Phonon transport in microscale regimes with binary species of atoms

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