Thermal Casimir Force
Finite-size contribution of long-wavelength fluctuations at criticality:
The thermal analog of the Casimir effect should lead to observable effects in wetting phenomena near critical points:
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)
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: