Simple Dense Fluids Research Articles

Generalized irreducible memory function

In a previous paper we presented a general scheme to reduce the memory function in nonequilibrium statistical physics for purely dissipative cases with detailed balance. Here we simplify and generalize further this scheme to include cases other than purely dissipative ones. As an illustration we discuss simple dense fluids.

Shock and detonation of liquid nitric oxide

A simple theoretical approach that was developed previously to calculate shock Hugoniot of simple dense fluids is used to calculate shocked states of liquid nitric oxide and liquid nitrogen-oxygen mixtures as well as the detonation wave structure of liquid nitric oxide. The theoretical calculations provide an adequate description of the shock compression and the detonation performance.

Integral equations of the correlation functions for polymeric liquids

The integral equations for intramolecular and intermolecular correlation functions are derived for nonrigid polymeric (polyatomic) liquids by the device of the Kirkwood charging parameters. These integral equations are cast into mean-field-type equations by using the potential elimination method, reported previously for dense simple fluids. Based on the mean-field integral equations, we examine the superposition approximations for various levels of correlation. The present theory provides a means to make systematic corrections for superposition approximations for correlation functions of various orders. Upon using the superposition approximations for the triplet correlation functions in the Kirkwood hierarchy and an assumption or another concerning the charging parameter dependence of the cavity functions, we derive a set of generalized Percus–Yevick and hypernetted chain integral equations for the intramolecular and intermolecular pair correlation functions for beads (sites) of polymeric (polyatomic) liquids. This set of integral equations allows the intramolecular and intermolecular correlation functions to be determined self-consistently. The connection of this set of integral equations to the bead–bead (molecular) Ornstein–Zernike relation is pointed out. The integral equations for the intramolecular correlation functions will be numerically solved for some properties of a single polymer chain in the infinite dilution limit in the sequel to this paper.

Theory of the nonequilibrium structure of dense simple fluids. II. High-shear-rate effects.

The integral equation for the dynamic pair correlation function derived previously from the modified moment method is solved for a non-Newtonian soft-sphere fluid undergoing a plane Couette flow. In this approach, the dynamic pair correlation function is a functional of the shear stress, which determines the macroscopic state of the nonequilibrium fluid. The distortions of the structure factor at high shear rates are examined for a non-Newtonian fluid. Normal stress effects are included in the study presented. It is found that as the shear rate increases, the structure factor fractures into domains of high intensity in the xy (shear), xy, and yz planes in the wave-vector space. At packing fractions in the range of \ensuremath{\eta}=0.3--0.45, the structure factor exhibits a plateau behavior at reduced shear rates \ensuremath{\gamma}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\ge}100, and this behavior is seen to be directly related to the thixotropy of the fluid. In all planes considered, the structure factor suggests, essentially, a distorted-fluid-like structure, although there is evidence indicating that the approach to an ordered phase is also a probable interpretation. These effects are in qualitative agreement with the observations made on colloidal suspensions and low-shear-rate molecular-dynamics simulation results. In the presence of normal stresses, the structure factor in the xy plane is rotated in the direction of the shear flow. The angle of rotation is determined by the magnitude of the primary normal stress difference and also by the thermodynamic state of the fluid. The structure factor in the yz plane is similar to the case without normal stresses, and the xz plane is undistorted.

Mode-coupling theory of the stress-tensor autocorrelation function of a dense binary fluid mixture.

We present a generalized mode-coupling theory for a dense binary fluid mixture. The theory is used to calculate molecular-scale renormalizations to the stress-tensor autocorrelation function (STAF) and to the long-wavelength zero-frequency shear viscosity. As in the case of a dense simple fluid, we find that the STAF appears to decay as ${\mathit{t}}^{\mathrm{\ensuremath{-}}3/2}$ over an intermediate range of time. The coefficient of this long-time tail is more than two orders of magnitude larger than that obtained from conventional mode-coupling theory. Our study focuses on the effect of compositional disorder on the decay of the STAF in a dense mixture.

Theory of dynamic pair correlation functions for nonequilibrium dense fluids

We present an integral equation for the dynamic pair correlation function for nonequilibrium dense simple fluids. The integral equation reduces to the well known Percus-Yevick integral equation or the hypernetted chain equation for the equilibrium pair correlation function for dense simple fluids, as the nonequilibrium fluxes vanish and the system approaches equilibrium. The integral equation is derived from the nonequilibrium Kirkwood hierarchy generated from the nonequilibrium canonical distribution function, which in a thermodynamically consistent manner solves the generalized Boltzmann equation for dense simple fluids. In this theory, the equilibrium theory of fluid structures is an integral part of the nonequilibrium theory presented. The integral equation is applied to study the nonequilibrium effects induced by shearing a non-Newtonian fluid. In the high shear-rate regime the structure factors break into diffraction-like patterns, which indicate that the fluid organizes into a local structure. The nonequilibrium effects also show a plateau behavior in the non-Newtonian regime in a qualitative agreement with the experimental observation on a non-Newtonian fluid - for example, a suspension of ciliated silica spheres.

Theory of the nonequilibrium structure of dense simple fluids: Effects of shearing.

The nonequilibrium canonical distribution function of the generalized Boltzmann equation entails a nonequilibrium Kirkwood hierarchy of integral equations for dynamic correlation functions. A sheared simple fluid at constant density and temperature is considered. Shear effects appear in the nonequilibrum potential as additional contributions to the intermolecular potential. Approximations are introduced into the hierarchy to derive a closed integral equation for the dynamic pair-correlation function that reduces identically to the Percus-Yevick integral equation as the shear rate vanishes. Two exact results are obtained: the dynamic pair-correlation function is proven to possess the symmetry of the nonequilibrium potential, and the corresponding structure factor is shown to be positive definite for all wave-number vectors. The dynamic pair-correlation function is expanded in terms of the spherical harmonics, and the equations for coupled radial components are solved numerically. The shear rate and angular dependences of the dynamic pair-correlation function and structure factor are shown. In the low-shear-rate limit, the shear stress ${\mathit{P}}_{\mathit{x}\mathit{y}}$, pressure difference p(\ensuremath{\gamma}\ifmmode\bar\else\textasciimacron\fi{})-p(0), and normal-stress differences ${\mathit{P}}_{\mathit{y}\mathit{y}}$-${\mathit{P}}_{\mathit{z}\mathit{z}}$ and ${\mathit{P}}_{\mathit{y}\mathit{y}}$-${\mathit{P}}_{\mathit{z}\mathit{z}}$ obey power laws with exponents 1, 2, and 2 respectively; ${\mathit{P}}_{\mathit{x}\mathit{x}}$-${\mathit{P}}_{\mathit{y}\mathit{y}}$ is zero identically.

Cluster expansion for transport coefficients for dense simple fluids

Cluster expansions are presented for the collision bracket integrals for transport cofficients of a dense simple fluid which appear in the kinetic theory of dense fluid reported previously. The density series calculated with the cluster expansions are given in exponential forms and their leading terms consist of a connected three-particle collision operator. The three-particle contributions are discussed in terms of mass-normalized coordinates which make it possible to put them in forms structurally rather similar to the two-particle collision bracket integrals in the Chapman-Enskog theory. The three particle contributions are thus cast into forms suitable for numerical computation.

Monte Carlo calculation of the free energy for a dense fluid

A simple and direct approach to the free energy of a dense simple fluid away from critical point is considered. Standard Monte Carlo sampling of free energy difference relative to a reference system for a range of model system sizes is employed. By using a range of a small number of particles, multi-stage samplings can be avoided and exponential extrapolation to the thermodynamic limit is assured in the absence of nearby critical point. The technique is demonstrated for the dense fluid interacting with the r-12 repulsive potential in three dimensions. The hard-sphere fluid reference system is used. The free energy estimate is in excellent agreement with published results from standard thermodynamic integration of the equation of state obtained from Monte Carlo simulation.

Sound-propagation gap in fluid mixtures.

We discuss the behavior of the extended sound modes of a dense binary hard-sphere mixture. In a dense simple hard-sphere fluid the Enskog theory predicts a gap in the sound propagation at large wave vectors. In a binary mixture the gap is only present for low concentrations of one of the two species. At intermediate concentrations sound modes are always propagating. This behavior is not affected by the mass difference of the two species, but it only depends on the packing fractions. The gap is absent when the packing fractions are comparable and the mixture structurally resembles a metallic glass.

Stability of dense simple fluids subjected to large shear: Shear-induced ordering.

The stability at finite wave numbers of a dense simple fluid subjected to a large shear is examined using generalized hydrodynamics and hard-sphere kinetic theory. For a fixed density below the equilibrium freezing density, for molecular-scale wave numbers, and for a critical shear rate, the fluid is found to become unstable with respect to density waves in the direction of the velocity gradient. For a given density the critical shear rates obtained are close to those found by Erpenbeck [Phys. Rev. Lett. 52, 1333 (1984)] in his nonequilibrium-molecular-dynamics simulations of shear-induced ordering.

Rheology of dense model fluids via nonequilibrium molecular dynamics: Shear thinning and ordering transition

Nonequilibrium molecular dynamics computer simulations are employed to investigate the rheology of dense simple model fluids. Besides the non-Newtonian behavior of the viscosity functions a shear-induced ordering transition is an essential feature of this presentation. Its occurrence in the simulation is supported by a hydrodynamic stability analysis. To illustrate the scenario preceding the instability, density and velocity profiles of the flow are considered as well as the static structure factor which enables a comparison with recent experimental results for dense suspensions. Problems related to experimental evidence of the ordering transition into layers are discussed in light of the derived stability criterion.

Transport in simple dense fluids

A transport theory for Lennard-Jones (LJ) fluids is described. The underlying mean-field kinetic theory models the LJ potential by adding a hard-sphere core to the attractive tail of the LJ potential. The transport coefficients discussed here — shear viscosity, thermal conductivity, and self-diffusion coefficient — exhibit Enskog-like forms, but now the radial distribution function (rdf) bears explicit dependence on the LJ tail as well as on the hard-sphere core. The hardsphere diameter is determined according to the well-known WCA method used in equilibrium statistical mechanics to mimic the LJ fluid. Hence the transport theory employs no adjustable parameters. Numerical results are compared to simulation and experimental results for many states, including saturated liquid, triple point, and dense gas. In general, a quantitatively accurate transport theory is obtained for the states considered. This represents improvement, both numerically and conceptually, over an earlier theory.

Translational and rotational dynamics of simple dense fluids

The Mori method and the pseudo-Liouville formalism have been combined in an analysis of the translational and rotational diffusion coefficients of a dense fluid of hard bodies. Correlated recollisions, due to caging, appear naturally in this theory and their effect is to increase the translational friction on a tagged spherical molecule in a hard sphere bath and to increase the rotational friction on a hard nonspherical convex body in a hard sphere fluid. The calculated increase in friction from liquid state correlated caging corrections is in rough accord with the molecular dynamics calculation of Alder et al. on spherical systems and brings kinetic theory predictions for rotational friction coefficients in closer accord with experiment.

Half width of neutron spectra.

We analyzed for the first time systematically the half widths of a great variety of neutron spectra of simple dense classical fluids as functions of wave number and density. We find that the observed behavior of the half width near its minimum value can be understood quantitatively on the basis of a generalization of a diffusion model, proposed before.

Theory of dynamic shear viscosity and normal stress coefficients of dense fluids

On the basis of the nonlinear evolution equation for the stress tensor derived from the kinetic equation for dense simple fluids, we examine the shear rate and frequency dependence of the shear viscosity and normal stress coefficients. An analytic expression for nonlinear shear viscosity has been obtained, which is in agreement with nonequilibrium molecular dynamic simulation results. Based on the material functions obtained in the analysis, a theory of rheological corresponding states is developed by showing that there exists a set of reduced material functions which depend on the reduced shear rate, reduced frequency, reduced static normal coefficients and limiting values of the reduced imaginary parts of dynamic normal stress coefficients. It is also shown that the dynamic normal stress coefficients can change its sign as the critical value of the frequency is crossed.

Density effect on excess electron mobility in dense fluids

From experimental data, the excess electron mobility in dense simple fluids (rare gases, hydrocarbons) is highly sensitive to the density N and the temperature T of the medium and to the electric field strenght F. Increasing density from dilute gas, the classical dependence μ=C F N disappears around N=0.1 N critical as the binary cross section model fails (Mott's localisation). Then the mobility exhibits a minimum in the critical region and a maximum near N=2 N critical. These features suggest that the motion of the excess electron reflects the dynamics of the atoms in the fluid. We propose a localisation concept and a collisional model relating the electronic motion with the atomic one. All experimental features are well described by our model. Reciprocally, the excess electron transport appears to be a powerful tool to study the intimate structure of the dense dielectric fluids.

Lennard-Jones triple-point conductivity via weak external fields

We have performed a nonequilibrium molecular-dynamics (NEMD) computation of thermal conductivity for a simple dense fluid near the triple point using the differential NEMD method and a translationally invariant algorithm recently proposed by Evans. We have simulated a set of thermal gradients in the range 75.8 K/cm to 2.54 \ifmmode\times\else\texttimes\fi{} ${10}^{8}$ K/cm. Our main conclusion concerns the response of the energy current at $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}=\stackrel{\ensuremath{\rightarrow}}{0}$, which is linear in the range indicated. To check the efficiency of the present NEMD technique we have compared the nonequilibrium results with our own and Levesque's equilibrium Green-Kubo results. The agreement found is remarkable.

Theory of non-Newtonian viscosity and normal stress coefficients of fluids

The evolution equation for the traceless symmetric part P̂ of the stress tensor derived previously for dense simple fluids is further investigated of its applicability to non-Newtonian fluid behaviors and normal stress effects. Nonlinear differential equations for three independent components of the stress tensor are obtained in the case of a unidirectional flow in an incompressible fluid. The asymptotic stability of the steady state (equilibrium) is studied with linearized equations and the stability conditions are derived. Approximate steady state solutions are calculated from the evolution equations for the three components and viscometric functions are obtained therefrom. By taking the evolution equations as a set of phenomenological evolution equations, we show that it is possible to apply them even to nonsimple fluids such as polymer solutions, by analyzing experimental data on the shear rate dependencies of the viscometric functions of some polymer solutions. We also show that the approximate viscometric functions used for analysis can be reduced to a set of corresponding-state viscometric functions to a good accuracy. Relations of the evolution equations for P̂ to some of the existing rheological equations of state are discussed. It is shown that suitable linearizations of the present nonlinear evolution equation for P̂ yield the same forms as those for the existing rheological equations of state.

Description of the influence of intermolecular interaction on IR spectra's frequencies of simple dense fluids by Monte-Carlo simulation

The solvent-induced shift in IR spectrum of liquid CO is investigated by Monte-Carlo computer simulation. The intramolecular potential is Morse function, pair intermolecular potential includes short-range and dispertion parts. The calculated shift is 5 cm −1 while the experimental value is 4 cm −1.