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.

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.

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.

Non-Newtonian behavior and molecular structure of Cooee bitumen under shear flow: A non-equilibrium molecular dynamics study.

The rheology and molecular structure of a model bitumen (Cooee bitumen) under shear are investigated in the non-Newtonian regime using non-equilibrium molecular dynamics simulations. The shear viscosity, normal stress differences, and pressure of the bitumen mixture are computed at different shear rates and different temperatures. The model bitumen is shown to be a shear-thinning fluid at all temperatures. In addition, the Cooee model is able to reproduce experimental results showing the formation of nanoaggregates composed of stacks of flat aromatic molecules in bitumen. These nanoaggregates are immersed in a solvent of saturated hydrocarbon molecules. At a fixed temperature, the shear-shinning behavior is related not only to the inter- and intramolecular alignments of the solvent molecules but also to the decrease of the average size of the nanoaggregates at high shear rates. The variation of the viscosity with temperature at different shear rates is also related to the size and relative composition of the nanoaggregates. The slight anisotropy of the whole sample due to the nanoaggregates is considered and quantified. Finally, the position of bitumen mixtures in the broad literature of complex systems such as colloidal suspensions, polymer solutions, and associating polymer networks is discussed.

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.

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 ß-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.

A new and effective method for thermostatting confined fluids.

We present a simple thermostatting method suitable for nanoconfined fluid systems. Two conventional strategies involve thermostatting the fluid directly or employing a thermal wall that couples only the wall atoms with the thermostat. When only a thermal wall is implemented, the temperature control of the fluid is true to the actual experiment and the heat is transferred from the fluid to the walls. However, for large or complex systems it can often be computationally prohibitive to employ thermal walls. To overcome this limitation many researchers choose to freeze wall atoms and instead apply a synthetic thermostat to the fluid directly through the equations of motion. This, however, can have serious consequences for the mechanical, thermodynamic, and dynamical properties of the fluid by introducing unphysical behaviour into the system [Bernardi et al., J. Chem. Phys. 132, 244706 (2010)]. In this paper, we propose a simple scheme which enables working with both frozen walls and naturally thermostatted liquids. This is done by superimposing the walls with oscillating particles, which vibrate on the edge of the fluid control volume. These particles exchange energy with the fluid molecules, but do not interact with wall atoms or each other, thus behaving as virtual particles. Their displacements violate the Lindemann criterion for melting, in such a way that the net effect would not amount to an additional confining surface. One advantage over standard techniques is the reduced computational cost, particularly for large walls, since they can be kept rigid. Another advantage over accepted strategies is the opportunity to freeze complex charged walls such as ß-cristobalite. The method furthermore overcomes the problem with polar fluids such as water, as thermalized charged surfaces require higher spring constants to preserve structural stability, due to the effects of strong Coulomb interactions, thus inevitably degrading the thermostatting efficiency.

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.

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.

Linear and nonlinear density response functions for a simple atomic fluid.

We use molecular dynamics simulations to investigate the linear and nonlinear density response functions for simple fluids under the influence of spatially periodic external fields. Using a direct Fourier space decomposition of the instantaneous microscopic density for the perturbed fluid we can clearly identify the distinct order of response. Using a single component sinusoidal longitudinal force for a set of wavelengths and amplitudes we show that in the linear response regime the proportionality between the external field amplitude and the density perturbation can be used to determine the linear density response function, and hence the pair correlation function, static liquid structure factor, and lowest order direct correlation function. We show also that for large external field amplitudes a single component external field can be used to determine the form for lowest order and second lowest order nonlinear response functions for restricted regions of the total response function spaces.

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.

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.

Interfacial slip friction at a fluid-solid cylindrical boundary.

Recently we proposed a method to calculate the interfacial friction coefficient between fluid and solid at a planar interface. In this work we extend the method to cylindrical systems where the friction coefficient is curvature dependent. We apply the method to methane flow in carbon nanotubes, and find good agreement with non-equilibrium molecular dynamics simulations. The proposed method is robust, general, and can be used to predict the slip for cylindrical nanofluidic systems.

Slip length of water on graphene: limitations of non-equilibrium molecular dynamics simulations.

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.