Repulsive Casimir Force I: Opposing boundaries


  Scalar Fields with Dirichlet (D) or Neumann (N) boundary conditions:

     Similar boundaries (DD or NN) lead to attraction, while opposing boundaries (DN) result in repulsion.

  In Lifshitz (DLP) theory, this is obtained by an intervening medium with dielectric constant intermediate to the  boundaries, as in the case of liquid helium climbing (wetting) a wall.  (dielectric constants: solid > helium > air).

 "Verification of Lifshitz theory of the van der Waals Potential using liquid-helium films,"

E.S. Sabisky and C.H. Anderson, Phys. Rev. A 7, 790 (1973)

 "Measured long-range repulsive Casimir–Lifshitz forces,"

J. N. Munday, F. Capasso & V. A. Parsegian, Nature 457, 170 (2009) (gold, bromobenzene, silica)

  Opposition of hydrophobic/hydrophilic surfaces in oil-water mixtures close to criticality:

"Critical Casimir forces in colloidal suspensions on chemically patterned surfaces,"

F. Soyka, O. Zvyagolskaya, C. Hertlein, L. Helden, & C. Bechinger, Phys. Rev. Lett. 101, 208301 (2008) (movie)

  

  Immersing MEMs in fluids is not practical.  Is repulsion across vacuum possible?

"Van der Waals forces and zero-point energy for dielectric and permeable materials,"

T.H. Boyer, Phys. Rev. A 9, 2078 (1974) (A perfect conductor repels a perfect magnet)

A material with large permeability is required for repulsion, but in ordinary materials permeability is close to one.

Metamaterials, incorporating arrays of microengineered circuitry mimic, at certain frequencies, a strong magnetic response and have been proposed as candidates for Casimir repulsion across vacuum.