but instead was wave vector dependent.

Effects of Confinement on the Dielectric Response of Water Extends up to Mesoscale Dimensions

The extent of confinement effects on water is not clear in the literature. While some properties are affected only within a few nanometers from the wall surface, others are affected over long length scales, but the range is not clear. In this work, we have examined the dielectric response of confined water under the influence of external electric fields along with the dipolar fluctuations at equilibrium. The confinement induces a strong anisotropic effect which is evident up to 100 nm channel width, and may extend to macroscopic dimensions. The root-mean-square fluctuations of the total orientational dipole moment in the direction perpendicular to the surfaces is 1 order of magnitude smaller than the value attained in the parallel direction and is independent of the channel width. Consequently, the isotropic condition is unlikely to be recovered until the channel width reaches macroscopic dimensions. Consistent with dipole moment fluctuations, the effect of confinement on the dielectric response also persists up to channel widths considerably beyond 100 nm. When an electric field is applied in the perpendicular direction, the orientational relaxation is 3 orders of magnitude faster than the dipolar relaxation in the parallel direction and independent of temperature.

Nonlocal response functions for predicting shear flow of strongly inhomogeneous fluids. II. Sinusoidally driven shear and multisinusoidal inhomogeneity

We use molecular-dynamics computer simulations to investigate the density, strain-rate, and shear-pressure responses of a simple model atomic fluid to transverse and longitudinal external forces. We have previously introduced a response function formalism for describing the density, strain-rate, and shear-pressure profiles in an atomic fluid when it is perturbed by a combination of longitudinal and transverse external forces that are independent of time and have a simple sinusoidal spatial variation. In this paper, we extend the application of the previously introduced formalism to consider the case of a longitudinal force composed of multiple sinusoidal components in combination with a single-component sinusoidal transverse force. We find that additional harmonics are excited in the density, strain-rate, and shear-pressure profiles due to couplings between the force components. By analyzing the density, strain-rate, and shear-pressure profiles in Fourier space, we are able to evaluate the Fourier coefficients of the response functions, which now have additional components describing the coupling relationships. Having evaluated the Fourier coefficients of the response functions, we are then able to accurately predict the density, velocity, and shear-pressure profiles for fluids that are under the influence of a longitudinal force composed of two or three sinusoidal components combined with a single-component sinusoidal transverse force. We also find that in the case of a multisinusoidal longitudinal force, it is sufficient to include only pairwise couplings between different longitudinal force components. This means that it is unnecessary to include couplings between three or more force components in the case of a longitudinal force composed of many Fourier components, and this paves the way for a highly accurate but tractable treatment of nonlocal transport phenomena in fluids with density and strain-rate inhomogeneities on the molecular length scale.

Nonlocal response functions for predicting shear flow of strongly inhomogeneous fluids. I. Sinusoidally driven shear and sinusoidally driven inhomogeneity

We present theoretical expressions for the density, strain rate, and shear pressure profiles in strongly inhomogeneous fluids undergoing steady shear flow with periodic boundary conditions. The expressions that we obtain take the form of truncated functional expansions. In these functional expansions, the independent variables are the spatially sinusoidal longitudinal and transverse forces that we apply in nonequilibrium molecular-dynamics simulations. The longitudinal force produces strong density inhomogeneity, and the transverse force produces sinusoidal shear. The functional expansions define new material properties, the response functions, which characterize the system's nonlocal response to the longitudinal force and the transverse force. We find that the sinusoidal longitudinal force, which is mainly responsible for the generation of density inhomogeneity, also modulates the strain rate and shear pressure profiles. Likewise, we find that the sinusoidal transverse force, which is mainly responsible for the generation of sinusoidal shear flow, can also modify the density. These cross couplings between density inhomogeneity and shear flow are also characterized by nonlocal response functions. We conduct nonequilibrium molecular-dynamics simulations to calculate all of the response functions needed to describe the response of the system for weak shear flow in the presence of strong density inhomogeneity up to the third order in the functional expansion. The response functions are then substituted directly into the truncated functional expansions and used to predict the density, velocity, and shear pressure profiles. The results are compared to the directly evaluated profiles from molecular-dynamics simulations, and we find that the predicted profiles from the truncated functional expansions are in excellent agreement with the directly computed density, velocity, and shear pressure profiles.

Computation of thermodynamic and transport properties to predict thermophoretic effects in an argon-krypton mixture

Thermophoresis is the movement of molecules caused by a temperature gradient. Here we report the results of a study of thermophoresis using non-equilibrium molecular dynamics simulations of a confined argon-krypton fluid subject to two different temperatures at thermostated walls. The resulting temperature profile between the walls is used along with the Soret coefficient to predict the concentration profile that develops across the channel. We obtain the Soret coefficient by calculating the mutual diffusion and thermal diffusion coefficients. We report an appropriate method for calculating the transport coefficients for binary systems, using the Green-Kubo integrals and radial distribution functions obtained from equilibrium molecular dynamics simulations of the bulk fluid. Our method has the unique advantage of separating the mutual diffusion and thermal diffusion coefficients, and calculating the sign and magnitude of their individual contributions to thermophoresis in binary mixtures.

Molecular dynamics study of nanoconfined water flow driven by rotating electric fields under realistic experimental conditions

In our recent work, J. Chem. Phys. 2013, 138, 154712, we demonstrated the feasibility of unidirectional pumping of water, exploiting translational-rotational momentum coupling using nonequilibrium molecular dynamics simulations. Flow can be sustained when the fluid is driven out of equilibrium by an external spatially uniform rotating electric field and confined between two planar surfaces exposing different degrees of hydrophobicity. The permanent dipole moment of water follows the rotating field, thus inducing the molecules to spin, and the torque exerted by the field is continuously injected into the fluid, enabling a steady conversion of spin angular momentum into linear momentum. The translational-rotational coupling is a sensitive function of the rotating electric field parameters. In this work, we have found that there exists a small energy dissipation region attainable when the frequency of the rotating electric field matches the inverse of the dielectric relaxation time of water and when its amplitude lies in a range just before dielectric saturation effects take place. In this region, that is, when the frequency lies in a small window of the microwave region around ∼20 GHz and amplitude ∼0.03 V Å(-1), the translational-rotational coupling is most effective, yielding fluid velocities of magnitudes of ∼2 ms(-1) with only moderate fluid heating. In this work, we also confine water to a realistic nanochannel made of graphene giving a hydrophobic surface on one side and β-cristobalite giving a hydrophilic surface on the other, reproducing slip-and-stick velocity boundary conditions, respectively. This enables us to demonstrate that in a realistic environment, the coupling can be effectively exploited to achieve noncontact pumping of water at the nanoscale. A quantitative comparison between nonequilibrium molecular dynamics and analytical solutions of the extended Navier-Stokes equations, including an external rotating electric field has been performed, showing excellent agreement when the electric field parameters match the aforementioned small energy dissipation region.

Electropumping of water with rotating electric fields

Pumping of fluids confined to nanometer dimension spaces is a technically challenging yet vitally important technological application with far reaching consequences for lab-on-a-chip devices, biomimetic nanoscale reactors, nanoscale filtration devices and the like. All current pumping mechanisms require some sort of direct intrusion into the nanofluidic system, and involve mechanical or electronic components. In this paper, we present the first nonequilibrium molecular dynamics results to demonstrate that non-intrusive electropumping of liquid water on the nanoscale can be performed by subtly exploiting the coupling of spin angular momentum to linear streaming momentum. A spatially uniform rotating electric field is applied to water molecules, which couples to their permanent electric dipole moments. The resulting molecular rotational momentum is converted into linear streaming momentum of the fluid. By selectively tuning the degree of hydrophobicity of the solid walls one can generate a net unidirectional flow. Our results for the linear streaming and angular velocities of the confined water are in general agreement with the extended hydrodynamical theory for this process, though also suggest refinements to the theory are required. These numerical experiments confirm that this new concept for pumping of polar nanofluids can be employed under laboratory conditions, opening up significant new technological possibilities.

Effects of nanoscale density inhomogeneities on shearing fluids

It is well known that density inhomogeneities at the solid-liquid interface can have a strong effect on the velocity profile of a nanoconfined fluid in planar Poiseuille flow. However, it is difficult to control the density inhomogeneities induced by solid walls, making this type of system unsuitable for a comprehensive study of the effect on density inhomogeneity on nanofluidic flow. In this paper, we employ an external force compatible with periodic boundary conditions to induce the density variation, which greatly simplifies the problem when compared to flow in nonperiodic nanoconfined systems. Using the sinusoidal transverse force method to produce shearing velocity profiles and the sinusoidal longitudinal force method to produce inhomogeneous density profiles, we are able to observe the interactions between the two property inhomogeneities at the level of individual Fourier components. This gives us a method for direct measurement of the coupling between the density and velocity fields and allows us to introduce various feedback control mechanisms which customize fluid behavior in individual Fourier components. We briefly discuss the role of temperature inhomogeneity and consider whether local thermal expansion due to nonuniform viscous heating is sufficient to account for shear-induced density inhomogeneities. We also consider the local Newtonian constitutive relation relating the shear stress to the velocity gradient and show that the local model breaks down for sufficiently large density inhomogeneities over atomic length scales.

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.

Generalized extended Navier-Stokes theory: correlations in molecular fluids with intrinsic angular momentum

The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies. To account for the correlations at these scales, we derive a phenomenological expression for the frequency dependent rotational viscosity and wavevector and frequency dependent longitudinal spin viscosity. From this we observe a significant coupling enhancement between the molecular angular velocity and translational velocity for large frequencies in the gas phase; this is not observed for the supercritical fluid and liquid state points.

Effect of kinetic and configurational thermostats on calculations of the first normal stress coefficient in nonequilibrium molecular dynamics simulations

Thermostats for homogeneous nonequilibrium molecular dynamics simulations are usually designed to control the kinetic temperature, but it is now possible control any combination of many different types of temperature, including the configurational and kinetic temperatures and their directional components. It is well known that these temperatures can become unequal in homogeneously thermostatted shearing steady states. The microscopic expressions for these temperatures are all derived from equilibrium distribution functions, and it is pertinent to ask, what are the consequences of using these equilibrium microscopic expressions for temperature in thermostats for shearing nonequilibrium steady states? Here we show that the answer to this question depends on which properties are being investigated. We present numerical results showing that the value of the zero shear rate viscosity obtained by extrapolating results of nonequilibrium molecular dynamics simulations of shearing steady states is the same, regardless of the type of temperature that is controlled. It also agrees with the value obtained from the equilibrium stress autocorrelation function via the Green-Kubo relation. However, the values of the limiting zero shear rate first normal stress coefficient obtained from nonequilibrium molecular dynamics simulations of shearing steady states are strongly dependent on the choice of temperature being controlled. They also differ from the value of the first normal stress coefficient that is calculated from the equilibrium stress autocorrelation function. We show that even when all of the directional components of the kinetic and configurational temperatures are simultaneously controlled to the same value, the agreement with the result obtained from the equilibrium stress autocorrelation function is poor.

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.