Particle current on flexible surfaces excited by harmonic waves

In this paper, a study on the directed particle current on flexible surfaces excited by a harmonic wave is reported. The proposed theory considers three different models for the kinematics of the surface, namely the Euler-Bernoulli, Timoshenko, and Rayleigh surface wave models. The particle-surface interaction terms in the theory incorporate Coulomb friction and inelastic collision between the particle and the surface. Three possible phases of motion, namely sticking, sliding, and jumping, are considered, and the phase transition boundaries are estimated analytically for a general surface model. The effect of various parameters on the particle current and certain statistical features of the particle motion are then studied numerically. Remarkably, the particle current spectra exhibit, in addition to resonance modes, antiresonance and secondary resonance modes and transversal zero crossings. These features have interesting implications for the particle dynamics in terms of dynamic jamming states and particle eddies, which are pointed out. Under certain restricted conditions, averaging calculations are also performed and compared with the corresponding numerical simulations.