Article: Louge MY (2012). “”Phonon” conductivity along a column of spheres in contact Relation to volume fraction invariance in the core of granular flows down inclines.” Granular Matter 14(2): 203-208.
Abstract: We calculate energy conduction and dissipation along a column of spheres linked with linear springs and dashpots to illustrate how grains in simultaneous contact may produce a constant “phonon” conductivity of granular fluctuation kinetic energy. In the core of dense unconfined granular flows down bumpy inclines, we show that phonon conductivity dominates its counterpart calculated from gas kinetic theory. However, the volume dissipation rate of phonon fluctuation energy is of the same order as the kinetic theory prediction.