Size effect on phonon Knudsen minimum in three-dimensional graphite ribbons

Phonon Poiseuille flow has been recently demonstrated in graphite ribbons via both theory and experiment through super-ballistic temperature-dependent thermal conductivity. However, the super-ballistic size dependence of thermal conductivity in the hydrodynamic regime, i.e., phonon Knudsen minimum, remains to be further studied. In this work, we investigate the size effect on phonon Knudsen minimum in three-dimensional graphite ribbons based on a direct solution of real- and reciprocal-space-dependent phonon Boltzmann transport equation with first-principles input. We also quantify the strength of the phonon Knudsen minimum by introducing two metrics: the depth and breadth of super-linear size dependence of thermal conductivity. Our quantitative analysis of phonon Knudsen minimum in the width or thickness direction reveals critical thickness or width, respectively, for its occurrence. This work, thus, promotes deeper understanding of size effect on phonon Knudsen minimum and gives helpful guidance for future experimental detection in realistic graphitic structures.