Thermal Casimir Force
Wetting
M.P. Nightingale
and J.O. Indekeu, Phys.
Rev. Lett. 54 , 1824 (1985)
Wetting by a Superfluid Film
Garcia and Chan monitored
thickness of a wetting film of helium near the superfluid transition.
"Critical Fluctuation-Induced Thinning
of He Films near the Superfluid Transition,"
R. Garcia and M.H.W. Chan,
Phys. Rev. Lett. 83, 1187 (1999)
Thickness
of the film (denoted by d ) is obtained by minimizing its energy,
as
The
film is thinner at the transition, and in the superfluid
phase
Phonons in the superfluid
The superfluid
phase of helium supports phonons ("mass-less" Goldstone
modes)
.
The
interaction resulting from (thermal) fluctuations of these modes is:
H. Li . Kardar, Phys.
Rev. Lett. 67 , 3275 (1991) ; Phys.
Rev. A 46 , 6490 (1992)
Surface Undulations
Can surface
fluctuations account for the (additional) thinning of the superfluid film?
"Casimir Forces, Surface Fluctuations,
and Thinning of Superfluid Films,"
Zandi, Rudnick, &
Kardar, Phys. Rev. Lett. 93 , 155302 (2004)
The normal
fluid is clamped due to viscosity, while the superfluid has
a velocity
Undulations
of the surface set up a superfluid velocity field that extends through
the film, and vanishes at the substrate. The corresponding Hamiltonian,
and free energy, give
There
is a corresponding force:
[Dzyaloshinskii, Lifshitz,
Pitaevskii (1961); Mahale and Cole (1986)]
The
net effect of phonons and surface undulations appear to account for the
thinning of superfluid films:
Next (Membranes)
Outline
QED Casimir force
Thermal Critical Casimir
Thermal Casimir in Helium
Membrane inclusions
Scale-invariant shapes
Entropic force in polymers
Phantom polymers
Self-avoiding polymers
Summary
Finite-size
contribution of long-wavelength fluctuations at criticality: 
Garcia and Chan monitored
thickness of a wetting film of helium near the superfluid transition.
.
