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.     

Mixing displacement of viscoplastic fluids feom a channel with a rectangular cavity

Different mixing displacement regimes for viscoplastic fluids are investigated theoretically and experimentally.Notation x and y Cartesian coordinates - h half-width of the gap - H, L dimensionless depth and length of the cavity - v_x, v_y velocity components - density - _ik components of the viscous stress tensor - e_ik components of the deformation rate tensor - dynamic viscosity - dynamic viscosity for infinitely high displacement velocity - ₀ analog of the limiting shear stress in Bingham's fluid - W parameter in Williamson's model - =/gh dimensionless viscosity - stream function - vorticity - ₀, ₀ distributions of and at the inlet - r,a, b, and c auxiliary constants - C concentration of the displacing fluid - D diffusion coefficient - Pe Peclet's number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 432–439, March, 1981.     

Hydrodynamic reaction to accelerated onedimensional motion of gas bubbles of variable volume in an unbounded liquid

A solution is given for the problem of the hydrodynamic reaction of an ellipsoidal gas bubble of variable volume to accelerated motion and the relation between the value of the apparent mass and the eccentricity of the bubble.Notation (,) velocity potential - V velocity of motion of the bubble with respect to the liquid - (, ) velocity potential of the near field - T₂ kinetic energy of the liquid due to the variation in bubble volume - F_r reaction force of the liquid - B₁ momentum of the liquid - _e apparent mass of the ellipsoid - density of the liquid - V_e volume of the ellipsoidal bubble Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 47–50, July, 1980.     

A note on the solution of a differential equation arising in boundary-layer theory

Summary The differential equation f + ff + f² = 0 (where dashes denote differentiation with respect to the independent variable ) subject to the boundary conditions f(0)=0, f()=0 and either f(0)=1 or f(0)=–1 is considered. It is shown that by using pf as dependent variable and =C–f (where C=f()) as independent variable and then expanding in powers of , a very good approximation to the solution can be obtained using only a few terms in the expansion.     

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.     

Separable functions in load separation for the ηpl and ηpl CMOD plastic factors estimation

The objective of this paper is to develop the load separation method for evaluating the _pl and _pl ^CMOD plastic factors used in the J estimation approach based on load versus displacement records. Appropriate forms for the geometry and deformation functions have been suggested from the EPRI Handbook solutions to produce the separable form for the load. The obtained functions are applied to evaluate the _pl and _pl ^CMOD plastic factors for center cracked tension specimen. The present load separation method gave results which are somewhat different from the estimated values of _pl given in the literature. For shallow cracks, the _pl and ^CMOD _pl plastic factors show considerable variation with crack size and the strain hardening exponent. For a deeply cracked CCT specimen, the ^CMOD _pl factor tends to the _pl factor and equals approximately unity. Abbreviations: CCT – center cracked specimen; CMOD – Crack Mouth Opening Displacement; EPRI – Electric Power Research Institute; FEM – Finite Element Method; LLD – Load Line Displacement.     

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.     

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, ).     

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.     

Natural damped frequencies and axial response of a rotating finite viscous liquid column

Summary For a finite solidly rotating cylindrical liquid column the damped natural axisymmetric frequencies have been determined. The liquid was considered incompressible and viscous. The cases of freely slipping edges and that of anchored edges have been treated. It was found that instability appears in a purely aperiodic root for the spinning liquid bridge. This is in contrast to the instability appearing in the damped oscillatory natural frequency of a nonspinning liquid column at . The spinning viscous liquid column exhibits the same instability as the frictionless liquid. It appears at for axisymmetric oscillations.List of symbols a radius of liquid column - I _m modified Bessel function of first kind and orderm - s complex frequency ( ) - r, ,z polar cylindrical coordinates - p pressure - t time - u, v, w radial-, azimuthal- and axial velocities of liquid, respectively - Weber number - h height of liquid column - dynamic viscosity of liquid - v kinematic viscosity of liquid (v=/) - density of liquid - surface tension of liquid - _r , _rz shear stress - (r, z, t) circulation - (r, z, t) streamfunction - ₀ angular velocity of liquid column about the axis of symmetry - (,t) free surface displacement     

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.     

Simulation of the Process of Water Freezing in a Round Pipe

The problem of freezing of pure water in a round pipe is treated with due regard for convection under asymmetric thermal boundary conditions in the absence of motion along the pipe. The problem is solved numerically using the control volume approach, SIMPLER algorithm, and the enthalpy method. Results are obtained for three Grashof (Gr) and six Biot (Bi) numbers: Gr = 1.55 × 10⁶, Bi = 0.305 (0 < ), Bi = 0.044 ( < 2); Gr = 1.24 × 10⁷, Bi = 0.610 (0 < ), Bi = 0.087 ( < 2); Gr = 9.89 × 10⁷, Bi = 1.220 (0 < ), Bi = 0.174 ( < 2). The correctness of calculation of the problem disregarding free-convection flows is analyzed.     

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 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.     

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      

Ageing characteristics of cast Zn-Al based alloy (ZnAl7Cu3)

Microstructure and ageing characteristics of a cast Zn-Al based alloy (ZnAl7Cu3) were studied using X-ray diffraction, electron scanning microscopy and back-scattered diffraction techniques. Two stages of phase transformation, i.e., decomposition of zinc rich phase and four phase transformation, + T + , were detected during ageing at 150°C. Electron back-scattered diffraction technique was applied in distinguishing both zinc rich and phases.     

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.     

Effect of annealing upon decomposition of electrodeposited iron-zinc alloy coatings

As-deposited electrodeposited iron-zinc alloy coatings containing phase, decompose upon heating through a sequence of metastable phases. The h c p phase transforms to b c c G, or -like phase via a rapid diffusional phase transformation in the vicinity of 150 °C. For bulk iron contents of 8–13 wt%, transforms to 100% G phase. The G phase subsequently transforms at 240 °C to phase, which in turn transforms to or ₁ phase near 300 °C by depletion of iron from the surrounding matrix. The decomposition process may be driven by supersaturation of with iron.     

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 .     

The quantitative application of Fermi-Dirac functions to two- and three-dimensional systems

Expressions for the various physical parameters of the ideal Fermi-Dirac gas in two dimensions are derived and compared to the corresponding three-dimensional expressions. These derivations show that the Fermi-Dirac functions most applicable to the two-dimensional problem are F ₀(), F ₁(), and F₀(). Analogous to the work of McDougall and Stoner in three dimensions, these functions and parameters derived from them are tabulated over the range of the argument, –420. The physical applications of the tabulated 2D and 3D functions to ³He monolayer and bulk liquid ³He nuclear magnetic susceptibilities, respectively, are considered. Calculational procedures of fitting data to theoretical parameters and criteria for judging the quality of fit of data to both two- and three-dimensional Fermi-Dirac values are discussed.This work was performed under the auspicious of the U.S. Department of energy, Office of Solar Application. Work also supported in part by the National Science Foundation and a Navy Equipment Lone Contract.