Third Sound
Superfluids
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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