Simple theoretical model of shear viscosity in isotopic fluid mixtures

We propose a simple hybrid model for the shear viscosity of isotopic fluid mixtures by coupling the contribution of the Stokes–Einstein relation with the existing linear model of Roults's law for the shear viscosity. The calculated values of shear viscosity using this simple hybrid model are found to be in excellent agreement with the molecular dynamics (MD) simulation results. The calculated value of the shear viscosity obtained from the theoretical model as well as the MD simulation increases with increasing mass ratio.     

Microscopic relationship between colloid–colloid interactions and the rheological behaviour of suspensions: a molecular dynamics-stochastic rotation dynamics investigation

ABSTRACT

We investigate the dependence of the shear viscosity of suspensions of spherical colloids as a function of the volume fraction of the suspension, the colloid–colloid interactions and the shear rate. We couple molecular dynamics to describe the motion of the colloids with stochastic rotation dynamics (MD–SRD) for the fluid environment by means of stochastic collisions, in order to incorporate hydrodynamics effects leading to non-newtonian responses. The shear viscosity is computed using non-equilibrium simulations by imposing explicit velocity gradients. The impact of the colloid–colloid interactions is examined by modelling the inter-colloid pair potential with a repulsive power law, that allows interpolating different degrees of colloidal softness. The general rheological behaviour of our suspensions can be described with a Krieger–Dougherty like equation, which must be corrected to account for the variations in the maximum packing fraction and non-equilibrium effects arising from the flux of momentum imposed to the suspension, which appear when varying the softness of the inter-colloidal interactions. We further show evidence for non-newtonian behaviour at high Péclet numbers, characterised both by shear thinning and shear thickening, and thus demonstrate these effects can be successfully captured using MD–SRD methods.     

Multiscale modeling of the effect of carbon nanotube orientation on the shear deformation properties of reinforced polymer-based composites

A combination of molecular dynamics (MD), continuum elasticity and FEM is used to predict the effect of CNT orientation on the shear modulus of SWCNT-polymer nanocomposites. We first develop a transverse-isotropic elastic model of SWCNTs based on the continuum elasticity and MD to compute the transverse-isotropic elastic constants of SWCNTs. These constants are then used in an FEM-based simulation to investigate the effect of SWCNT alignment on the shear modulus of nanocomposites. Furthermore, shear stress distributions along the nanotube axis and over its cross-sectional area are investigated to study the effect of CNT orientation on the shear load transfer.     

200 A GeV Au + Au collisions serve a nearly perfect quark-gluon liquid

A new robust method to extract the specific shear viscosity (η/s)(QGP) of a quark-gluon plasma (QGP) at temperatures T(c) < T ? 2T(c) from the centrality dependence of the eccentricity-scaled elliptic flow v2/ε measured in ultrarelativistic heavy-ion collisions is presented. Coupling viscous fluid dynamics for the QGP with a microscopic transport model for hadronic freeze-out we find for 200 A GeV Au + Au collisions that v2/ε is a universal function of multiplicity density (1/S)(dN(ch)/dy) that depends only on the viscosity but not on the model used for computing the initial fireball eccentricity ε. Comparing with measurements we find 1<4π(η/s)(QGP) < 2.5 where the uncertainty range is dominated by model uncertainties for the values of ε used to normalize the measured v2.     

Computing Raman and infrared wavenumbers of nanostructures: application to silicon nanowires

The characterization of nanostructures with spectroscopic methods is a fundamental tool in nanoscience. For novel nanostructures, the interpretation of spectral features is a challenging task. To address this issue, we present the “Symmetry‐Filtered Molecular Dynamics (SFMD)” method to calculate Raman and infrared wavenumbers from molecular dynamics (MD) simulations, employing only the symmetry of the atomic structure. Explicit and expensive calculations of the electric polarizability or the dipole moment are not required. Therefore, our method can be easily used with any standard MD software. On the basis of the density functional tight‐binding method for the MD simulations, we apply our method to bulk silicon and small‐diameter hydrogen‐passivated silicon nanowires. For bulk silicon, we study the wavenumber shift of the Raman peak with temperature and obtain results that are in good agreement with experiments. We further show that thermal lattice expansion is a minor effect (22%) and that temperature‐driven anharmonic effects (78%) are the main contributions to that wavenumber shift. By analyzing the bond lengths of different silicon nanowires, we found that surface stress manifests as a 0.37% shortening of bonds only in the outermost silicon layer. We further analyzed the diameter‐dependent wavenumber shift of a Raman peak in silicon nanowires. We found that the main contribution to the wavenumber shift comes from the phonon confinement effect and surface stress leads to an additional shift of 9–22%. Our results indicate that our method is able to produce quantitative results that can be compared with experiments. We propose our method to be used for the understanding of Raman and infrared spectra of novel bulk and nanostructures. Copyright © 2012 John Wiley & Sons, Ltd.     

Properties of hadron and quark matter studied with molecular dynamics

We study the hadron-quark phase transition in a molecular dynamics (MD) of quark degrees of freedom. The hadron state at low density and temperature, and the deconfined quark state at high density and temperature are observed in our model. We investigate the equations of state and draw the phase diagram at wide baryon density and temperature range. We also discuss the transport property, e.g. viscosity, of $q\bar q$ matter. It is found that the ratio of the shear viscosity to the entropy density is less than one for quark matter.     

Molecular Dynamics Simulations of Warm Dense Carbon

We present classical and DFT‐based molecular dynamics (MD) simulations of carbon in the warm dense matter regime (? = 3.7 g/cc, 0.86 eV < T < 8.62 eV [T < 100 eV for classical MD]). Two different classical interatomic potentials are used: 1. LCBOP, designed to simulate condensed (e.g. solid) phases of C, and 2. linearly screened Coulomb (Yukawa) potentials. It is shown that LCBOP over‐predicts minima and maxima in the pair correlation functions of liquid‐C in this regime when compared to the DFT‐MD results. The screened Coulomb model, while under‐correlating at low‐T, seems to produce the correct qualitative features in the static ionic pair distributions at the highest‐T. However, both approaches predict the decay in the ionic contribution of the specific heat as T → ∞ to be much slower than that predicted by a model based on DFT‐MD. These differences in the MD‐derived equations of state in warm dense regimes could have important consequences when using classical inter‐ionic forces such as these in large‐scale MD simulations aimed at studying, for instance, processes of relevance to inertial confinement fusion when C is used as an ablator material. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure,thermodynamic and transport properties of imidazolium-based bis(trifluoromethylsulfonyl)imide ionic liquids from molecular dynamics simulations

Molecular dynamics (MD) simulations have been performed in order to investigate the properties of [C _n mim⁺][Tf₂N^?] (n?=?4,?8,?12) ionic liquids (ILs) in a wide temperature range (298.15?498.15?K) and at atmospheric pressure (1 bar). A previously developed methodology for the calculation of the charge distribution that incorporates ab initio quantum mechanical calculations based on density functional theory (DFT) was used to calculate the partial charges for the classical molecular simulations. The wide range of time scales that characterize the segmental dynamics of these ILs, especially at low temperatures, required very long MD simulations, on the order of several tens of nanoseconds, to calculate the thermodynamic (density, thermal expansion, isothermal compressibility), structural (radial distribution functions between the centers of mass of ions and between individual sites, radial-angular distribution functions) and dynamic (relaxation times of the reorientation of the bonds and the torsion angles, self-diffusion coefficients, shear viscosity) properties. The influence of the temperature and the cation's alkyl chain length on the above-mentioned properties was thoroughly investigated. The calculated thermodynamic (primary and derivative) and structural properties are in good agreement with the experimental data, while the extremely sluggish dynamics of the ILs under study renders the calculation of their transport properties a very complicated and challenging task, especially at low temperatures.     

Hybrid Particle–Continuum Simulations of Polymer Brushes in Shear Flow

A hybrid particle–continuum method is used to study the shear flow confined between two opposing walls, one of which is coated with polymer chains. Molecular dynamics (MD) is used in the particle region near the brush and Navier–Stokes (NS) equations are applied in the remaining region where the continuum assumption holds. The information exchange from the continuum region to the particle region is implemented using the constrained particle dynamics. Both Couette shear flow and oscillatory flow are considered in the present work. The effect of the shear flow on the conformational characteristics of polymer brushes is analyzed. In the overlap region, the velocities obtained from MD simulations are smoothly connected with those from NS equations. Our investigations demonstrate that the hybrid particle–continuum model is valid in exploring the shear behavior of polymer brushes.     

Many body forces between long conducting molecules

Non-equilibrium molecular dynamics is used to calculate the wavevector and strain rate dependence of shear viscosity in a soft sphere fluid. The calculations are consistent with a non-analytic functional dependence of viscosity with wavevector. A consequence of such non-analyticity would be that the linear and non-linear Burnett coefficients for viscosity would not exist for fluids in three dimensions. The calculations also show the numerical consistency of three different non-equilibrium simulation methods for calculating shear viscosity.     

Simulation of screw dislocation motion in iron by molecular dynamics simulations

Molecular dynamics (MD) simulations are used to investigate the response of a/2<111> screw dislocation in iron submitted to pure shear strain. The dislocation glides and remains in a (110) plane; the motion occurs exclusively through the nucleation and propagation of double kinks. The critical stress is calculated as a function of the temperature. A new method is developed and used to determine the activation energy of the double kink mechanism from MD simulations. It is shown that the differences between experimental and simulation conditions lead to a significant difference in activation energy. These differences are explained, and the method developed provides the link between MD and mesoscopic simulations.     

Dynamic Shear Viscosity in a 2D Yukawa System

We present non‐equilibrium molecular dynamics simulation studies on the dynamic (complex) shear viscosity of a 2D many‐particle system interacting via a Yukawa (Debye‐Hückel) type inter‐particle potential. Our investigations reveal the complex interplay of dissipative and elastic processes, as well as the effect of single particle resonances and enhanced collective excitations, and the influence of the external forces on the structural correlations in the system (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of the Pressure Dependence of the Shear Viscosity of Polymer Melts Using a Capillary Rheometer with an Attached Counter Pressure Chamber

A capillary rheometer with an attached counter pressure chamber was used to determine the effect of pressure on the shear viscosity of several polymer melts, i.e., poly(?-caprolactam) (PA6), poly(ethylene terephthalate) (PET), low-density polyethylene (LDPE), and polypropylene (PP). In order to study the rheological properties of the polymer melts at a constant pressure, the measured values of shear viscosity were recalculated with respect to a series of pressures by the least square fitting based on the Barus equation. Different calculation methods were used to calculate the pressure coefficients from the recalculated viscosity values. The resulting pressure coefficients of the shear viscosity demonstrated that the degree of the pressure dependence was highest for PP, followed by PET and then LDPE. PA6 exhibited the lowest pressure coefficient.     

并行化光滑分子动力学方法及其与分子动力学的耦合

提出光滑分子动力学方法(SMD)的并行化计算方法,编制光滑分子动力学以及光滑分子动力学-分子动力学(SMD-MD)耦合的并行程序,并分析铜纳米单晶的单向拉伸和带裂纹板的拉伸问题.光滑分子动力学在分子动力学基础上引入背景网格,在背景网格点上求解运动方程,由此将控制MD临界时间步长的因素化为背景网格单元尺寸,扩大可用的时间积分步长,缩短总计算时间.通过单晶拉伸和带裂纹板拉伸等较大规模问题的计算,验证方法的正确性.与传统分子动力学相比,SMD和SMD-MD耦合方法可以节约计算时间.     

Rotational viscosity of a liquid crystal mixture: a fully atomistic molecular dynamics study

Fully atomistic molecular dynamics (MD) simulations at 293, 303 and 313~K have been performed for the four-component liquid crystal mixture, E7, using the software package Material Studio. Order parameters and orientational time correlation functions (TCFs) were calculated from MD trajectories. The rotational viscosity coefficients (RVCs) of the mixture were calculated using the Nemtsov--Zakharov and Fialkowski methods based on statistical-mechanical approaches. Temperature dependences of RVC and density were discussed in detail. Reasonable agreement between the simulated and experimental values was found.     

Shear Viscosity of Liquid‐Phase Yukawa Plasmas from Molecular Dynamics Simulations on Graphics Processing Units

We have carried out million‐particle equilibrium molecular dynamics simulations of 3‐dimensional Yukawa liquids in order to determine the shear viscosity coefficient. The computations have been executed on Graphics Processing Unit (GPU) architectures with our largely parallelized code. The results cover the strongly coupled liquid phase, with Γ up to the vicinity of the freezing transition, for the 1 ≤ κ ≤ 3 domain of the screening parameter of the Yukawa potential. The good agreement of the present results with those obtained from earlier simulations of significantly smaller systems (consisting of several hundred to several thousand particles) verifies that the viscosity data derived in these smaller scale simulations are also acceptable (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equilibrium molecular dynamics simulation of shear viscosity of two-dimensional complex (dusty) plasmas

Shear viscosity is examined throughout the entire range of strongly coupled states of two-dimensional complex (dusty) plasma liquids (CDPLs). We have employed equilibrium molecular dynamics (EMD) simulation to compute the shear viscosity coefficients of CDPLs. In the strongly coupled liquid region, the values of valid viscosity coefficient can be estimated only in order of magnitude. The variations in the valid viscosity coefficients with screening strength (κ) and Coulomb coupling strengths (Γ) are observed. A systematic dependence of shear viscosity on κ is observed for an intermediate and higher Γ. The investigations showed that the position of the minimum viscosity coefficient shifts towards higher Γ as κ increases. The computational results for the entire range of liquid states of the strongly coupled dusty plasma obtained using the shear autocorrelation functions are in good agreement with the available simulation results and experimental data. It is shown that new simulations extended the range of plasma states (Γ, κ) used in our earlier simulation results for the existence of a finite minimum possible viscosity coefficient and it is also dependent on plasma states.     

液态Co物性的平衡及非平衡分子动力学模拟

本文采用EAM作用势,通过平衡分子动力学(EMD)模拟的方法计算了Co熔体的自扩散系数、剪切粘度等物理性质.同时采用非平衡分子动力学(NEMD)方法计算了Co的剪切粘度.研究表明有关传输性质的计算是可与实验比较的,能够反映出液态Co典型的动力学特性.     

Modified Nosé–Hoover thermostat for solid state for constant temperature molecular dynamics simulation

Nosé–Hoover (NH) thermostat methods incorporated with molecular dynamics (MD) simulation have been widely used to simulate the instantaneous system temperature and feedback energy in a canonical ensemble. The method simply relates the kinetic energy to the system temperature via the particles’ momenta based on the ideal gas law. However, when used in a tightly bound system such as solids, the method may suffer from deriving a lower system temperature and potentially inducing early breaking of atomic bonds at relatively high temperature due to the neglect of the effect of the potential energy of atoms based on solid state physics.     

Numerical methods for computing ground states and dynamics of nonlinear relativistic Hartree equation for boson stars

Efficient and accurate numerical methods are presented for computing ground states and dynamics of the three-dimensional (3D) nonlinear relativistic Hartree equation both without and with an external potential. This equation was derived recently for describing the mean field dynamics of boson stars. In its numerics, due to the appearance of pseudodifferential operator which is defined in phase space via symbol, spectral method is more suitable for the discretization in space than other numerical methods such as finite difference method, etc. For computing ground states, a backward Euler sine pseudospectral (BESP) method is proposed based on a gradient flow with discrete normalization; and respectively, for computing dynamics, a time-splitting sine pseudospectral (TSSP) method is presented based on a splitting technique to decouple the nonlinearity. Both BESP and TSSP are efficient in computation via discrete sine transform, and are of spectral accuracy in spatial discretization. TSSP is of second-order accuracy in temporal discretization and conserves the normalization in discretized level. In addition, when the external potential and initial data for dynamics are spherically symmetric, the original 3D problem collapses to a quasi-1D problem, for which both BESP and TSSP methods are extended successfully with a proper change of variables. Finally, extensive numerical results are reported to demonstrate the spectral accuracy of the methods and to show very interesting and complicated phenomena in the mean field dynamics of boson stars.