Time-of-flight of solitary waves in dry and wet chains of beads: experimental results and phenomenological models

A solitary wave is generated by impacting a dry chain of beads on one of its ends. Its speed depends on the speed $v_0$ of the striker and the details of the contact force. The time-of-flight (ToF) of the wave was measured as a function of $v_0$, along with the effect of adding a fluid around the contact points. The ToF displays a complex dependence on the fluid's rheological properties not seen in previous works. A power-law dependence of the ToF on $v_0$ in both, dry and wet cases was found. It turned out that the Hertz plus viscoelastic interactions are not enough to account for our results. Two phenomenological models providing a unified and accurate account of our results were developed.