The force between two parallel rigid plates due to the radiation pressure of phonons

lLarraza et al. measured the force between two plates in an external high-intensity sound field. In analogy to the conventional "Casimir effect" it was called the "acoustical Casimir effect." The purpose of this paper is to derive the force between two plates without external sound fields, that is, induced only by thermal-pressure fluctuations, i,e., by phonons in air. For this reason, the approximated Debye method will be used. Thereby, air will be described as a phonon field and the number of modes in free air and between the plates with distance d will be estimated. A deficiency of modes in the cl-space results in a deficiency of radiation pressure and therefore leads. to an attractive plate pressure f = pi kT/18 d(3) Pa. In ambient air and for a plate distance d = 10(-5) m the pressure f = 0.7 10(-6) Pa follows. In comparison to the Casimir forces due to the zero-point field of the vacuum, the pressure is of the same size and can also be measured. (C) 1999 Acoustical Society, of America. [S0001-4966(99)07512-8].