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.     

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.     

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 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.     

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, ).     

A finite volume technique to simulate the flow of a viscoelastic fluid

Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D rate of strain tensor - L slit halfheight - P pressure, indeterminate part of the Cauchy stress tensor - R the Reynolds number - t time - U average velocity in the slit - u velocity vector - u,v velocity components - W the Weissenberg number based on the difference between stress relaxation time and retardation time - W ₁ the Weissenberg number based on stress relaxation time - x,y rectangular Cartesian coordinates - ratio of retardation time to stress relaxation time - zero-shear-rate viscosity, ₁ + ₂ - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to - ₁ stress relaxation time - ₂ retardation time - density - (, , ) xx, yy and xy components of ₁, respectively - determinate part of the Cauchy stress tensor - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to      

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 Density at High Pressures in an Associative Ternary

The dynamic viscosity and the density of the associative ternary mixture water+diacetone alcohol+2-propanol have been measured as a function of temperature T (303.15, 323.15, and 343.15 K) and pressure P (100 MPa). The experimental results correspond to 698 values of and . With reference to the 54 values previously published on pure substances and 486 values for three corresponding binaries, the system is globally described by 1188 experimental values for various values of P, T and composition. The results for are discussed in terms of excess activation energy of viscous flow.     

Cross-Correlated Dynamic Resistance of a Direct Current Superconducting Quantum Interference Device

This paper presents experimental data on a comparative study of a dc SQUID with voltage and current bias. We introduce a cross-correlated dynamic resistance of the device defined as a ratio R _dCV = _VC/_IV, where _VC = (V/) _A is the slope of the voltage-to-flux characteristics measured in the current bias mode and _IV = (I/) _A is the slope of the current-to-flux characteristics measured with voltage bias. It has been found that R _dCV may deviate strongly from the dynamic resistance observed in the current bias mode of operation. The intrinsic energy resolution of the SQUID remains unchanged for both modes of operation, but the current noise of the voltage biased device scales with the cross-correlated dynamic resistance. In our SQUID with the loop inductance L = 105 pH, is equal to 37 h in the white noise region at a temperature of 4.2 K.     

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 .     

Phase decomposition in extruded Zn-Al based alloy

Ageing characteristics of an extruded eutectoid Zn-Al based alloy were investigated using X-ray diffraction and scanning electron microscopy techniques. The extruded alloy consisted of Al rich phase and Zn rich _E and phases. The original cast eutectoid Zn-Al alloy was extruded at 250 °C. Both supersaturated _s and _s phase decomposed during extrusion and appeared as fine and coarse lamellar structures. The _E and phases particles formed in the original interdendritic region. It was found that two Zn rich phases _E and decomposed sequentially during ageing at 170, 140 °C. The decomposition of the _E phase occurred as a discontinuous precipitation in the early stage of ageing and the decomposition of the phase took place in a four phase transformation: + T + in the prolonged ageing. Two typical morphologies of the decomposition of the Zn rich phases _E and were distinctive in back-scattered scanning electron microscopy.     

Precipitation hardening in Cu 1.81 wt % Be 0.28 wt % Co

The structure of the precipitation hardening alloy Cu 1.81 wt % Be 0.28 wt % Co has been studied as a function of ageing temperature and time, by transmission electron microscopy. The continuous precipitation sequence found is: supersaturated solid solution G.P. zones .The G.P. zone is an ordered platelet precipitate, which is coherent on {100} matrix planes and is nucleated in very high densities (>10²⁴ m^–3). The coherency stress fields, due to the misfit of the G.P. zone and matrix, overlap to produce a net matrix contrast along {110} 10, and give the characteristic tweed structure, which can be described by the kinematical theory of diffraction. The semi-coherent intermediate precipitate is nucleated by the G.P. zones and the transformation is characterized from the changes in the arrowhead structure produced in the electron diffraction patterns. No transformation of to the equilibrium precipitate is found for the ageing times investigated.     

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.     

Morphological and crystallographic features of γ-γ′ Ni-Al and Ni-Al-Ti two-phase bicrystals

Several- Ni-Al and Ni-Al-Ti two-phase bicrystals were made by the solid-state diffusion couple method. Each couple consisted of a-phase single crystal and a pure-Ni polycrystal, and was annealed at 1473 K in an Ar gas atmosphere. Single crystal layers of-phase with uniform thickness always grow into the parent-phase single crystals. The resultant/ interface has no voids or facets regardless of the orientation of interface and the chemical composition of the-phase. Porosity formation due to the Kirkendall effect is observed in the diffused region. Concentration profiles exhibit nearly constant gradients in-phase. The orientation relationship between both phases is found to be 001//001, that is, the-phase grows epitaxially along the crystal orientation of-phase.     

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.     

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.     

Chemical Transformations of γ-Al(OH)3during Closed-System Heat Treatment

The chemical transformations of -Al(OH)₃during closed-system heat treatment in a self-generated gaseous atmosphere (water vapor) were studied. At t 200°C, -Al(OH)₃was found to convert into -AlOOH, which, in turn, converts into the equilibrium phase -Al₂O₃at t 400°C. The processes underlying the effect of water vapor on the kinetics and mechanisms of the chemical transformations of -Al(OH)₃and -AlOOH in a closed system are discussed.     

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.     

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. 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.