On the nature of the fourth sound

The density-density correlation function of He II bounded by solid walls is calculated in the hydrodynamic region. The migration of its poles as a function of the resistance parameter is investigated, and it is found that the fourth-sound pole can only be related to the first-sound pole far enough (_s0/₀>1/9) from the critical temperature. Otherwise, it arises from a mixture of the first- and second-sound poles. The contributions of poles to the sum rules are also discussed.     

Experimental studies on fourth sound in superfluid helium

In a superfluid liquid-helium cavity packed with a fine powder, only the supercomponent is free to move and pressure waves transmitted by the supercomponent are called fourth sound. We have observed that the resonance frequency of the powder-filled chamber may be shifted by introducing vortices. Both static and dynamic measurements were made on the resonance frequency and signal height in order to explore the effect of exceeding the critical velocity of the superfluid in the powder-filled chamber.Supported by the Robert A. Welch Foundation, Houston, Texas.     

Superfluid density of3He measured by fourth sound

Superfluid density of³He has been measured using fourth sound in two superleaks: “confined,” packed powder and “open,” parallel channels. The superleak pore size has little effect on the superfluid density near the melting pressure, but it has surprisingly large effects at lower pressures. The open, parallel channel superleak results show an unexpected pressure dependence of “strong coupling” effects and an unexpectedly small superfluid density change at the B→A transition.     

Size effects in He II as measured by fourth sound

Fourth-sound measurements are used to determine the depletion in the superfluid density _s which occurs in the helium filled small pores of packed powders. The measurements also give the reduction in superfluid onset temperature. The pore size distribution of several samples was determined from desorption isotherms. Using this distribution and an independent pore model, calculations based on the Ginzburg-Pitaevskii ansatz with a healing length first proposed by Mamaladze are found to be in good agreement with experimental results in several cases. The superfluid onset temperature seems to be determined by the average pore size. Fourth-sound measurements as a function of temperatureT in large pore geometries accurately give _s (T –T)^2/3 in the neighborhood of the lambda temperatureT .     

Tearing of blast loaded plates with clamped boundary conditions

Extensive experimental results for the prediction of the onset of thinning (necking) and hence subsequent tearing at the boundary of clamped circular plates subjected to uniformly loaded air blasts are presented. The experiments include: plates of diameter ranging from 60mm to 120mm; different clamped edge conditions; (sharp edge; and radii of 1.5mm and 3.2mm) and an examination of the microstructural behaviour. Observations of thinning at the boundary show similar trends for all plate diameters with sharp edge conditions, and where the boundary edge condition is relaxed the deflections are larger before thinning and tearing occurs. Three phases within Mode I (large inelastic deformation) are identified as; Mode I (no visible necking at the boundary); Mode Ia (necking around part of the boundary); and Mode Ib (necking around the entire boundary). Predictions using the code ABAQUS provide, in particular for Mode I, favourable correlations with the experiments.     

Measurement of the velocity and attenuation of fourth sound in helium II

The velocity and the attenuation of fourth sound have been measured in liquid helium at temperatures between 0.8 K and the point, along the vapor pressure curve. The measurements were made using the resonance technique and the helium was contained between small pores in packed powder specimens. From the velocity, it could be determined that the sound propagates under adiabatic conditions. According to theory, the attenuation of fourth sound consists of two contributions: surface losses due to heat exchange with the resonator body and volume losses due to dissipative processes associated with the viscosity coefficients and ₃. The results of our attenuation measurements are in agreement with this theory; however, it appears that the attenuation is affected at low temperatures, if the mean free path of an elementary excitation becomes comparable to or larger than the mean pore diameter of the packed powder samples.This work was supported in part by the Deutsche Forschungsgemeinschaft. It is part of the dissertation (D77) of H.-J. Lauter.     

The effect of a magnetic field on fourth sound in 3He

The influence of a magnetic field on the propagation of fourth sound in superfluid ³He is studied. The field and temperature dependences of the average superfluid density \- _s / and fourth sound Q are measured. The field dependence of \- _s / is very different in a porous medium than predicted by Ginzburg-Landau theory applied to bulk liquid. In particular, a magnetic suppression of \- _s / is observed in the temperature and pressure ranges corresponding to the A phase in bulk liquid. There is strong evidence of a magnetic suppression of T _c itself. The measured \- _s / has a slight history dependence in a magnetic field, but none in zero field. The fourth-sound Q values are compared to the theoretical work of Smith, Jensen, and Wolfle. Quantitative confirmation of their work is problematic.     

Damping of fourth sound in4He due to normal fluid flow

Measurements of the attenuation of fourth sound were made in superfluid⁴He contained in several porous media with characteristic sizes sufficiently large to permit some normal fluid flow. The data are for pressures between vapor pressure and 25 bar and for temperatures between 1.4 K and the-line. The attenuation was dominated by viscous dissipation associated with the normal fluid flow. For a given medium, it varied by nearly two orders of magnitude over the pressure and temperature range of the experiment. Analysis of the data along isobars and isotherms in terms of an idealized model for the porous medium yielded a unique temperature- and pressure-independent characteristic size for each medium.     

Doppler shift in third and fourth sound in 3He-4He mixtures

The Doppler-shifted velocity of third sound in a system where the superfluid flows with velocity v _s is given. The calculations are to first order in v _s/u₃ where u ₃ is the third-sound velocity in the rest frame. We take into account the effects of the pressure and ³He concentration gradients normal to the substrate. Corresponding calculations for fourth sound are also given.Supported in part by the GFK, West Germany, through the Israel National Council for Research and Development.     

Pitfalls of the relaxation time approximation: Hydrodynamic sound in a multicomponent Fermi liquid

When transport in a Fermi liquid is treated in the relaxation time approximation, the quasiparticle energy appearing in the local equilibrium distribution must have the form determined by the nonequilibrium distribution function. Sometimes this requirement is overlooked and the equilibrium quasiparticle energy is used. In applications to unpolarized normal³He the resulting error can be repaired by a simple rescaling of the relaxation rates 1/₁ by the Fermi liquid corrections 1+F ^l/(2l+1). The distinction between the two forms of the relaxation time approximation is thus of little consequence, and quantities independent of the relaxation time are entirely unaffected. We point out that more significant damage results from using this wrong relaxation time approximation in a multicomponent (or spin-polarized single-component) Fermi liquid. In particular, it is essential to use the correct form to derive the velocity of hydrodynamic sound, even though the incorrect form also satisfies all the conservation laws, and even though the sound velocity is independent of the relaxation time.     

Vorticity and the theory of aerodynamic sound

Lighthill strongly advocated the use of vortex methods in most areas of fluid mechanics with the notable exception of the theory of aerodynamic sound. But it is straightforward to transform his famous `acoustic analogy' to make vorticity rather than Reynolds stress the ultimate `source' of sound in homentropic flows. `Vortex sound' theory becomes especially useful in applications involving acoustically compact flow-structure interactions, where it actually emerges as an extension of Kelvin's theory of `vortex impulse', a notion that Lighthill regarded as important enough to be given special treatment in undergraduate lectures on fluid mechanics. The `impulse source' can be recast in a form more suited for numerical or analytical evaluation, and is closely related to the `compact Green's function'. Convergence difficulties encountered in the casual application of the acoustic analogy to non-compact flow-structure interactions are resolved in a natural manner by the methods of vortex sound theory. New illustrations of these methods are given in this paper by consideration of the unsteady development of lift by a starting airfoil, of the production of sound by a `vortex whistle', and of the infrasound generated when a high-speed train enters the tunnel.     

Effects of4He coverage on the propagation of fourth sound in superfluid3He

We report measurements on the effects of⁴He coverage and pressure on the fourth sound propagation in superfluid³He in confined geometries of four different pore sizes.     

Hydrodynamic potential-modulated reflectance spectroscopy: theory and experiment

This article describes the development and application of a new electrochemical methodology based on potential-modulated UV-vis reflectance spectroscopy (PMRS). The device configuration is based upon a thin-layer flow-through channel cell incorporating a platinum working electrode. Reagent solutions are pumped through the cell under well-defined hydrodynamic conditions and electrolyzed at the platinum working electrode. Measurements are presented for linear sweep and fixed dc potentials with a superimposed small amplitude sinusoidal potential perturbation. A UV-vis source is employed to irradiate the electrode region, and the resulting reflected signal is analyzed using a phase sensitive detector. Experimental studies using tris(4-bromophenyl) amine (TBPA) in acetonitrile are presented which quantify the relationship between the absorption spectrum and reflected light intensity as a function of the transport rate, electrolysis reactions, and the modulation frequency of the incident irradiation. The experimental results are analyzed using numerical simulations based on a finite difference strategy. These permit the quantitative prediction of the concentration distribution of reagents within the cell. A fast Fourier transform (FFT) routine was used to analyze the frequency response of the numerically predicted reflectance signal. Excellent agreement was observed between the numerical predictions and experimental observations.     

Boundary conditions for second sound in superfluid 4He

Standing surface waves produced by second sound in superfluid ⁴He have been observed optically. A spectrum of 84 frequencies was obtained. The theoretical spectrum calculated by using the conventional boundary condition of zero heat transfer does not agree with the experimental spectrum. Good agreement is obtained by assuming nonzero heat transfer at the boundary. An empirical heat transfer coefficient is defined and calculated. The amplitudes of the surface waves are discussed and related to the heat transfer.Supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlischen Forschung.     

Hydrodynamic conditions in a fixed three-phase granular layer. Experimental investigation

An experimental investigation of the hydrodynamic conditions in a three-phase granular layer for direct upward flow of a gas and a liquid has been performed. The floating-up speeds of gas bubbles and pistons have been determined for different operating conditions A diagram of hydrodynamic conditions has been plotted.     

Steady-state heat conduction in composite systems with boundary conditions of the fourth kind

A method is proposed for solving steady-state heat-conduction problems in a system of contacting regions, and examples are presented to illustrate its effectiveness.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 1, pp. 147–151, January, 1979.     

Hydrodynamic theory of heat transfer to through-flow gas and liquid suspensions

A derivation of the heat transfer equation is based on an extension of the Reynolds analogy to turbulent gas and liquid dispersed suspensions with a low solids concentration at Pr1 with allowance for the motion of the boundary layer.     

Second viscosity and the attenuation of fourth and second sound in superfluid3He near the transition temperature

The relevant coefficient of second viscosity ₃ is calculated exactly near the transition in terms of the quasiparticle scattering amplitude in the normal state. ₃ is shown to dominate the attenuation of fourth and second sound. Second sound should be well defined only at frequencies below about 1 Hz.     

Healing and relaxation in flows of helium II. Part II. First,second, and fourth sound

In Part I of this series, a theory of helium II incorporating the effects of quantum healing and relaxation was developed. In this paper, the propagation of first, second, and fourth sound is discussed. Particular attention is paid to sound propagation in the vicinity of the point where the effects of relaxation and quantum healing become important.Supported in part by a special research grant GR/A/0556 from the Science Research Council of Great Britain, and (for RNH) by U.S. Air Force grant AFOSR 76-2880 and National Science Foundation grant ENG-76-07354.