Real Liquids Research Articles

Oscillating sedimentation of spheres in viscoplastic fluids

In applications of chemical engineering often the sedimentation is used to separate disperse particles from liquid phases. Some real liquids, e.g., polymer fluids, paints, and skin creams show viscoplastic flow behavior, i.e., they have a yield stress. In such fluids it is possible that suspended particles do not move under action of gravity although the density of the particles is greater than the fluid density. A possibility to sediment stuck spherical particles is shown. The fluid is set in sinusoidal vibration so that the particles undergo forced oscillations. This effect is investigated for single spheres. A model is given and several theoretical results are discussed. A criterion is presented that allows one to predict the combinations of the vibration parameters (amplitude and frequency) which are needed to sediment the spheres. The theoretical investigations are confirmed by experiments. The motion of several glass and steel spheres in an oscillating tube filled with aqueous carbopol solutions are detected. The comparison between theory and experiment shows good agreement.

The spinodal as a reference curve for the high-pressure volumetric behavior of liquids

Experimental and theoretical studies suggest that the thermal expansion coefficients α p of liquids follow a power law up to extremely high pressures along isothermal paths. Accurate experiments reveal that intersections between α p isotherms occur at high pressure for many liquids. It is shown how the high-pressure behavior of α p can be accurately predicted for real liquids from surface tension and low-pressure α p measurements. The method proposed here is based on the assumption that the spinodal curve does exist and can be estimated from surface tension measurements using Fürth's hole theory.

Molecular theory of ion solvation dynamics in water, acetonitrile and methanol: A unified microscopic description of collective dynamics in dipolar liquids

A recently developed microscopic theory of solvation dynamics in real dipolar liquids is used to calculate, for the first time, the solvation time correlation function in liquid acetonitrile, water and methanol. The calculated results are in excellent agreement with known experimental and computer simulation studies.

Langevin models for shear-stress fluctuations in flows of viscoelastic liquids.

From the principle of virtual work it is shown that, if equilibrium stress fluctuations are described by a Langevin equation, there is only one possible extension of this equation to describe stress fluctuations in a shear flow. It is shown that the resulting equation is consistent with linear-response theory. The formalism developed may be looked upon as a method for extending differential constitutive relations to incorporate thermal fluctuations. A few simple models are discussed as illustrations. These include a model where the stress fluctuates freely below a certain limit, and a model constructed to mimic the Tobolsky-Eyring phenomenological theory [J. Chem. Phys. 11, 125 (1942)] of viscoelastic liquids. It is concluded that these and similar models, however, do not realistically describe real polymeric liquids. To reach this goal, models involving several stress degrees of freedom will have to be considered.

Fractal character of two-dimensional fluid mixing at both continuum and atomic levels.

Studies in two dimensions have been made of the evolution of an initially linear interface between two liquid areas by both continuum hydrodynamics and molecular dynamics. It was found that at both levels the interface evolves into a fractal curve. While the limiting fractal dimensionalities (D) of the continuum and molecular interfaces differ, this difference is no greater than that that can be induced in the hydrodynamic results by marked changes in the initial conditions and/or fluid parameters. There is, however, a marked qualitative difference in the initial values of D. This is discussed and shown to be a natural consequence of the molecular discreteness of the real liquids.

Models for relaxation in glass-forming liquids based on sequentially correlated displacements

Among the simplest models for correlated molecular motion in dense liquids are vacancy-mediated displacements in which only those molecules immediately adjacent to vacancies (packing defects of suitable topography) can be displaced at any instant. Any other molecule must await the arrival of a vacancy which requires an appropriate sequence of prior displacements. Examples of this kind of model for hard spheres and idealized polymer chains (chains of hard spheres) are reviewed. Configurational relaxation of the liquid may be represented by the auto-correlation for spheres adjacent to vacancies, a function which is derived and solved for various concentrations of vacancies. Relaxation is found to include a time domain which is non-exponential and resembles the empirical relaxation laws observed for dielectric and mechanical properties of real supercooled liquids. In particular, for independent hard spheres relaxation always converges to a simple exponential at long times, similar to the empirical Davidson-Cole expression which gives a good account of relaxation in many small molecule liquids. On the other hand, for chains of hard spheres, where adjacent pairs are required to move simultaneously, non-exponential decay can persist indefinitely for vacancy concentrations below a critical value which is consistent with the form of decay observed for polymeric liquids and glasses (Kohlrausch-Williams-Watts and Havriliak-Negami equations).

Effect of surface tension on the collapse of a cavitation bubble

By means of numerical calculations on the BeSM6 computer, we study the effect of surface tension on the size and rate of collapse of a cavitation bubble for the entire region of surface tensions of real liquids σ=(160)·10 -2 N/m (at temperatures 290 K). The effect of two parallel solid walls bounding the liquid is taken into account.

Decay of multiparticle correlations in real liquids and gases.

The explicit form of the condition of multiparticle correlation-function (CF) weakening in simple equilibrium classical liquids and gases is found. The result, which is a rigorous theorem of the real fluid statistical theory, is based only on the CF's definition and the fact that the long-range forces determining the asymptotic value are due to the interaction of the equilibrium long-wavelength electromagnetic field with matter. To prove this theorem one does not have to suppose the existence of the microscopic potential energy of the fluid molecule interaction, or any model of it. The correlations weaken more slowly than predicted by the theories based on the microscopic potential energy, and there is no higher-order correlation connection with or decoupling to the lower-order ones. In the dilute gas where the intermolecular potential energy can be used, the n-particle CF asymptotic value is determined by the n-atom potential irreducible part, i.e., the corresponding nonadditive contribution to the potential energy determines the most slowly vanishing part of the n-particle CF.

Specific heat of simple liquids

Residual specific heats c v/* are calculated from a Weeks-Chandler-Andersen-type perturbation theory for Lennard-Jones (LJ) and two-centre-Lennard-Jones (2CLJ) liquids. For spherical molecules the theory predicts that as the density is increased up to slightly above three times the critical density (ρc), c v/* increases to 2R. Corresponding states considerations indicate that rotational degrees of freedom in 2CLJ fluids make no contributions to c v/*. Comparing with real liquids, the theoretical predictions of c v/* agree, within the accuracy of the experiments, with experimental data for liquid argon, methane, and oxygen, at densities ρ/ρc > 2·5. For ethane, the theoretical predictions of c v/*, assuming a 2CLJ fluid with elongation L = 0·67, are too low. This deficiency in the theory for long molecules is attributed to the neglect of the angle-dependence of the background correlation function. However, computer simulation results for c v/* in 2CLJ fluids of elongation L = 0·67 agree with the perturbatio...

Joule—Thomson effect in liquid He II

It has been shown in the present study that the Joule—Thomson coefficients of liquid He II are extraordinarily high for temperatures far below the lambda point as compared with ordinary real gases or liquids. Its effect on the throttling process of He II was shown to be quite significant and should be taken into account when dealing with transport processes of He II.

Shear-induced phase changes in mixtures

A thermodynamic theory to account for the behavior of liquid mixtures exposed to a shear is developed. One consequence of the theory is that shear-induced phase changes are predicted. The theory is based on a thermodynamics that includes specifically the shear rate in the formalism and is applied to mixtures by a straightforward modification of the corresponding states, conformalsolution approach. The approach is general but is used here for a mixture of Lennard-Jones particles with a Lennard-Jones equation of state as a reference fluid. The results are discussed in the context of the Scott and Van Konynenberg phase classification. It is shown that the influence of a shear does affect substantially the type of the phase behavior. Results from the model mixture are equated loosely with those from real polymeric liquids.

The chemical potential of a liquid on the liquid-vapour coexistence line and the lattice-gas model

The lattice-gas model predicts that a certain chemical potential is constant along the liquid-vapour coexistence line. It is shown that this is true to a few percent for two simulated atomic liquids and for several real liquids (argon, nitrogen and hydrogen chloride). More complex liquids (water) show substantial deviations.

Vibrational relaxation and νs(AH) absorption band profiles of weak hydrogen-bonded complexes in liquids

Abstract The ν > (AH) IR absorption band profile of a weak hydrogen-bonded complex AH … B embedded in liquid is calculated within the two-mode (ν > (AH)) and ν AB coupling scheme. The generalized Langevin equation is invoked to describe the dynamics of the low-frequency (harmonic) ν AB oscillator influenced by the random force from surrounding molecules. The main goal is to take account of not very short correlation times τ c of this force, which is likely to be the case in real liquids. The non- zero τ c value results in an appearance of a purely dissipative mode when A and B approach each other. This is shown to be responsible for the ν > (AH) bandshaping in the hydrogen-bonded species exhibiting ν > (AH) band halfwidths smaller than or of the order of the ν AB vibration frequency. As for the ν AB absorption band profile, it is formed by the damped oscillatory A→ ← B motional mode. The relationships connecting the characteristics of the ν > (AH) and ν AB bandshapes are obtained. It is shown that such entities as the mean-squared A … B length dispersion in solution, the mean-squared fluctuating force acting on the ν AB oscillator and its correlation time τ c can be estimated from the joint analysis of the experimental ν > (AH) and ν AB band profiles. Comparison with the experimental data for phenol(OD)-pyridine in CCl 4 yields τ c = (O.6–1.0)x10 −2 s.

Intermolecular Nuclear Relaxations and Molecular Site‐Site Pair Correlation Functions in Liquids

AbstractIntermolecular nuclear relaxation studies of real liquids and the results of theoretical calculations for model potential functions have provided significant information on the role of molecular interactions in the structure of liquids. The intermolecular proton‐proton paircorrelation function (pcf), obtained from the reference interaction site model (RISM) is used as the equilibrium distribution and is used to obtarn an effective force for the calculation of intermolecular proton relaxation rates in liquid benzene, 1,3,5‐trideuterobenzene and ethane. For liquid ethane, better agreement with experiment is observed with the pcf obtained from the Monte Carlo simulation than with the RISM result.

A simple model for associated fluids

A simple site–site interaction type of model fluid is proposed to describe, on a primitive level, fluids which exhibit association (H bonding). Computer simulations have been performed on the model to obtain the site–site correlation functions, equation of state, average internal energy, specific heat, g1 and g2 factors, and concentration of polymeric species. The results show that the model is able to capture the basic qualitative properties of real associated liquids.

The Boyle line

The author investigates the possibility that the density of a fluid is a virtually linear function of temperature over a wide range of temperature when subject to the restriction that the compressibility factor is unity. The relation is well obeyed for a variety of real liquids, for some semi-empirical equations of state, and for the Lennard-Jones 12-6 fluid. The assumption that the Boyle line is straight is useful in predicting the Boyle temperature, third virial coefficients and equation-of-state data in difficult regions. The fundamental reason, if any, for this remarkable behaviour remains obscure.

MSA and GMSA for charged hard spheres of different diameters: Comparison with RHNC and MC calculationsa)

The excess internal energies and the radial distribution functions of systems of charged hard spheres with two species of different diameters are calculated by using the mean spherical approximation (MSA) and the generalized mean spherical approximation (GMSA). The results obtained are compared with reference hypernetted chain (RHNC) and Monte Carlo (MC) calculations performed by other authors. The MSA estimates of the excess internal energies are often very close to the computer simulation values. The MSA radial distribution functions, on the whole, compare qualitatively well with the MC gij(r), being less satisfactory when the difference in the diameters of the particles is large. The GMSA appears to improve in a systematic manner over the MSA and, when the whole range of the physical situations investigated in this paper is considered, the agreement of this theory with the MC simulation can be considered very good. Similar remarks apply to the RHNC, so that it is possible to conclude that the GMSA and the RHNC, in the present case, are more or less equally accurate. Different possibilities both to improve upon some still unsatisfactory aspects of the GMSA, and to apply this approximation in the future in order to describe the physical properties of real ionic liquids, are also discussed.

Perturbed hard sphere equations of state of real liquids. I. Examination of a simple equation of the second order

Utility of a perturbed hard sphere equation of state based on a simplified Barker-Henderson theory for a square well fluid inclusive of the three-body contributions is examined for orthobaric densities and both sub- and supercritical isotherms of simple fluids. An attempt is made to interpret parameters of the equation and their temperature dependence in terms of independent molecular properties. Finally, some general conclusions on the family of perturbed hard sphere equations of state are drawn.

Onset of convection in a variable-viscosity fluid

The Rayleigh number R, in a horizontal layer with temperature-dependent viscosity can be based on the viscosity at T0, the mean of the boundary temperatures. The critical Rayleigh number Roc for fluids with exponential and super-exponential viscosity variation is nearly constant at low values of the ratio of the viscosities at the top and bottom boundaries; increases at moderate values of the viscosity ratio, reaching a maximum at a ratio of about 3000, and then decreases. This behaviour is explained by a simple physical argument based on the idea that convection begins first in the sublayer with maximum Rayleigh number. The prediction of Palm (1960) that certain types of temperature-dependent viscosity always decrease Roc is confirmed by numerical results but is not relevant to the viscosity variations typical of real liquids. The infinitesimal-amplitude state assumed by linear theory in calculating Roc does not exist because the convection jumps immediately to a finite amplitude at R0c. We observe a heat-flux jump at R0c exceeding 10% when the viscosity ratio exceeds 150. However, experimental measurements of R0c for glycerol up to a viscosity ratio of 3400 are in good agreement with the numerical predictions when the effects of a temperature-dependent expansion coefficient and thermal diffusivity are included.

The thermodynamics of symmetric two centre Lennard-Jones liquids

We have carried out molecular dynamic simulations for the thermodynamic properties of two centre Lennard-Jones fluids at lower densities and higher temperatures than have been studied previously, and have also made simulations for one additional shape. The results, together with results already given in the literature, are presented in a parameterized form which is very convenient to use in testing the simulation results against data for real liquids. Tables of second virial coefficients are also provided. We illustrate the use of our results by an analysis of pure liquid ethane, which is found to be well represented by such a model with L* = 0·67, e/k = 137·5 K and σ = 3·506 A. We also suggest that the experimental thermodynamic properties of suitable liquid mixtures can, with the aid of a theory for the equivalent pure liquid parameters (L x *, e x , σ x ), be satisfactorily interpreted using the general results given in this paper.