Third Sound


 The weak interaction between helium atoms results in a liquid phase that persists all the way down in temperature to absolute zero.  In the low temperature regime, below 2.17 K at SVP, helium liquid is dominated by a "zero point" quantum energy which completely changes the behavior of the fluid.  It is actually best thought of as a Bose-condensed many particle system with every atom in the fluid occupying a single quantum state.  With all of the particles sharing same state, and contributing collectively to the state's quantum energy level, single particle atomic scale interactions become impossible, essentially overwhelmed by the macroscopic quantum state changes that are favored by the huge numbers of particles involved.

Amazing properties result from this suppression of microscopic interaction.  Foremost is the motivation of the term superfluid: in many experiments, fluid flow exists as one of the macroscopic quantum states mentioned above, and persists indefinitely without decay.  This is a frictionless flow, or zero viscosity.

An accurate description of the fluid's behavior is with a model where thermal agitation in the fluid is treated in the same way as black body radiation for a vacuum.  Instead of electromagnetic agitation, there are acoustic modes called phonons and rotons that are quantized and thermally populated.  These excitations act as a second, gaseous like fluid, distinct from the quantum state serving as their propagation medium.  In this "two fluid model", the superfluid (ground state medium) flows without viscosity or thermal energy, and the normal fluid (excitation gas) flows relatively independent as a regular fluid with drag and heat content.

Third Sound

If a thin film of helium is adsorbed on a surface, the van der Waals attraction responsible for the adsorption acts like a local gravity.  Surface displacements of the film will propagate as waves along the film, just as water waves do under the influence of gravity.   Even microscopically thin films support this wave motion, and if the wavelength is much longer than the depth, the motion is dominated by lateral flow of the film.  This is "third sound".

The third sound film flow involves only the superfluid component within the two fluid model.  The normal component excitations are viscously clamped to the substrate through scattering.  As the superfluid wave sloshes about, the normal component, containing the heat, is rarefied and diluted resulting in temperature oscillations that are coupled to the thickness oscillations.  The relative amplitude of the temperature oscillations can be as large as the thickness oscillations ( DT/T = - Dh/h ) in an adiabatic limit, but is often smaller due to thermal conduction within the film and to the substrate.

 Generation and Detection

 It is possible to couple transducers to either the temperature or the thickness oscillations. Applying heat couples to the wave through a thermo-mechanical effect and a sensitive enough thermometer can respond to the temperature fluctuations. Thickness oscillations can be capacitively coupled, taking advantage of the (unfortunately very weak) dielectric constant of liquid helium. Applying an electric field will pull the film into high electric field regions. A sensing electrode containing some of the active region of the film in its gap will detect thickness changes.

Pulsed time of flight and resonance methods have been successfully used, with the latter the method of choice for accurate amplitude and attenuation measurement.

Useful Relationships

These topics refer to Mathcad 14 documents as either Adobie PDF print images or the source .xmcd files.

van der Waals potential   ( PDF or xmcd )

Film - Vapor Equilibrium   ( PDF or xmcd )

Third Sound Speed vs. Film Thickness   ( PDF or xmcd )

Equations of motion including thermal and vapor coupling   ( PDF or xmcd )

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