Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

Response of a spinning liquid column to axial excitation

Summary The response of a solidly rotating finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀).Notation a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - P liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _02n –1 natural frequency of harmonic axial response With 8 Figures     

Response of differently axially excited spinning liquid columns

Summary A solidly rotating finite liquid column consisting of frictionless liquid is subjected to various axial excitation modes. The response of the free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic range (<2₀). Differences of the various cases are presented.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2₀) - hyperbolic case (<2₀) - liquid density - surface tension - liquid surface displacement - _n damping factor - phase angle - acceleration potential - ₀ rotational speed - , ₁,₂ axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

On the maximum reduced upper critical magnetic field in Eliashberg theory

Consideration of the functional derivative of the zero-temperature reduced upper critical magnetic fieldh _c2(0) with electron-phonon spectral density ² F() suggests that its value can be maximized, for a given areaA under ² F(), with the choice of a delta-function spectral density. We show thath _c2(0) is then independent ofA and that it increases steadily as the Einstein frequency _E of the delta function is lowered. We argue that there is a local maximum inh _c2(0) at _E=0. The value at maximum is very sensitive to impurity content and increases sharply from a clean-limit value of 1.5 atT _c /_E=1.33 to more than 3.45 in the dirty limit.     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.     

Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

Summary The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequency/2 ₀. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - z₀ axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

Ultrasonic dispersion and attenuation near the liquid-gas critical point of 3He

We report ultrasonic dispersion and attenuation measurements near the liquid-gas critical point of ³He at frequencies from 0.5 to 5.0 MHz and densities from 0.89 _c to 1.15 _c . The singular part of the sound attenuation and the dispersion on the critical isochore _c = 0.0414 g/cm³ are analyzed in terms of the Kawasaki-Mistura theory. If the Ornstein-Zernike order parameter correlation function is assumed in the analysis, good agreement with our data is achieved, except close to the critical temperature T _cin the high-frequency region, where ^* = /_D 1. Here _D is the characteristic relaxation rate of the critical fluctuations. From a fit of the theory to our data, and assuming the inverse correlation length is expressed by = ₀, where = (T–T_c)/T_c with = 0.63, we obtain ₀ = (3.9 ± 0.4) × 10⁹ m^–1. It is found that a more realistic form of the correlation function, as proposed by Fisher and Langer and calculated by Bray, yields even poorer agreement with out data than does the classical Ornstein-Zernike form for ^* > 10. The same difficulties appear in the analysis of the available data for xenon. Thus, the present mode coupling theory is unable to satisfactorily describe the acoustic experiments on fluids near the liquid-vapor critical point over a large range of reduced frequencies ^*. In the appendix, we reanalyze previously reported ultrasonic data in ⁴He, taking into account the nonsingular term of the thermal conductivity. Using = 0.63, we obtain a good fit of the experiment to the theory in the hydrodynamic region with ₀ = (5.5 ± 1) × 10⁹ m^–1.Supported by a grant from the National Science Foundation.     

Transient two-dimensional diffusion along a high-diffusivity lamina which bisects a half-space

Summary The right half-space is bisected by a high-diffusivity planar sheet which lies along the x-axis. A sudden increase in the potential on (y-axis) causes longitudinal diffusion along coupled with transverse diffusion from into . Restricting to the case of large diffusivity ratio, to , it is demonstrated that the problem possesses a sequence of three distinct time domains in which self-similar solutions become asymptotically valid. The early, intermediate, and late solutions are each functions of only two independent variables; they are universally valid for all parameter values; and they are easily computed and readily applied. Transitions between asymptotics are described by expansions in time, the perturbations being regular in the early-intermediate period but singular in the intermediate-late period. The considered problem is a linear example which affords the opportunity for comparison with Fourier-Laplace analysis, and has application to thermal or electric conduction, diffusion mass transfer, and Darcy-flow of fluid in a fractured or layered porous medium. Methodology and qualitative observations are applicable to more complex nonlinear problems of the same class.This work supported by the U.S. Department of Energy under Contract DE-ACO4-76D00789.A U.S. DOE Facility.     

Thermodynamic properties of the superconductorsBaPb 0.7 Bi 0.3 O 3 andBa 0.7 K 0.3 BiO 3 using Eliashberg theory

We present results of a thermodynamic analysis for the superconductors compounds BaPb_0.7Bi_0.3O₃ and Ba_0.7K_0.3BiO₃. The physical quantities are calculated making use of the Eliashberg theory and the electron-phonon spectra ²()F() as calculated by Shirai et al. For the superconductor BaPb_0.7Bi_0.3O₃, several models of the ²()F() were studied looking for a better agreement with experimental data. The best fit is achieved with a simple constant scaling (C = 1.25) of the Shirai's spectra. The functional derivative of the deviation function D(t) with respect to changes in ²()F() is also calculated.     

Impulse approximation in solid helium

The incoherent dynamic form factorS _i(Q, ) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine theQ values for which the IA is valid for systems such as helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For³He,S _i(Q, ) is evaluated from first principles, beginning with the pair potential. The density of statesg() is evaluated using the self-consistent phonon theory andS _i(Q, ) is expressed in terms ofg(). For solid⁴He reasonable models ofg() using observed input parameters are used to evaluateS _i(Q, ). In both casesS _i(Q, ) is found to approach the impulse approximationS _IA(Q, ) closely for wave vector transfersQ20 Å^–1. The difference betweenS _i andS _IA, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (–_R), where _R is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium.     

High-frequency dielectric properties of Mg-Al-Si,Ca-Al-Si and Y-Al-Si oxynitride glasses

Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-_t8)^(n–1) and '^(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies.     

Axisymmetric stagnation-point flow impinging on a transversely oscillating plate with suction

The viscous fluid motion generated by axisymmetric stagnation-point flow of strain rate a impinging on a flat plate oscillating in its own plane with velocity amplitude U0 and frequency , including uniform suction of strength W0 is considered. A coordinate decomposition transforms the full Navier-Stokes equations into a primary equation describing the steady flow and a secondary equation describing the unsteady motion coupled to the primary solution. The solution to the boundary-value problem is governed by two dimensionless groups: the suction parameter S = W0 a and the frequency parameter = /a, where is the kinematic viscosity. Numerical integrations performed with a Runge-Kutta routine provide an exact solution to the Navier-Stokes equations. Values of the steady shear stress are found to agree with asymptotic results for large values of |S|, with S>0 representing suction and S<0 representing blowing. The magnitude and phase of the unsteady shear stress are given over a range of frequencies sufficient to recover analytical asymptotic results at large values of . The unsteady shear stress lags the wall motion by radians for 0 and by 5/4 radians when . Velocity profiles at selected parameter values during a period of plate oscillation are presented and discussed.     

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.     

Local optical-parameter distributions in tubular shear flows

Schlieren measurements have been made on the scattering-coefficient distributions in a two-dimensional nonisothermal turbulent air jet.Notation I averaged radiation intensity - (·) scattering indicatrix as a function of the cosine of the scattering angle - surface of unit sphere - s photographic sensitivity - t exposure time - h nozzle end thickness Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 715–718, May, 1989.     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

Scattering in a Spin-Charge Separated Non-Fermi Liquid

The electron self-energy due to the scattering on nonmagnetic impurities in a spin-charge separated non-Fermi liquid is calculated. The frequency dependence of the inverse scattering time is proportional to , for the case when the anomalous parameter = 0, and to ¹⁺ for 0. The scattering time is cutoff dependent when the anomalous parameter is nonzero.     

Nonlinear Response of a Continuous Wave NMR Spectrometer for Samples with a Large Magnetization

We present a new insight in the response of a CW NMR spectrometer for highly magnetized samples above 100 MHz. The spectrometer is a bridge made of a magic T. The output of the bridge is proportional to the reflection coefficient, , of a resonant circuit, which is built with a coil containing the sample. The sensitivity of the reflection coefficient to the complex susceptibility of the sample, () = () – j(), depends on the quality factor, Q, of the circuit and filling factor, . When the condition Q 1 is not fulfilled, we show indeed that the use of a simple crystal detector, which is only sensitive to || gives rise to a strong nonlinear response of the spectrometer. Measurements of the complex value of by means of phase sensitive detection allow to recover a linear behavior. We discuss and illustrate those issues with a few circuits we designed for our measurements on liquid ³ He with spin polarizations up to 15 %. A method is described to build in a reproducible and predictable way resonant circuits matched to 50 in the frequency range 100 – 400 MHz with a quality factor as high as 1000 at 4 K.     

Thermodynamic properties of superconducting niobium

The thermodynamic properties of superconducting Nb are calculated numerically from the solution of the Eliashberg equations on the imaginary axis for several possible electron-phonon spectral densities ²()F(). Comparison with experiment is made in order to see which spectrum gives the best agreement, and functional derivatives with respect to ²()F() are used to estimate how this agreement might be improved by small changes in ²()F(). Possible gap anisotropy effects are also considered with the help of a simple model anisotropy for the interaction.Research supported by Natural Science and Engineering Research Council of Canada.     

Delayed retardation phenomena of fatigue crack growth in various steels and alloys

The delayed retardation phenomena of fatigue crack growth resulting from a single application of overload were investigated for five steels, two aluminium alloys and a titanium alloy. As long as the small scale yielding condition was satisfied at the overloaded crack tips, the retardation behaviour of these materials was expressed consistently by four parameters; the peak/baseline stress ratio, r, the exponent in the Paris equation, m, the overload-affected zone size, _D, and the crack distance at the minimum rate of crack growth, _B. Then the parameters, _B and _D, characterizing the retardation phenomena for these materials were determined. The retardation of aluminium alloys was stronger than that of the other materials. This is attributed to the lower value of _B/ _D in aluminium alloys than in the other materials. In the case of r=2, the overload-affected zone sizes, _D, were nearly equal to 1.5 ₀ in HT80 steel and aluminium alloys, slightly lower than 1.5 ₀ in SNCM8 steel and much larger than 1.5 ₀ in A553 steel and the titanium alloy, where ₀ is the monotonic plastic zone size calculated according to the Dugdale model. The dependence of retardation on baseline stress intensity, K ₁, appeared somewhat complicated. In the cases of A553 steel and A2017 aluminium alloy the amount of retardation increased with increasing K ₁ value, while in the cases of HT80 steel and Ti-6A1-4V titanium alloy the tendency appeared in the reverse direction. The former behaviour was related to the change in the stress state from plane strain to plane stress at the overloaded crack tips and the latter was related to the threshold of stress intensity.     

Paramagnetic resonance in a “dirty” spin-glass

For a spin-glass with nonmagnetic defects (n _m ^1/3l 1, where n _m is the magnetic impurity concentration and l is the mean free path) an absorption function () is derived. Three ranges of temperature and external magnetic field are considered. In the vicinity of the transition the value of () d is estimated as a function of temperature and field.