Kapitza resistance in the lattice Boltzmann-Peierls-Callaway equation for multiphase phonon gases

The interface thermal resistance becomes more and more important as device miniaturization for better performance renders a large surface-to-volume ratio and invariably requires a device design with multiple materials inducing thermal interfaces across the material heterogeniety. Toward developing a comprehensive computational methodology for thermal transport prediction, incorporating the interface effects in a heterogeneous medium, a novel boundary collision rule is devised in the lattice Boltzmann computational scheme to realize a thermal interface between phonon gases with dissimilar dispersion relations. Consistent with the Callaway collision operator for Umklapp process, the interface phonon collision process is regarded as a linear relaxation mechanism toward the local pseudo-equilibrium phonon distribution, which is uniquely defined by the energy conservation principle. The Kapitza length and the interface thermal resistance are determined by the relaxation parameter and the local phonon properties. The implementation of the proposed mesoscopic boundary collision rule in the lattice Boltzmann computational framework provides a methodology of predicting the thermal properties of a heterogeneus medium incorporating both normal and Umklapp collision processes of phonon.