Self-diffusion coefficients and shear viscosity of inverse power fluids: from hard- to soft-spheres

Molecular dynamics computer simulation has been used to compute the self-diffusion coefficient, D, and shear viscosity, eta(s), of soft-sphere fluids, in which the particles interact through the soft-sphere or inverse power pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The simulations were carried out on monodisperse systems for a range of n values from the hard-sphere (n --> infinity) limit down to n = 4, and up to densities in excess of the fluid-solid co-existence value. A new analytical procedure is proposed which reproduces the transport coefficients at high densities, and can be used to extrapolate the data to densities higher than accurately accessible by simulation or experiment, and tending to the glass transition. This formula, DX(c-1) proportional, variant A/X + B, where c is an adjustable parameter, and X is either the packing fraction or the pressure, is a development of one proposed by Dymond. In the expression, -A/B is the value of X at the ideal glass transition (i.e., where D and eta(s)(-1) --> 0). Estimated values are presented for the packing fraction and the pressure at the glass transition for n values between the hard and soft particle limits. The above expression is also shown to reproduce the high density viscosity data of supercritical argon, krypton and nitrogen. Fits to the soft-sphere simulation transport coefficients close to solid-fluid co-existence are also made using the analytic form, ln(D) = alpha(X)X, and n-dependence of the alpha(X) is presented (X is either the packing fraction or the pressure).     

Rheology of double emulsions

New equations for the viscosity of concentrated double emulsions of core-shell droplets are developed using a differential scheme. The equations developed in the paper predict the relative viscosity (eta(r)) of double emulsions to be a function of five variables: a/b (ratio of core drop radius to shell outer radius), lambda(21) (ratio of shell liquid viscosity to external continuous phase viscosity), lambda(32) (ratio of core liquid viscosity to shell liquid viscosity), phi(DE) (volume fraction of core-shell droplets in double emulsion), and phi(m)(DE) (the maximum packing volume fraction of un-deformed core-shell droplets in double emulsion). Two sets of experimental data are obtained on the rheology of O/W/O (oil-in-water-in-oil) double emulsions. The data are compared with the predictions of the proposed equations. The proposed equations describe the experimental viscosity data of double emulsions reasonably well.     

On the relation between virial coefficients and the close-packing of hard disks and hard spheres

The question of whether the known virial coefficients are enough to determine the packing fraction η(∞) at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Pade? approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that η(∞) is equal to the maximum packing fraction corresponding to an ordered crystalline structure.     

How "sticky" are short-range square-well fluids?

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range lambda at a given packing fraction eta and reduced temperature T* = kBT/epsilon can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter tau(T*,lambda). Such an equivalence cannot hold for the radial distribution function g(r) since this function has a delta singularity at contact (r = sigma) in the SHS case, while it has a jump discontinuity at r = lambda sigma in the SW case. Therefore, the equivalence is explored with the cavity function y(r), i.e., we assume that [formula: see text]. Optimization of the agreement between y(SW) and y(SHS) to first order in density suggests the choice tau(T*,lambda) = [12(e(1/T* - 1)(lambda - 1)](-1). We have performed Monte Carlo (MC) simulations of the SW fluid for lambda = 1.05, 1.02, and 1.01 at several densities and temperatures T* such that tau(T*,lambda) = 0.13, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel[J. Phys.: Condens. Matter 16, S4901 (2004)]. Although, at given values of eta and tau, some local discrepancies between y(SW) and y(SHS) exist (especially for lambda = 1.05), the SW data converge smoothly toward the SHS values as lambda-1 decreases. In fact, precursors of the singularities of y(SHS) at certain distances due to geometrical arrangements are clearly observed in y(SW). The approximate mapping y(SW)-->y(SHS) is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for y(SHS) the solution of the Percus-Yevick equation as well as the rational-function approximation, the radial distribution function g(r) of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.     

Structural and dynamical properties of ionic liquids: the influence of ion size disparity

The influence of ion size disparity on structural and dynamical properties of ionic liquids is systematically investigated employing molecular dynamics simulations. Ion size ratios are varied over a realistic range (from 1:1 to 5:1) while holding other important molecular and system parameters fixed. In this way we isolate and identify effects that stem from size disparity alone. In strongly size disparate systems the larger species (cations in our model) tend to dominate the structure; the anion-anion distribution is largely determined by anion-cation correlations. The diffusion coefficients of both species increase, and the shear viscosity decreases with increasing size disparity. The influence of size disparity is strongest up to a size ratio of 3:1, then decreases, and by 5:1 both the diffusion coefficients and viscosity appear to be approaching limiting values. The conventional Stokes-Einstein expression for diffusion coefficients holds reasonably well for the cations but fails for the smaller anions as size disparity increases likely due to the neglect of strong anion-cation correlations. The electrical conductivity is not a simple monotonic function of size disparity; it first increases up to size ratios of 2:1, remains nearly constant until 3:1, then decreases such that the conductivities of the 1:1 and 5:1 systems are similar. This behavior is traced to the competing influences of ion diffusion (enhancing) and ion densities (reducing) on conductivities at constant packing fraction. The temperature dependence of the transport properties is examined for the 1:1 and 3:1 systems. In accord with experiment, the temperature dependence of all transport properties is well represented by the Vogel-Fulcher-Tammann equation. The dependence of the diffusion coefficients on the temperature/viscosity ratio is well described by the fractional Stokes-Einstein relation D proportional to (T/eta)(beta) with beta approximately = 0.8, consistent with the exponent observed for many molten inorganic salts.     

Centroid molecular dynamics approach to the transport properties of liquid para-hydrogen over the wide temperature range

Fundamental transport properties of liquid para-hydrogen (p-H(2)), i.e., diffusion coefficients, thermal conductivity, shear viscosity, and bulk viscosity, have been evaluated by means of the path integral centroid molecular dynamics (CMD) calculations. These transport properties have been obtained over the wide temperature range, 14-32 K. Calculated values of the diffusion coefficients and the shear viscosity are in good agreement with the experimental values at all the investigated temperatures. Although a relatively large deviation is found for the thermal conductivity, the calculated values are less than three times the amount of the experimental values at any temperature. On the other hand, the classical molecular dynamics has led all the transport properties to much larger deviation. For the bulk viscosity of liquid p-H(2), which was never known from experiments, the present CMD has given a clear temperature dependence. In addition, from the comparison based on the principle of corresponding states, it has been shown that the marked deviation of the transport properties of liquid p-H(2) from the feature which is expected from the molecular parameters is due to the quantum effect.     

Diffusion, sedimentation, and rheology of concentrated suspensions of core-shell particles

Short-time dynamic properties of concentrated suspensions of colloidal core-shell particles are studied using a precise force multipole method which accounts for many-particle hydrodynamic interactions. A core-shell particle is composed of a rigid, spherical dry core of radius a surrounded by a uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ(-1). The solvent flow inside the permeable shell is described by the Brinkman-Debye-Bueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact non-hydrodynamically by a hard-sphere no-overlap potential of radius b. Numerical results are presented for the high-frequency shear viscosity, η(∞), sedimentation coefficient, K, and the short-time translational and rotational self-diffusion coefficients, D(t) and D(r). The simulation results cover the full three-parametric fluid-phase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Many-particle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Our simulation results show that for thin or hardly permeable shells, the core-shell systems can be approximated neither by no-shell nor by no-core models. However, one of our findings is that for κ(b - a) ? 5, the core is practically not sensed any more by the weakly penetrating fluid. This result is explained using an asymptotic analysis of the scattering coefficients entering into the multipole method of solving the Stokes equations. We show that in most cases, the influence of the core grows only weakly with increasing concentration.     

Transport Coefficients Of Ar—Kr Mixtures by Molecular Dynamics Computer Simulation

Abstract

Equilibrium molecular dynamics computer simulations have been used to determine the transport coefficients of model Ar—Kr mixtures, which are represented by Lennard-Jones pair potentials with Lorentz—Berthelot rules for the cross-species interactions. The component self-diffusion and mutual-diffusion coefficients are calculated from time correlation functions and mean square displacements. Time correlation functions are used to evaluate the shear and bulk viscosity, thermal conductivity and the thermal diffusion coefficient (Soret/Dufour coefficient). In the case of the thermal transport coefficients, the partial enthalpy of the two species is required at each state point to define the heat flux rigorously. We obtain this and the partial volume (and species resolved chemical potential) using particle-exchange (and particle insertion) techniques implemented in separate [NPT] simulations at the same state point.

The viscoelasticity of the fluids is characterised by the relaxation times for bulk and shear stress relaxation. The results are for dense liquids close to the triple point temperature and density. Agreement with experiment and previous simulation is particularly good for the density of the mixtures, the shear modulus, shear viscosity, shear stress relaxation time and thermal conductivity. As for the single component noble gas fluids (simulated and experiment) there is a significant qualitative difference in the temperature and, for mixtures, composition dependence of the bulk viscosity.     

System size and control parameter effects in reverse perturbation nonequilibrium molecular dynamics

The issue of system size effects in the reverse perturbation nonequilibrium molecular dynamics method for determining transport coefficients of fluids is examined for the case of the Lennard-Jones model. It is found that when adequate precautions are observed in obtaining linear temperature or momentum profiles, a 250 atom system is adequate for determining the thermal conductivity and the shear viscosity. Also, a means of determining the uncertainties in the transport coefficients is described. The conclusion is that this method is computationally competitive with other simulation methods for estimating transport coefficients.     

Viscosity and thermal conductivity of some refrigerants at moderate and high densities on the basis of Rainwater–Friend theory and the corresponding states principle

The initial density dependence of viscosity and thermal conductivity was formulated on the basis of Rainwater–Friend (RF) theory. In this work, we have first focused on the calculation of viscosity and thermal conductivity of moderately dense argon by using RF theory and an accurate ab initio potential function. This theory which was originally presented for spherical potentials have been adapted for calculation of viscosity and translational contribution of thermal conductivity of some refrigerants by introducing the corresponding states correlations for the second transport virial coefficients. Then the internal states contribution for the thermal conductivity has been determined based on the Mason–Monchick and modified Enskog theories. So, we have calculated the viscosity and thermal conductivity of some refrigerants, R32, R14, R12, R13, R22, R134a, R143a, R125, R123, R142b, at moderate densities up to about 2 mol dm⁻³. At high densities, beyond the validity range of RF theory, we have applied correlation expressions for the viscosity and thermal conductivity residual functions to calculate the viscosity and thermal conductivity of supercritical refrigerants and then compared with the available experimental data. In conclusion, we have shown that the RF theory in conjunction with the corresponding states residual functions present the reliable model for calculation of viscosity and thermal conductivity of refrigerants over a comparatively wide temperature and pressure range up to 65 MPa within the experimental errors.     

Stokes-Einstein relations for a square-well fluid

A Stokes-Einstein relation, relating the shear viscosity eta to the self-diffusion coefficient D, is constructed for a classical fluid subject to an effective two-body intermolecular force, derived from a square-well potential, undergoing dynamics as described by a Smoluchowski equation for pair diffusion. The time correlation functions for eta and 1D are separated into contributions from delta function, hard-sphere forces, and from delta function, square-well soft forces. Furthermore, D is separated into its two- and three-body time correlation functions, and eta into its two- to four-body terms. D shows activated diffusion, as in Arrhenius behavior, and on the level of two-body dynamics, the Deta product adheres to the Stokes-Einstein relation, subject to a small correction for potential softness. Three-body time correlation functions increase D, whereas three- and four-body correlation functions in eta are partially offsetting. The deviation of Deta product from the Stokes-Einstein law arises from the three-body time correlations functions in D.     

Adsorption behavior of oxyethylated surfactants at the air/water interface

The low-shear viscosity eta(0) of colloidal suspensions of acrylic latex or silica in aqueous gelatin has been measured at a temperature above the sol-gel transition. Measurements were made on dilution of a concentrated suspension with water or a gelatin solution. Thus, either the gelatin : colloid ratio was maintained or it was varied at constant aqueous gelatin concentration. Systems were studied with four lime-processed gelatins of different molecular weights at two concentrations of added salt. In addition, the latex particle size and the thickness of the adsorbed gelatin layer were measured by photon correlation spectroscopy (PCS) under dilute conditions. The dependence of the low-shear viscosity eta(0) on particle concentration was exponential and did not follow the well-established Krieger-Dougherty model for simple hard-sphere suspensions over the concentration range studied. A simple phenomenological model, eta(0)=eta(o)10(phi(e)/phi(s)), was found to predict the behavior well. Here, eta(o) is the viscosity of a gelatin solution of the corresponding solution concentration, phi(e) is proportional to the volume fraction of the particles, and phi(s) is a scaling factor, which was determined to have a value of 0.85. With this value of phi(s), the dimensions determined from PCS could be used to predict the viscosity values.     

Combination of RSM and NSGA-II algorithm for optimization and prediction of thermal conductivity and viscosity of bioglycol/water mixture containing SiO2 nanoparticles

The fluids containing nanoparticles have enhanced thermo-physical characteristics in comparison with conventional fluids without nanoparticles. Thermal conductivity and viscosity are thermo-physical properties that strongly determine heat transfer and momentum. In this study, the response surface method was firstly used to derive an equation for the thermal conductivity and another one for the viscosity of bioglycol/water mixture (20:80) containing silicon dioxide nanoparticles as a function of temperature as well as the volume fraction of silicon dioxide. Then, NSGA-II algorithm was used for the optimization and maximizing thermal conductivity and minimizing the nanofluid viscosity. Different fronts were implemented and 20th iteration number was selected as Pareto front. The highest thermal conductivity (0.576 W/m.K) and the lowest viscosity (0.61 mPa.s) were obtained at temperature on volume concentration of (80 °C and 2%) and (80 °C without nanoparticle) respectively. It was concluded that the optimum thermal conductivity and viscosity of nanofluid could be obtained at maximum temperature (80 °C) or a temperature close to this temperature. An increase in the volume fraction of silicon dioxide led to the enhancement of thermal conductivity but the solution viscosity was also increased. Therefore, the optimum point should be selected based on the system requirement.     

Effect of pressure on transport properties of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate

The self-diffusion coefficients (D) of the cation and anion in the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM]PF6) have been determined together with the electrical conductivity (kappa) under high pressure. All three quantities strongly decrease with increasing pressure to approximately 20% of their atmospheric pressure values at 200 MPa. D(PF6-) is always less than D([BMIM]+), despite the larger van der Waals volume of the cation. The pressure effect on the transport coefficients is discussed in terms of velocity correlation coefficients (VCCs or fij), the Nernst-Einstein equation (ionic diffusivity-conductivity), and the fractional form of the Stokes-Einstein relation (viscosity-conductivity and viscosity-diffusivity). It was found that the VCCs for the cation-cation, anion-anion, and cation-anion pairs are all negative and strongly pressure-dependent, increasing (becoming less negative) with increasing pressure. However, when the values of the VCCs for a given isotherm are normalized relative to the corresponding atmospheric pressure values, they collapse onto a single curve, as might be expected because the pressure should affect the interionic velocity correlations in the same way for each type of interaction. These isothermal curves can be represented by the form exp(alphap + betap2). The Nernst-Einstein deviation parameter, Delta, which depends on the differences between the like-like ion and unlike ion VCCs (f++ + f-- - 2f+-), is very nearly constant under the conditions examined. The diffusion and molar conductivity (Lambda) data are found to fit fractional forms of the Stokes-Einstein relationship with the viscosity, (LambdaT) proportional, variant (T/eta)t and Di proportional, variant (T/eta)t , with t = (0.92 +/- 0.05), independent of both temperature and pressure within the ranges studied and common to the three independently determined properties.     

Transport Coefficients of Two-temperature Lithium Plasma for Space Propulsion Applications

Lithium has been proposed as an attractive metal propellant for advanced electric propulsion. In our current work, transport coefficients including the viscosity, thermal conductivity, and electrical conductivity of lithium plasma under both the equilibrium and non-equilibrium conditions are calculated based on a two-temperature model. The collision integrals used in calculating the transport coefficients are significantly more accurate than values used in previous theoretical studies, resulting in more reliable values of the transport coefficients. Results are computed for different degrees of thermal non-equilibrium, i.e. the ratio of electron to heavy particle temperatures, from 1 to 15, with the electron temperature ranging from 300 to 60,000 K in a wide pressure range from 0.0001 to 100 atm. We compare our calculated results with existing published results and discrepancies are found and explained.     

Ionic-Liquid-Based Nanofluids and Their Heat-Transfer Applications: A Comprehensive Review

Due to the improved thermophysical characteristics of ionic liquids (ILs), such as their strong ionic conductivity, negligible vapor pressure, and thermal stability at high temperatures, they are being looked at viable contender for future heat transfer fluids. Additionally, the dispersing nanoparticles can further improve the thermophysical characteristics and thermal performance of ionic liquids, which is one of the emerging research interests to increase the heat transfer rates of the thermal devices. The latest investigations about the utilization of ionic liquid nanofluids as a heat transfer fluid is summarized in this work. These summaries are broken down into three types: (a) the thermophysical parameters including thermal conductivity, viscosity, density, and specific heat of ionic liquids (base fluids), (b) the thermophysical properties like thermal conductivity, viscosity, density, and viscosity of ionic liquids based nanofluids (IL nanofluids), and (iii) utilization of IL nanofluids as a heat transfer fluid in the thermal devices. The techniques for measuring the thermophysical characteristics and the synthesis of IL nanofluids are also covered. The suggestions for potential future research directions for IL nanofluids are summarized.     

Physical properties of soft repulsive particle fluids

Molecular dynamics computer simulation has been applied to inverse power or soft-sphere fluids, in which the particles interact through the soft-sphere pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The focus of the study is on very soft particles with n values down to 4 considered, at densities up to and along the fluid-solid co-existence density. It is shown that in the soft-particle limit the local structure is dominated by the lengthscale associated with the average nearest neighbour distance of a random structure, which is proportional, variantrho(-1/3) and increasingly only very weakly dependent on n. This scaling is also manifest in the behaviour of the average energy per particle with density. The self-diffusion coefficient and shear viscosity are computed along the fluid-solid co-existence line as a function of n, for the first time. The product Deta(s) steadily increases with softness for n < 10, whereas the modified Stokes-Einstein relationship of Zwanzig, Deta(s)/rho(1/3), where rho is the number density, is within statistics constant over the same softness range. This is consistent with our observation that the static properties are determined by a characteristic lengthscale (i.e., l) which is proportional, variantrho(-1/3) in the soft-particle limit. The high frequency elastic moduli of these fluids are examined, which reveals that the mechanical properties become more 'rubbery' as the particles get softer.     

Transport Properties of Simple Fluids from the Soft‐Core Double Yukawa Potential

The present work is concerned with checking a new and simple pair potential function (soft‐core double Yukawa potential) for noble gases by calculation of the transport properties. The viscosity, thermal conductivity and self diffusion coefficient in dilute gas limit in the temperature range of 298‐1400 K are calculated and agreement with the measurements is, in general, within the experimental error. A comparison of the calculated and experimental values of the viscosity, thermal conductivity and the diffusion coefficients yields an average absolute deviation of 0.5%, 1.5% and 1.2%, respectively. Also, the calculated transport properties from this potential have been compared with those calculations via the accurate experimental potential and also the corresponding state.     

Transport properties of Mie(14,7) fluids: molecular dynamics simulation and theory

An extensive computer simulation study is presented for the self-diffusion coefficient, the shear viscosity, and the thermal conductivity of Mie(14,7) fluids. The time-correlation function formalism of Green-Kubo is utilized in conjunction with molecular dynamics (MD) simulations. In addition to molecular simulations, the results of a recent study [A. Eskandari Nasrabad, J. Chem. Phys. 128, 154514 (2008)] for the mean free volume are applied to calculate the self-diffusion coefficients within a free volume theory framework. A detailed comparison between the MD simulation and free volume theory results for the diffusion coefficient is given. The density fluctuation theory of shear viscosity is used to compute the shear viscosity and the results are compared to those from MD simulations. The density and temperature dependences of different time-correlation functions and transport coefficients are studied and discussed.     

Transport properties of helium in the temperature range 400–2300 K

The thermal conductivity of helium measured in the temperature range 400 to 2300 K is employed to establish a realistic interaction potential for it. This information together with kinetic theory enables the prediction of viscosity and diffusion coefficients.