Viscosity and Excess Volume at High Pressures in Associative Binaries

The dynamic viscosity and the density of three pure substances (water, 2-propanol, diacetone alcohol) and the three associated binaries were measured versus temperature T (303.15, 323.15, and 343.15 K) and pressure P. For the binary systems the mole fractions x of each component were, successively, 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1. For viscosity the experimental results (P100 MPa) represent a total of 540 data points: 54 for the pure substances and 486 for the binary mixtures (x0 and x1). For density the experimental results (P70 MPa) represent 1260 values: 126 for the pure substances and 1134 for the binary mixtures (x0 and x1). The mixtures with water are highly associative and the curves for the variation of with composition exhibit a maxima. The variations of the excess activation energy of viscous flow G ^E are discussed. Moreover, the measurements of are sufficiently accurate to determine the excess volumes V ^E versus pressure, temperature, and composition.     

Nonisothermal film flow of a magnetizable liquid

The problem of the flow of a nonisothermal magnetizable liquid with a free surface in a nonuniform magnetic field is formulated and investigated theoretically by considering a specific example.Notation H magnetic field intensity - M magnetization - _o magnetic permeability of vacuum - I current (r, , z), cylindrical coordinates - (, gz) coordinates of free surface - R radius of current-carrying conductor - p pressure - v axial component of velocity - viscosity - R₁, R₂ principal radii of curvature of surface - surface tension - Q flow rate of liquid - G characteristic value of gradient of magnetic field intensity - density - g acceleration due to gravity Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 881–885, November, 1979.     

Shear viscosity of liquid4He and3He-4He mixtures,especially near the superfluid transition

High-resolution measurements of are reported for liquid⁴He and³He-⁴He mixtures at saturated vapor pressures between 1.2 and 4.2 K with particular emphasis on the superfluid transition. Here is the mass density, the shear viscosity, and in the superfluid phase both and are the contributions from the normal component of the fluid ( _n and _n ). The experiments were performed with a torsional oscillator operating at 151 Hz. The mole fraction X of³He in the mixtures ranged from 0.03 to 0.65. New data for the total density and data for _n by various authors led to the calculation of . For⁴He, the results for are compared with published ones, both in the normal and superfluid phases, and also with predictions in the normal phase both over a broad range and close to T. The behavior of and of in mixtures if presented. The sloped/dT near T and its change at the superfluid transition are found to decrease with increasing³He concentration. Measurements at one temperature of versus pressure indicate a decreasing dependence of on molar volume asX(³He) increases. Comparison of at T, the minimum of _n in the superfluid phase and the temperature of this minimum is made with previous measurements. Thermal conductivity measurements in the mixtures, carried out simultaneously with those of , revealed no difference in the recorded superfluid transition, contrary to earlier work. In the appendices, we present data from new measurements of the total density for the same mixtures used in viscosity experiments. Furthermore, we discuss the data for _n determined for⁴He and for³He-⁴He mixtures, and which are used in the analysis of the data.     

First viscosity of dilute3He-4He mixtures below 0.6 K

Starting with the Boltzmann transport equation, the first viscosity of dilute³He-⁴He mixtures for various³He concentrations x is evaluated up to around T 0.6 K by including the contribution from three-phonon processes (3PP) in the anomalous elementary excitation spectrum of liquid⁴He. Due to 3PP, the characteristic time for³He viscosity at high temperatures, i.e., T2T_F where T_F is the³He Fermi temperature, is evaluated as 5 × 10^–12/xT, which is smaller than the value estimated by Rosenbaum et al. This is interpolated with in the degenerate (quantum) region, TT_F. The obtained viscosities are in better agreement with experimental results than those of Baym and Saam, whose theory does not include 3PP. However, at very low concentrations there exists a discrepancy between the present theory and experiments, so that an alternate treatment should be considered.     

A Viscosity Equation of State for R123 in the Form of a Multilayer Feedforward Neural Network

A multilayer feedforward neural network (MLFN) technique is adopted for developing a viscosity equation =(T, ) for R123. The results obtained are very promising, with an average absolute deviation (AAD) of 1.02% for the currently available 169 primary data points, and are a significant improvement over those of a corresponding conventional equation in the literature. The method requires a high-accuracy equation of state for the fluid to be known to convert the experimental P, T into the independent variables , T, but such equation may not be available for the target fluid. With a view to overcoming this difficulty, a viscosity implicit equation of state in the form of T=T(P, ), avoiding the density variable, is obtained using the MLFN technique, starting from the same data sets as before. The prediction accuracy achieved is comparable with that of the former equation, =(T, ).     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

Shear viscosity measurements of liquid 4He and 3He-4He mixtures near the tricritical point

A torsional oscillator cell is described, by means of which simultaneous precision measurements of () and of the molar volume can be made in liquid ⁴He-⁴He mixtures over the temperature range between 0.5 and 3 K. Here is the mass density, the shear viscosity and in the superfluid phase they become the contributions _n and _n of the normal component. The results of for ⁴He near the superfluid transition are compared with the predictions by Schloms, Pankert and Dohm, and by Ferrell. Measurements of () are reported for mixtures with 0.64X0.74, where X is the ³He mole fraction. Those for X = 0.67 and 0.70 are compared with data by Lai and Kitchens. The viscosity experiments show no evidence of a weak singularity at the tricritical point.     

Coupling of order parameter collective modes to spin density in3He-B

We derive a general expression for the dynamic spin susceptibility of³He-B which is valid for all magnetic fields. The coupling of real and imaginary modes by particle-hole asymmetry is taken into account. Then we calculate the contribution of the mode at frequency =2 – 1/4 ( is the effective Larmor frequency) to the transverse susceptibility. The spectral weight of this mode in magnetic resonance absorption is proportional to (/)^1/2 (–)², where and are particle-hole asymmetry parameters. From the experimental coupling strength of the real squashing mode to sound we estimate (–)²10^–4. The dynamic susceptibility satisfies the sum rules of Leggett. Finally we point out the difficulties in calculating the transverse NMR frequency of³He-B. These difficulties arise from theS _z =0 Cooper pairs and from the coupling ofJ _z =±1 modes forJ=1 andJ=2.     

Shear viscosity measurements of liquid 3He-4He mixtures above 0.5 K

Simultaneous measurements of () and of the molar volume are reported for liquid mixtures of ³He in ⁴He over the temperature range between 0.5 and 2.5 K. Here is the shear viscosity and is the mass density. In the superfluid phase, the product of the normal components, _n and _n , is measured. The mixtures with ³He molefractions 0.30 < X < 0.80 are studied with emphasis on the region near the superfluid transition T and near the phase-separation curve. Along the latter, they are compared with data by Lai and Kitchens. For X > 0.5, the viscosity singularity near T becomes a faint peak, which however fades into the temperature-dependent background viscosity as X tends to the tricritical concentration X _t. Likewise, no singularity in is apparent when T _t is approached along the phase separation branches _– and ₊. Furthermore, viscosity data are reported for ³He and compared with previous work. Finally, for dilute mixtures with 0.01 X 0.05, the results for are compared with previous data and with predictions.     

Viscosity of binary mixtures. I. mono-, di-, and tri-n-butyl and -n-octylamine with cyclohexane

Viscosities for six binary mixtures of n-butylamine, di-n-butylamine, tri-n-butylamine, n-octylamine, di-n-octylamine, and tri-n-octylamine with cyclohexane have been measured at 303.15 K with an Ubbelohde suspendedlevel viscometer. Deviations of viscosities from a rectilinear dependence on mole fraction are attributed to H-bonding and to the size of alkylamine compounds. The application of the Eyring's theory of activation energy is examined. The free volume theory of Prigogine-Flory-Patterson (PFP) and the experimental excess enthalpy have been used to estimate excess viscosity ln = (ln / ₁ ⁰ – x ₂ ln ₂ ⁰ / ₁ ⁰ ) and corresponding free volume, enthalpy, and entropy contributions for five binary mixtures of tri-n-alkylamine: triethyl, tripropyl, tributyl, trihexyl, and trioctylamine with cyclohexane. A comparison of experimental and theoretical excess viscosities indicates a failure of the PFP theory when two components of the mixture differ considerably in size. The size difference contribution to excess viscosity is related to (V ₂ ^*1/2 – V ₁ ^*1/2 ), where V ₁ ^* and V ₂ ^* are hard-core volumes of two components of the mixture.     

Correlation of high-pressure thermal conductivity,viscosity, and diffusion coefficients for n-alkanes

Thermal conductivity, viscosity, and self-diffusion coefficient data for liquid n-alkanes are satisfactorily correlated simultaneously by a method based on the hard-sphere theory of transport properties. Universal curves are developed for the reduced transport properties ^*, ^*, and D ^* as a function of the reduced volume. A consistent set of equations is derived for the characteristic volume and for the parameters R , R , and R _D, introduced to account for the nonsphericity and roughness of the molecules. The temperature range of the above scheme extends from 110 to 370 K, and the pressure range up to 650 MPa.     

The Viscosity Surfaces of Propane in the Form of Multilayer Feed Forward Neural Networks

The present work focuses on the development of a viscosity equation =(,T) for propane through a multilayer feedforward neural network (MLFN) technique. Having been successfully applied to a variety of fluids so far, the proposed technique can be regarded as a general approach to viscosity modeling. The MLFN viscosity equation has been based on the available experimental data for propane: validation on the 969 primary data shows an average absolute deviation (AAD) of 0.29% in the temperature, pressure, and density range of applicability, i.e., 90 to 630 K, 0 to 60 MPa, and 0 to 730 kgm^–3. This result is very promising, especially when compared with experimental data uncertainty. The minimum amount of required data for setting up the MLFN has been investigated, to explore the minimum cost of the model. Comparisons with other viscosity models are presented regarding amount of input data, claimed accuracy, and range of applicability, with the aim of providing a guideline when viscosity has to be calculated for engineering purposes. A high accuracy equation of state for the conversion of variables from experimental P,T to operative ,T has to be provided. To overcome this requirement, two viscosity explicit equations in the form =(P,T) are also developed, for the liquid and for the vapor phases. The respective AADs are 0.58 and 0.22%, comparable with those of the former =(,T) equation. Finally, the trend of the experimental viscosity second virial coefficient is reproduced and compared with that obtained from the MLFN.     

Viscosities and Excess Molar Volumes of Binary Mixtures of Alkyl Acetates with Di-, Tri-, and Tetrachloroethane

The excess molar volume V ^E, viscosity deviation , excess viscosity ^E, and excess Gibbs energy of activation G*^E of viscous flow have been investigated from density and viscosity measurements of nine binary mixtures of methyl acetate, ethyl acetate, and amyl acetate with dichloroethane, trichloroethane, and tetrachloroethane at 303.15 K. The results were fitted to polynomials of variable degree. The viscosity data have been correlated with the equations of Grunberg and Nissan, Hind, McLaughlin, and Ubbelohde, Tamura and Kurata, Katti and Chaudhri, McAllister, Heric, and Auslaender. The results have been analyzed in terms of molecular interactions between alkyl acetates and chloroethanes.     

Viscoelastic and rheological behavior of concentrated colloidal suspensions

Molecular approaches are discussed to the density (), viscoeleastic (), and rheological () behavior of the viscosity(,,) of concentrated colloidal suspensions with 0.3 < < 0.6, where, is the volume fraction, the applied frequency, and ; the shear rate. These theories are based on the calculation of the pair distribution functionP ₂(r,,), wherer is the relative position of a pair of colloidal particles. The linear viscoelastic behavior(,,=0) follows from an equation forP ₂(r,,) derived from the Smoluchowski equation for small, generalized to large by introducing the spatial ordering and (cage) diffusion typical for concentrated suspensions. The rheological behavior(,,=0) follows from an equation forP ₂(r,) of a dense hard-sphere fluid derived from the Liouville equation. This leads to a hard-sphere viscosity^hs(,) which yields the colloidal one(,) by the scaling relation(,) ₀=^hs(,) _B, where ₀ is the solvent viscosity. _B is the dilute hard-sphere (Boltzmann ) viscosity and the's are appropriately scaled,(,) and(,) agree well with experiment. A unified theore for(,,) is clearly needed and pursued.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994. Boulder, Colorado, U.S.A.     

Tests of Predictive Viscosity Models for Pure Liquids

It is of considerable importance to be able to predict accurately the viscosity of liquids over a wide range of conditions. In the present work, the ability of the three-parameter generalized corresponding states principle (GCSP) for the prediction of the viscosity of pure liquids is demonstrated. The viscosity of six different classes of pure liquids, viz., alkanes (19 compounds; 207 data points), cycloalkanes (6 compounds; 74 data points), alkenes (9 compounds; 146 data points), aromatics (4 compounds; 123 data points), alkanols (8 compounds; 89 data points), and esters (4 compounds; 28 data points) have been predicted over a wide range of temperatures using the three-parameter (T _c, P _c, ) GCSP. Five options for the third parameter () were studied, viz., Pitzer's acentric factor , molar mass M, characteristic viscosity *, critical compressibility factor Z _c, and modified acentric factor , in addition to groups Z _c and Z _c being treated as composite third parameters. Pressure effects were neglected. Good agreement between experimental and predicted values of viscosity was obtained, especially with either or * being used as the third parameter. Furthermore, the viscosities of alkanes predicted by the TRAPP method and an empirical, generalized one-parameter model for liquid hydrocarbons provide comparisons with the more accurate GCSP method. The GCSP provides a simple and yet a powerful technique for the correlation and prediction of viscosities of a variety of pure liquids over a wide range of temperatures.     

The viscosity and some related properties of liquid3He at the melting curve between 1 and 100 mK

The viscosity of liquid ³ He has been measured along the melting curve from 1 to 100 mK by means of a vibrating wire viscometer. In the normal Fermiliquid region we find 1/T² = 1.17–3.10T, where is in P and T in K. At the transition temperature T _A = 2.6 mK a rapid decrease occurs in _n , the viscosity of the normal component. Within 0.3 mK below T _A , _n decreases to about 25% of _A, but then becomes essentially constant. In the B phase _n first decreases to 20% of _A and then seems to increase below 1.4 mK. Data on _n , the density of the normal component, are also presented in the A and B phases. The results show that viscous flow is accompanied by a flow of zero dissipation, thus proving superfluidity in the A and B phases. The viscosity data at magnetic fields up to 0.9T have been related to theoretical calculations of the energy gap of superfluid ³ He near T _A . The splitting of the A transition and the suppression of the B phase in an external field were also measured.     

Shear viscosity of the B phase of superfluid3He

The shear viscosity (T) in the Balian-Werthamer (BW) state of superfluid ³ He is calculated variationally throughout the region 0t 1(t=T/T _c) from the transport equation for Bogoliubov quasiparticles. Coherence factors are treated exactly in the calculation of the collision integral. The numerical result for =_s= _s(T)/_n(T_c) agree very well with experiment in the range 0.8t1.0. Analytic expressions = 0.577 (1–1.0008t) and =1–(23/64) [=(T)/k _B T] are obtained in the low-temperature region and in the vicinity ofT _c, respectively. From the numerical analysis it is shown that the latter equation is valid only in the temperature range 0.9997t1.0.Supported by the Research Institute for Fundamental Physics, Kyoto University.     

Fermi liquid behaviour of the viscosity of3He-4He mixtures

We have investigated³He-⁴He mixtures at³He-concentrations 0.98%x9.5% by the vibrating wire technique in the temperature range 1 mKT 100 mK and at pressures 0 bar p 20 bar. In the degenerate regime of the mixtures the Landau theory of Fermi liquids predicts a temperature dependence of the viscosity proportionalT ^–2. We report on the first observation of this behaviour at 3 mKT 10 mK for all investigated concentrations and pressures. At temperatures below about 20 mK slip corrections had to be taken into account due to the increase of the quasiparticle mean free path at very low temperatures. The low-temperature cut-off in T ² = constant indicates the transition into the ballistic regime of the mixtures, where the mean free path of the quasiparticles exceeds the radius of the vibrating wire. Our results for the pressure dependence of the viscosity as well as for its magnitude show substantial differences from predictions based on pseudopotential theory. However, a calculation of with the quasiparticle interaction potential of recent solubility measurements in mixtures agrees well with our experimental data, in particular the pressure independence of .     

Inhomogeneous shear flows of linear polymers

Solutions of a system of equations of nonlinear viscoelastic fluid motion describing inhomogeneous shear flows of linear polymers are indicated.Notation _ij stress tensor - p pressure - F_i mass force vector - _ij Kronecker delta - coefficient of shear viscosity - relaxation time - _ij inner parameter - _ij=vi/x_j velocity gradient tensor - ₀ initial value of the shear viscosity coefficient - ₀ initial value of the relaxation time - D dimensionless first invariant of the additional stress tensor - A, B, C constants of integration - f(D) universal function characterizing the material - r, , z cylindrical coordinates - u=v_z axial component of the velocity vector - v=v circumferential component of the velocity vector - ₁, ₂ first and second differences of the normal stress - Q volume mass flow rate - R radius of a circular tube - R₁, R₂ radii of the inner and outer cylinders, respectively - M moment per unit length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 449–456, September, 1981.     

Effects of pressure sensitivity on the η factor and the J integral estimation for compact tension specimens

In this paper, the effects of pressure-sensitive yielding on the factor and the J integral estimation for compact tension specimens are investigated. The analytical expressions for and J for pressure-insensitive von Mises materials are generalized to pressure-sensitive Drucker-Prager materials using a lower bound approach. The factor as a function of the pressure sensitivity and the normalized crack depth for compact tension specimens is derived under plane stress and plane strain conditions. The numerical results indicate that the factor decreases as the pressure sensitivity increases. The effects are more pronounced under plane strain conditions than under plane stress conditions. However, the effects of the pressure sensitivity on are found to be mild in general. For rigid perfectly-plastic materials, the J estimation for pressure-sensitive materials is also reduced to a simple expression of the tensile yield stress times the crack tip opening displacement as for the von Mises materials.