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.     

Excess volumes and excess viscosities of binary mixtures of some cyclic ethers + bromocyclohexane at 298.15 and 313.15 K

Excess Volumes,V ^E, and excess viscosities, ^E, at 293.15 and 313.15 K are reported for binary mixtures of some cyclic ethers (tetrahydrofuran, tetrahydropyran, 2-methyltetrahydrofuran and 2,5-dimethyltetrahydrofuran) + bromocyclohexane. These properties were obtained from density and viscosity measurements. ^E and ^E show negatives values for all the mixtures.     

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.     

Densities,Viscosities, and Refractive Indices of Binary Mixtures of Benzene with Isomeric Butanols at 30°C

The densities, , viscosities, , and refractive indices, n, of binary mixtures of benzene with 1-butanol, 2-methyl-1-propanol, 2-butanol, and 2-methyl-2-propanol, including those of the pure liquids, were measured over the complete composition range at 30°C. The dependence of , , and n on composition was checked by using an empirical relation. The experimental data were used to calculate excess molar volumes, V^E, deviations in viscosity, , excess free energies of activation of viscous flow, G^*E, deviations in refractive index, n, apparent molar volumes, V_,1 and V_{, 2}, and partial molar volumes, , of benzene in alcohols and alcohols in benzene, respectively, at infinite dilution. The variations of these parameters with composition and the effect of branching in alcohols were discussed from the point of view of intermolecular interactions in these mixtures.     

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.     

Viscosities of nonelectrolyte liquid mixtures. I. binary mixtures containing p-dioxane

Viscosity measurements are reported for p-dioxans with cyclohexane, n-hexane, benzene, toluene, carbon tetrachloride, tetrachloroethane, chloroform, pentachloroethane, and ethyl acetate at 303.15 K. Excess Gibbs energies of activation G ^*E of viscous flow have been calculated with Eyring's theory of absolute reaction rates. The deviations of the viscosities from a linear dependence on the mole fraction and values of G ^*E for binary mixtures have been explained in terms of molecular interactions between unlike pairs. The Prigogine-Flory-Patterson theory has been used to estimate the excess viscosity, ln , and corresponding enthalpy ln _H, entropy ln _S, and free volume ln _v terms for binary mixtures of p-dioxane with cyclohexane, n-hexane, benzene, toluene, carbon tetrachloride, and chloroform. Estimates of excess viscosities from this theory for p-dioxane with benzene, toluene, and carbon tetrachloride are good, while for the other three mixtures they are poor. The local-composition thermodynamic model of Wei and Rowley estimates the excess viscosity quite well even for p-dioxane mixtures with cyclohexane and n-hexane.     

Viscosity of biniary mixtures. III. Tri-n-butylamine with alkanes and monoalkylamines at 303.15 and 313.15 K

Viscosities of seven binary systems of n-propylamine, n-butylamine, n-hexylamine, n-octylamine, n-hexane, n-octane, and isoctane (2,2,4-trimethylpentane) with tributylamine have been measured at 303.15 and 313.15 K with an Ubbelohde suspended-level viscometer. Based on Eyring's theory, values of excess Gibbs energy of activation G ^*E of viscous flow have been calculated. Deviations of viscosities from linear dependence on the mole fraction and values of G ^*E are attributed to the H-bonding and to the size of alkylamine and alkane molecules. The free volume theory of Prigogine-Flory-Patterson in combination with work by Bloomfield-Dewan has been used to estimate the excess viscosity ln and the terms corresponding to enthalpy, entropy, and free volume contributions for the present binary mixtures.     

Viscosity of binary mixtures. II. n-butyl,n-hexyl,n-octyl,n-decyl,and n-dodecylamine with benzene and n-hexyl,n-decyl,and n-dodecylamine with cyclohexane

Viscosities of eight binary systems of n-butylamine, n-hexylamine, n-octylamine, n-decylamine, and n-dodecylamine with benzene and n-hexylamine, n-decylamine, and n-dodecylamine with cyclohexane have been measured at 303.15 K with an Ubbelohde suspended level viscometer. Based on Eyring's theory, values of excess Gibbs energy of activation G ^*E of viscous flow have been calculated. Deviations of viscosities from linear dependence on the mole fraction and values of G ^*E are attributed to H-bonding and to the size of alkylamine molecules. The free volume theory of Prigogine-Flory-Patterson in combination with the work of Bloomfield-Dewan has been used to estimate the excess viscosity In and the terms corresponding to enthalpy, entropy, and free volume contributions for 10 binary mixtures containing n-butyl, n-hexyl, n-octyl, n-decyl, and n-dodecylamine with benzene and cyclohexane.     

Viscosity of nonelectrolyte liquid mixtures. IV. Binary mixtures containingp-Dioxane

Measurements of the viscosity and densityp are reported for eight binary mixtures ofp-dioxane with methylcyclohexane, l-chlorohexane, l-bromohexane, p-xylene, propylbenzene, methyl acetate, butyl acetate. anyl acetate at 303.15 K. The viscosity data haw been correlated with the equations of Grunbeng Nissan. of McAllister, and of Auslaendcr. The relation among the excess viscosity In, excess Gibbs energy of activationG* ^E of viscous flow. and intermolecular interaction in these mixtures is discussed.     

Viscosity of Binary Mixtures of Alkyl Acetates with Hexane, Tetrachloromethane, and Trichloromethane

The viscosity for binary mixtures of methyl acetate (MA), ethyl acetate (EA), n-amyl acetate (nAA), isoamyl acetate (iAA), decyl acetate (DeA), and dodecyl acetate (DoA) with hexane and of MA, EA, nAA, and iAA with tetrachloromethane and trichloromethane has been measured at 303.15 K over the entire range of composition. 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 Brewer; and Auslaender. The viscosity deviations and excess Gibbs energy of activation G*^E of viscous flow based on Eyring's theory have been calculated. The results have been analyzed in terms of disruption of dipolar association of alkyl acetate and molecular interaction between alkyl acetate and chloromethane.     

Viscosities of Nonelectrolyte Liquid Mixtures Containing Acrylonitrile

The measurements of viscosity are reported for seven binary mixtures of acrylonitrile (AN) with ethanenitrile (EN), methyl acetate (MA), ethyl acetate (EA), n-butyl acetate (BA), dimethylformamide (DMF), dimethylacetamide (DMA), and dimethyl sulphoxide (DMSO) at 303.15 K temperature. 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 Brewer; and of Auslaender. The relations between the viscosity deviations , excess Gibbs energy of activation G*^E of viscous flow, and the intermolecular interaction in these mixtures are discussed.     

Viscosity of nonelectrolyte liquid mixtures. III Binary mixtures of methyl methacrylate with hydrocarbons,haloalkanes, and alkylamines

Measurements of the viscosity and the density are reported for 14 binary mixtures of methyl methacrylate (MMA) with hydrocarbons, haloalkanes, and alkylamines at 303.15 K. The viscosity data have been correlated with equations of Grunberg and Nissan, of McAllister, and of Auslaender. Furthermore, excess viscosity In and excess Gibbs energy of activationG* ^E of viscous flow have been calculated and have been used to predict molecular interactions occurring in present binary mixtures. The results show the existence of specific interactions in MMA + aromatic hydrocarbons, MMA + haloalkanes, and MMA + primary amines.     

Density and Viscosity of the 1-Methylnaphthalene+2,2,4,4,6,8,8-Heptamethylnonane System from 293.15 to 353.15 K at Pressures up to 100 MPa

The dynamic viscosity of the binary mixture 1-methylnaphthalene+2,2,4,4,6,8,8-heptamethylnonane was measured in the temperature range 293.15 to 353.15K (in progressive 10K steps) at pressures of 0.1, 20, 40, 60, 80, and 100MPa. The composition of the system is described by nine molar fractions (0 to 1 in 0.125 progressive steps). The density was measured at pressures from 0.1 to 60MPa in progressive 5 MPa steps. The measurements of are used to determine the excess viscosity ^E and the excess activation energy of flow G ^E as a function of pressure, temperature, and composition. Some models have been used to represent the viscosity of this binary mixture.     

Effect of the temperature dependence of thermal properties on the thermal shock tests of ceramics

Thermal stress generated during a thermal shock is closely related to the fracture of ceramics. An attempt has been made to obtain thermal stress in a specimen by numerical calculation. The temperature dependence of thermal conductivity and diffusivity were introduced to realize the practical thermal conditions. The maximum thermal stress, _max ^* , was recognized at the Fourier number, but differed from the temperature dependence. Correlative equations of _max ^* and _max ^* with the Biot number, _i, under cooling or heating tests, have been proposed. These equations resulted in the exact _max ^* and _max ^* compared with the previous equations, in which temperature dependence was ignored. The thermal shock resistance parameter was expressed by the correlative equations of _max ^* in order to suggest adequate experimental conditions and specimen size. A comparison of the measured and calculated time to failure of the specimen led to confirmation of the fracture criterion. The measured time disagreed with the calculated one, if the fracture by thermal shocking was not predominant. The correlative equations were also useful to select the kind of ceramics subjected to thermal shocking.     

p-Version hierarchical three dimensional curved shell element for heat conduction

This paper presents a finite element formulation for a three dimensional nine node p-version hierarchical curved shell element for heat conduction where the element temperature approximation can be of arbitrary order p , p , and p in the , and directions. This is accomplished by first, constructing one dimensional hierarchical approximation functions and the corresponding nodal variable operators for each of the three directions , and using Lagrange interpolating polynomials and then taking their products (sometimes also called tensor products). The element approximation functions as well as the nodal variables are hierarchical and therefore the element matrices and the equivalent heat vectors are hierarchical also i.e. the element properties corresponding to polynomial orders p , p , and p are a subset of those corresponding to (p +1), (p +1), and (p +1). The element formulation ensures C ⁰ continuity. The curved shell geometry is constructed in the usual way by taking the coordinates of the nodes lying on the middle surface of the element (=0) and the nodal thickness vectors. The element properties i.e. element matrices and the equivalent heat vectors are derived using weak formulation (or quadratic functional) of the three dimensional F ourier heat conduction equation and the hierarchical element temperature approximation. The element formulation is equally effective for very thin as well as extremely thick shells. Numerical examples are presented to demonstrate the accuracy, efficiency, modeling convenience, faster rate of convergence and over all superiority of the present formulation. The h-approximation results are presented for comparison purposes.     

Excess Molar Volumes and Viscosities of Mixtures of Diethylene Glycol Dibutyl Ether with Dialkyl Carbonates at 298.15, 308.15, and 318.15 K

Excess molar volumes,V ^E _m, and viscosities,, were measured as a function of composition for the binary mixtures of diethylene glycol dibutyl ether+dimethyl carbonate, +diethyl carbonate, and +propylene carbonate at temperatures of 298.15, 308.15, and 318.15 K and atmospheric pressure over the whole range of mixture compositions. From the experimental results, deviations in the viscosity,ln, and excess free energies of activation of viscous flow,G*^E, were calculated. The experimental results were correlated using the Redlich–Kister equation. The experimental and calculated quantities were used to analyze the mixing behavior of the components. Furthermore, activation enthalpies,H*, and entropies,S*, of viscous flow were evaluated and their variation with concentration is discussed.     

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.     

Hydrodynamic similarity in an oscillating-body viscometer

Hydrodynamic similarity can be used to calibrate simply and accurately an oscillating-body viscometer of arbitrarily complicated geometry. Usually, an explicit hydrodynamic model based on a simple geometry is required to deduce viscosity from the transfer function of an oscillating body such as a vibrating wire or a quartz torsion crystal. However, at low Reynolds numbers the transfer function of any immersed oscillator depends on the fluid's viscosity only through the viscous penetration depth(2/)^1/2. (Here and are the fluid's viscosity and density and/2 is the oscillator's frequency.) This hydrodynamic similarity can be exploited if the oscillator is overdamped and thus is sensitive to viscosity in a broad frequency range. Even an oscillator of poorly known geometry can be characterized over a range of penetration depths by measurements in a fluid of known and over the corresponding range of frequencies. The viscosity of another fluid can then be compared to that of the calibrating fluid with high accuracy by varying the frequency so that the penetration depth falls within the characterized range. In the present work, hydrodynamic similarity was demonstrated with a highly damped viscometer comprised of an oscillating screen immersed in carbon dioxide. The fluid's density was varied between 2 and 295 kg·m^–3 and the fluid's temperature was varied between 25 and 60°C. The corresponding variation of the viscosity was 50%.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

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.     

Viscosity of Some Binary Mixtures of Arenes

The viscosity of 12 binary mixtures of benzene+toluene, +ethylbenzene, +isopropylbenzene, +tert-butylbenzene; toluene+ethylbenzene, +isopro- pylbenzene, +tert-butylbenzene; ethylbenzene+isopropylbenzene; isopropylbenzene+tert-butylbenzene; o-xylene+m-xylene; m-xylene+p-xylene; and p-xylene+o-xylene has been measured over the entire range of composition. The viscosity deviations and excess Gibbs energy of activation G ^*E of viscous flow based on Eyring's theory have been calculated. The results have been analyzed in terms of the change in the structure of pure component molecules. The viscosity data have been correlated with the equations of Grunberg and Nissan; Hind, McLaughlin, and Ubbelohde; Tamura and Kurata; Katti and Chaudhri; McAllister; and Heric and Brewer. The Prigogine–Flory–Patterson– Bloomfield–Dewan (PFPBD) theory has been applied to analyze the excess viscosity of the present binary mixtures.