Theoretical studies of the propagation of sound in narrow channels filled with helium II. I. The dispersion relations of fourth sound and of the fifth wave mode

Wiechert, H.; Meinhold-Heerlein, L.

doi:10.1007/bf00629714

Cited by 18 publications

(2 citation statements)

References 10 publications

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“…In this low-frequency limit, the second sound mode becomes diffusive in character, q$ = iw/D, with a diffusivity given by -Heerlein 1970). This mode wm unambiguously observed by Weichert & Passing (1982) in plane-parallel capillaries of width 2d for which k,/# = d2/3.…”

Section: P Pmentioning

confidence: 57%

Theory of dynamic permeability and tortuosity in fluid-saturated porous media

1987

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We consider the response of a Newtonian fluid, saturating the pore space of a rigid isotropic porous medium, subjected to an infinitesimal oscillatory pressure gradient across the sample. We derive the analytic properties of the linear response function as well as the high- and low-frequency limits. In so doing we present a new and well-defined parameter Λ, which enters the high-frequency limit, characteristic of dynamically connected pore sizes. Using these results we construct a simple model for the response in terms of the exact high- and low-frequency parameters; the model is very successful when compared with direct numerical simulations on large lattices with randomly varying tube radii. We demonstrate the relevance of these results to the acoustic properties of non-rigid porous media, and we show how the dynamic permeability/tortuosity can be measured using superfluid 4He as the pore fluid. We derive the expected response in the case that the internal walls of the pore space are fractal in character.

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Section: P Pmentioning

confidence: 57%

Theory of dynamic permeability and tortuosity in fluid-saturated porous media

1987

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“…Since, in this paper, we are only interested in the velocity and the attenuation of fourth sound, the contribution of the coefficient of thermal conductivity K can be neglected compared to other contributions, which can be estimated from the results of Ref. 18. However, contributions from K cannot be neglected in the case of the fifth wave mode, ~8 but this problem does not concern us here.…”

Section: Theorymentioning

confidence: 92%

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

Läuter

Wiechert

1979

J Low Temp Phys

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The velocity and the attenuation of fourth sound have been measured in liquid helium at temperatures between 0.8 K and the A 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 ~7 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. L INTRODUCTIONIn helium II several modes of sound propagation exist, 1 one of which is fourth sound. Fourth sound represents a density oscillation only in the superfluid component, when the normal fluid component is locked. This condition can be experimentally achieved by containing helium II in restricted geometries (capillaries), which have a characteristic linear dimension (diameter) d, small compared to the penetration depth of the viscous wave h~, defined as Xo = (2~7/pnto) 1/2(1) ~7 and pn are the viscosity and the density of the normal fluid component, respectively, and ~o is the angular frequency.

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The Boundary Value Problem for Helium II

Schmidt

1977

Annalen der Physik

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Considering all the dissipative processes in confined helium 11, it turns out that the boundary value problem, as given by the Khalatnikov equations and the already known boundary conditions has a unique solution only if one has a further condition concerning the behaviour of helium I1 a t the boundary. In this paper such an additional boundary condition is deduced from the thermodynamics of irreversible processes. The other already known boundary conditions are also generalized, to the extent that all dissipative processes in the helium are considered. Explicit calculations will be made for the free surface case as well as for the case of a rigid immovable wall.Das Randwertproblem fur Helium 11 I n h a l t s ubersicht. Wenn man alle dissipativen Prozesse in begrenztem Helium I1 beriicksichtigt, dann ist das Randwertproblem, das durch die Kalatnikov-Gleichungen und die bereits bekannten Randbedingungen gegeben ist, nicht eindeutig Iosbar. Erst durch Hinzunahme einer weiteren Bedingung, die das Verhalten von Helium I1 am Rand beschreibt, wird das Problem eindeutig losbar. I n dieser Arbeit wird eine solche zusLtzliche Randbedingung aus der Thermodynamik irreversibler Prozesse abgeleitet. Auch die anderen Randbedingungen werden unter Berucksichtigung aller dissipativen Prozesse in Helium I1 verallgemeinert. Explizite Rechnungen werden fur den Fall der freien OberflLche und der festen, unbeweglichen Wand durchgefuhrt.

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Theoretical studies of the propagation of sound in narrow channels filled with helium II. I. The dispersion relations of fourth sound and of the fifth wave mode

Cited by 18 publications

References 10 publications

Theory of dynamic permeability and tortuosity in fluid-saturated porous media

Theory of dynamic permeability and tortuosity in fluid-saturated porous media

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

The Boundary Value Problem for Helium II

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