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Consideration is given to a microscale structure consisting of a thin porous medium filled with interstitial Ouid or a microscale regime with binary species of atoms. An example is a cellular membrane. This paper treats a one-dimensional model consisting of atoms of heavier mass  M  alternating with atoms of lighter mass  m  arranged in a series. Like photons, elastic vibrations of atoms or phonons propagate as waves. The problem of phonon transport, referring to heat conduction in the microscale regime, is formulated in terms of the displacements of atoms from their equilibrium positions. With the displacements treated as a wave motion, the frequency-wave number relationship for the heterogeneous-atomic membrane is obtained. Two modes of wave transport are obtained and their roles in phonon transport are discussed.

Phonon Transport in Microscale Regimes With Binary Species of Atoms