Transient molecular dynamics simulations of viscosity for simple fluids

A transient molecular dynamics (TMD) method has been developed for simulation of fluid viscosity. In this method a sinusoidal velocity profile is instantaneously overlaid onto equilibrated molecular velocities, and the subsequent decay of that velocity profile is observed. The viscosity is obtained by matching in a least-squares sense the analytical solution of the corresponding momentum transport boundary-value problem to the simulated decay of the initial velocity profile. The method was benchmarked by comparing results obtained from the TMD method for a Lennard-Jones fluid with those previously obtained using equilibrium molecular dynamics (EMD) simulations. Two different constitutive models were used in the macroscopic equations to relate the shear rate to the stress. Results using a Newtonian fluid model agree with EMD results at moderate densities but exhibit an increasingly positive error with increasing density at high densities. With the initial velocity profiles used in this study, simulated transient velocities displayed clear viscoelastic behavior at dimensionless densities above 0.7. However, the use of a linear viscoelastic model reproduces the simulated transient velocity behavior well and removes the high-density bias observed in the results obtained under the assumption of Newtonian behavior. The viscosity values obtained using the viscoelastic model are in excellent agreement with the EMD results over virtually the entire fluid domain. For simplicity, the Newtonian fluid model can be used at lower densities and the viscoelastic model at higher densities; the two models give equivalent results at intermediate densities.     

A real‐time Mooney‐viscosity prediction model of the mixed rubber based on the Independent Component Regression‐Gaussian Process algorithm

With the rapid development of rubber industry, it becomes more and more important to improve the performance of the quality control system of rubber mixing process. Unfortunately, the large measurement time delay of Mooney viscosity, one of the most important quality parameters of mixed rubber, badly blocks the further development of the issue. The independent component regression‐Gaussian process (ICR‐GP) algorithm is used to solve such typical nonlinear “black‐box” regression problem for the first time to predict Mooney viscosity. In the ICR‐GP method, the non‐Gaussian information is extracted by the independent component regression method firstly, and then the residual Gaussian information is extracted by the Gaussian process method. Meanwhile, both the linear and nonlinear relationships between the input and output variables can be extracted through the ICR‐GP method. With the fact that there is no need to optimize parameters, the ICR‐GP method is especially suitable for “black‐box” regression problems. The highest prediction accuracy was achieved at M = 0.8765 (the root mean square error), which was high enough considering the measuring accuracy (M = ±0.5) of the Mooney viscometer. It is by using the online‐measured rheological parameters as the input variables that the measurement time delay of Mooney viscosity could be dramatically decreased from about 240 to 2 min. Consequently, such Mooney‐viscosity prediction model is very helpful for the development of the rubber mixing process, especially of the emerging one‐step rubber mixing technique. The practical applications performed on the rubber mixing process in a large‐scale tire factory strongly proved the outstanding regression performance of this ICR‐GP Mooney‐viscosity prediction model. Copyright © 2012 John Wiley & Sons, Ltd.     

Transient molecular dynamics simulations of liquid viscosity for nonpolar and polar fluids

A transient molecular dynamics (TMD) method for obtaining fluid viscosity is extended to multisite, force-field models of both nonpolar and polar liquids. The method overlays a sinusoidal velocity profile over the peculiar particle velocities and then records the transient decay of the velocity profile. The viscosity is obtained by regression of the solution of the momentum equation with an appropriate constitutive equation and initial and boundary conditions corresponding to those used in the simulation. The transient velocity decays observed appeared to include both relaxation and retardation effects. The Jeffreys viscoelastic model was found to model accurately the transient responses obtained for multisite models for n-butane, isobutane, n-hexane, water, methanol, and 1-hexanol. TMD viscosities obtained for saturated liquids over a wide range of densities agreed well for the polar fluids, both with nonequilibrium molecular dynamics (NEMD) results using the same force-field models and with correlations based on experimental data. Viscosities obtained for the nonpolar fluids agreed well with the experimental and NEMD results at low to moderate densities, but underpredicted experimental values at higher densities where shear-thinning effects and viscous heating may impact the TMD simulations.     

Including quantum decoherence in surface hopping

In this paper we set up a method called overlap decoherence correction (ODC) to take into account the quantum decoherence effect in a surface hopping framework. While keeping the standard surface hopping approach based on independent trajectories, our method allows to account for quantum decoherence by evaluating the overlap between frozen Gaussian wavepackets, the time evolution of which is obtained in an approximate way. The ODC scheme mainly depends on the parameter σ, which is the Gaussian width of the wavepackets. The performance of the ODC method is tested versus full quantum calculations on three model systems, and by comparison with full multiple spawning (FMS) results for the S(1)→S(0) decay in the azobenzene molecule.     

The effect of temperature and pressure on the retention time in series-coupled gas-chromatographic columns

The promising technique of controlling chromatographic selectivity by the adjustment of individual column temperatures in systems of series-coupled columns is investigated by means of a general model incorporating the effects of temperature and mobile phase compressibility. Expressions are derived for the linear flow velocity, the effective partition coefficient and the retention time for a system of n columns assuming an ideal mobile phase gas, under conditions of constant overall pressure drop and neglect of the temperature dependence of the mobile phase viscosity. The results indicate the importance of thermodynamic parameters, relative to parameters influencing the linear flow velocity, in determining the effect of temperature on the chromatographic retention time. Numerical results are illustrated graphically for two-column systems which are discussed in greater detail. Switching of columns is also discussed and it is shown that even if thermodynamic contributions remain unchanged, non-thermodynamic contributions have a notice-able effect.     

Excitation-emission-lifetime analysis of multicomponent systems—II. Synthetic model data

To determine the efficacy of three-dimensional principal component factor analysis (PCFA) for extracting non-exponential decay parameters from multicomponent data, we have constructed synthetic data matrices which mimic the possible outcomes of experiments in the nanosecond time domain with copper porphyrins. Our results demonstrate that PCFA is capable of determining non-exponential time decay in systems with two and three emitting species. The accuracy of the rate constants determined by this method is limited by the accuracy of the non-linear Marquardt algorithm that we have used for the final fits. Although extremely overlapped components have been resolved using this method, degeneracy in one of the dimensions is problematic.     

Anomalous viscoelasticity near the isotropic-nematic phase transition in liquid crystals

Recent optical Kerr effect experiments have shown that orientational relaxation of nematogens shows a pronounced slow down of the response function at intermediate times and also a power law decay near the isotropic-nematic (I-N) transition. In many aspects, this behavior appears to be rather similar to the ones observed in the supercooled liquid near-glass transition. We have performed molecular dynamics simulations of model nematogens (Gay-Berne with aspect ratio 3) to explore the viscoelasticity near the I-N transition and also investigated the correlation of viscoelasticity (if any) with orientational relaxation. It is found that although the viscosity indeed undergoes a somewhat sharper than normal change near the I-N transition, it is not characterized by any divergence-like behavior (like the ones observed in the supercooled liquid). The rotational friction, on the other hand, shows a much sharper rise as the I-N transition is approached. Interestingly, the probability distribution of the amplitude of the three components of the stress tensor shows anisotropy near the I-N transition-similar anisotropy has also been seen in the deeply supercooled liquid. Frequency dependence of viscosity shows several unusual behaviors: (a) There is a weak, power law dependence on frequency [eta(')(omega) approximately omega(-alpha)] at low frequencies and (b) there is a rapid increase in the sharp peak observed in eta(')(omega) in the intermediate frequency on approach to the I-N transition density. These features can be explained from the stress-stress time correlation function. The angular velocity correlation function also exhibits a power law decay in time. The reason for this is discussed.     

Numerical simulation of the hydrodynamics of an inverse liquid–solid fluidized bed using combined Lattice Boltzmann and smoothed profile methods

Knowledge of an inverse fluidized-bed fluid hydrodynamics is advantageous in optimal adjustment and designing high-efficiency beds. In the present study, a combination of a single relaxation time collision operator lattice Boltzmann method (LBM) and the smoothed profile method (SPM) is employed to simulate the hydrodynamics of an inverse liquid–solid fluidized bed comprising circular monodisperse and polydisperse particles in a rectangular channel. A numerical instance of inverse fluidization involving 231 particles is illustrated to show the capability of the combined methods. Moreover, comparison of the numerical results is performed with the Ergun equation and the Richardson–Zaki correlation. The comparison demonstrates that the present model can simulate the fluid flow behavior in an inverse fluidized bed. Several different models were also presented to investigate the effect of different fluid properties and size of particles in the bed. Simulations indicate that the more the superficial liquid velocity, the higher the porosity of the bed. The present simulations show that porosity of the bed increases by increasing the particles size, and also the vertical velocity of the bed decreases with an increase in liquid viscosity. Finally, polydisperse particle systems are also simulated. The results show that porosity in an inverse fluidized bed comprising polydisperse particles is more than that of a monodisperse particle bed.     

Flow-induced ordering of particles and flow velocity profile transition in a tube flow of graphene oxide dispersions

We measured the S- and P-order parameters of flow-induced ordered graphene oxide (GO) particles and the flow velocity profiles for a flowing aqueous GO dispersion in a tube, by using an optical method. The order parameters clearly exhibit increasing concentric biaxial ordering as the flow velocity increases, with the exception of a disordered centre. Newtonian to non-Newtonian transition in the flow velocity profile is found, changing from a parabolic shape to a fuller shape at very low Reynolds numbers less than 10. This is attributed to the shear thinning effect (i.e., an ordering-induced reduction in viscosity). In the Newtonian flow, a uniaxial ordering was dominant; whereas a biaxial ordering sharply increased in the non-Newtonian flow, indicating that both the ordering of GO particles and the interparticle interactions influence the flow profile transition.     

Mid-infrared (MIR) metabolic fingerprinting of amniotic fluid: A possible avenue for early diagnosis of prenatal disorders?

This work describes a mid-infrared (MIR) metabolic profiling study of 2^nd trimester amniotic fluid in relation to selected prenatal disorders, with results focusing on fetal malformations (FM), preterm delivery (PTD) and premature rupture of membranes (PROM), the latter two conditions occurring later in pregnancy. Partial least squares-discriminant analysis (PLS-DA) models were obtained for FM and pre-PTD subject groups, supported by Monte Carlo Cross Validation (MCCV), and identified specific MIR profile changes. For pre-PROM subjects, minor changes were noted. MIR interpretation was assisted by intra- (MIR/MIR) and inter- (MIR/NMR) domain statistical correlation analysis, the results unveiling possible biomarker MIR signatures for FM and pre-PTD subjects. Biofluid MIR metabolic profiling holds enticing possibilities as a low cost, easy to use, rapid method and the results presented have shown its sensitivity to clinically diagnosed conditions such as FM, and to the pre-clinical stages of PTD. Specific improvement needs are discussed, namely regarding sample numbers and experimental reproducibility.     

On the response of an ionic liquid to external perturbations and the calculation of shear viscosity

In this article, attention is directed to three related problems: (1) the response of the ionic liquid (IL) 1-hexyl-3-methylimidazolium chloride ([HMIM+][Cl-]) to different external perturbations, (2) the calculation of its shear viscosity, and (3) the investigation of the range of validity of linear response theory for these types of systems. For this purpose, we derive a set of equations linking bulk hydrodynamic predictions with microscopic simulations which are valid when linear response theory is applicable. As far as we are aware, this article reports results from the largest atomistic simulations ever performed on this liquid. Our study shows that even for systems with a box length as large as 0.03 mu the viscosities computed from perturbation frequencies compatible with this box size have not yet reached the bulk hydrodynamic limit. This is in sharp contrast with the case of other solvents such as water in which the hydrodynamic limit can be achieved by using perturbations on a length scale of typical molecular dynamics simulation box sizes. In order to achieve our goals, we comprehensively investigated how the IL relaxed upon weak external perturbations at different wavenumbers. We also studied the steady-state flow created by external shear acceleration fields. The short time behavior of instantaneous velocity profiles was compared with the results of linear response theory. The short time response appears to match the prediction from linear response theory, while the long time response deviates as the external field becomes stronger. From this study, the range on which a perturbation can be considered "weak" in the linear response sense can be established. The relaxation of initial velocity profiles was also examined and correlated to the decay of the transverse-current autocorrelation function. Even though none of our calculations reached the bulk hydrodynamic limit, we are able to make predictions for the shear viscosity of the bulk system at different temperatures which qualitatively agree with experimental data.     

Diffusing wave spectroscopy used to study the influence of shear on aggregation

In this study, diffusing wave spectroscopy (DWS) is used to investigate the effect of shear on a food-related aggregating emulsion. The principle of the method is validated using a nonaggregating, nearly monodisperse latex suspension. In general, with increasing shear rate the diffusive motion of the scatterers becomes negligible compared to the convective motion. This causes a decrease in the decay time of the autocorrelation curves and a change in the form of the autocorrelation curves from nearly exponential to Gaussian. This is reflected in the exponent of the mean square displacement that changes from 1 to 2. The effect of shear on the acidification of a sodium caseinate-stabilized emulsion was studied by DWS and by rheometry. The emulsion droplets in the food-related emulsion were uniformly dispersed at neutral pH. Upon acidification down to a pH of 5.2 +/- 0.05, the emulsion showed Newtonian behavior with constant viscosity over the whole pH range. At pH 5.17 +/- 0.05, independent of the applied shear rate during acidification, the viscosity suddenly increased. From this point on, the emulsion showed shear-thinning behavior. The photon-transport mean free path ( l*) was not influenced by the applied shear rate and did not change down to pH 5.2 +/- 0.05. Close to this pH, l* increased, and the decay of the autocorrelation curves shifted to longer correlation times when shear rates smaller than 1 s (-1) were applied. At lower pH (5.05 +/- 0.05), l* started to fluctuate, and the autocorrelation curves no longer decayed to zero, indicating that at these shear rates the system behaved nonergodicly. Assuming that the convective motion and the Brownian motion are independent of each other, the mean square displacement as a result of Brownian motion was determined. From this, the sol-gel point and the radius of the aggregates at this point as a function of the shear rate was determined. The results indicated that the radius of the aggregates at the sol-gel transition decreased with increasing shear rate and suggested that shear will result in a more open structure of the network formed by the aggregates.     

Effect of surface elasticity on the motion of a droplet in a viscous fluid

The motion of a droplet with adsorption layer in a viscous incompressible fluid is studied on the basis of the linearized Navier-Stokes equations. It is shown that dilatational elasticity of the layer has a strong effect on the decay of velocity after a sudden impulse. If the elasticity is sufficiently strong the droplet shows backtracking, i.e., during part of the time the velocity relaxation function becomes negative. The motion is independent of the surface shear modulus or surface shear viscosity. The friction coefficient of the droplet at zero frequency is the same as for a rigid sphere with stick boundary conditions, independent of the elasticity modulus.     

Poiseuille flow to measure the viscosity of particle model fluids

The most important property of a fluid is its viscosity, it determines the flow properties. If one simulates a fluid using a particle model, calculating the viscosity accurately is difficult because it is a collective property. In this article we describe a new method that has a better signal to noise ratio than existing methods. It is based on using periodic boundary conditions to simulate counter-flowing Poiseuille flows without the use of explicit boundaries. The viscosity is then related to the mean flow velocity of the two flows. We apply the method to two quite different systems. First, a simple generic fluid model, dissipative particle dynamics, for which accurate values of the viscosity are needed to characterize the model fluid. Second, the more realistic Lennard-Jones fluid. In both cases the values we calculated are consistent with previous work but, for a given simulation time, they are more accurate than those obtained with other methods.     

On two‐liquid AC electroosmotic system for thin films

Lab‐on‐chip devices employ EOF for transportation and mixing of liquids. However, when a steady (DC) electric field is applied to the liquids, there are undesirable effects such as degradation of sample, electrolysis, bubble formation, etc. due to large magnitude of electric potential required to generate the flow. These effects can be averted by using a time‐periodic or AC electric field. Transport and mixing of nonconductive liquids remain a problem even with this technique. In the present study, a two‐liquid system bounded by two rigid plates, which act as substrates, is considered. The potential distribution is derived by assuming a Boltzmann charge distribution and using the Debye–Hückel linearization. Analytical solution of this time‐periodic system shows some effects of viscosity ratio and permittivity ratio on the velocity profile. Interfacial electrostatics is also found to play a significant role in deciding velocity gradients at the interface. High frequency of the applied electric field is observed to generate an approximately static velocity profile away from the Electric Double Layer (EDL).     

Velocity profiles in simple shear flow of liquid-crystalline polymers

The velocity profiles of isotropic and anisotropic solutions of hydroxypro-pylcellulose in water have been measured by a tracer method. The velocity profile is the usual linear one for steady state experiments and also for transient experiments if a short waiting time (less than 3 hours) is left between loading and the experiment. For long waiting times (more than 12 hours), the profile is S-shaped. This could be due to the establishment of a cholesteric superstructure.     

Quantum statistical mechanics with Gaussians: equilibrium properties of van der Waals clusters

The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For an N-particle system a Gaussian exp[(r-q)(T)G(r-q)+gamma] is represented by its center qinR(3N), the width matrix GinR(3Nx3N), and the scale gammainR, all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at not-very-low temperatures the method is surprisingly accurate for a range of model systems including the case of double-well potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with 9(N(2)+N)/2 degrees of freedom. Furthermore, an approximation based on a direct product of single-particle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to 9N. The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of Ne(13) Lennard-Jones cluster. Our results agree very well with the available path-integral Monte Carlo calculations.     

Thermal Gaussian molecular dynamics for quantum dynamics simulations of many-body systems: application to liquid para-hydrogen

A new method, here called thermal Gaussian molecular dynamics (TGMD), for simulating the dynamics of quantum many-body systems has recently been introduced [I. Georgescu and V. A. Mandelshtam, Phys. Rev. B 82, 094305 (2010)]. As in the centroid molecular dynamics (CMD), in TGMD the N-body quantum system is mapped to an N-body classical system. The associated both effective Hamiltonian and effective force are computed within the variational Gaussian wave-packet approximation. The TGMD is exact for the high-temperature limit, accurate for short times, and preserves the quantum canonical distribution. For a harmonic potential and any form of operator A?, it provides exact time correlation functions C(AB)(t) at least for the case of B, a linear combination of the position, x, and momentum, p, operators. While conceptually similar to CMD and other quantum molecular dynamics approaches, the great advantage of TGMD is its computational efficiency. We introduce the many-body implementation and demonstrate it on the benchmark problem of calculating the velocity time auto-correlation function for liquid para-hydrogen, using a system of up to N = 2592 particles.     

Simulation of Flow Field for Pulsatile Blood Flow in a Femoral Artery Based on Cosserat Continua

This investigation describes unsteady, pulsatile, laminar, and locally fully developed blood flow velocity and rotation fields during cardiac cycle in the femoral artery using Cosserat continuum mechanics approach. After solving the continuity, linear momentum, and angular momentum equations for flow of blood through artery, the time and position dependent velocity and rotation fields have been calculated. It is shown that the maximum values of velocity occur at the inlet core, while the maximum values of rotation occur on the arterial boundary. It is also demonstrated that the flow of blood in artery is laminar and a good agreement with existing data is established. A time dependent Gaussian equation for non-Newtonian blood viscosity coefficient γ_v has also been found.