The liquid and solid states of highly dissipative vibrated granular columns: one-dimensional computer simulations

One-dimensional arrangements of inelastically colliding spheres moving in a vertically oscillating vessel in the gravity field are investigated numerically. These arrangements are used to study the liquid and solid states of layers composed of granules with high energy dissipation properties. We found that the liquid state may be characterized by the kinetic energy of the particlesʹ relative motion, Erel, and the particlesʹ mean free path, λ. The layersʹ dissipative properties may be characterized by parameter D1=N(1−e1) where N is the particle number, e1 the particlesʹ restitution coefficient measured for a binary particle collision with a fixed relative velocity. For highly dissipative layers, i.e., those with D1>3, maximal value of Erel is found to be independent of D1, proportional to the square of vibrational amplitude and frequency, and inversely proportional to N2/3. The mean free path λ is found to have minimum when D1 is about 3 and increases when D1>3. This occurs because of the layerʹs interchangeable transitions between two granular states: liquid and solid. The vibrational regimes, where in spite of extensive vibrations, the layer prevails in the solid state, were investigated. A stability criterion of the solid state was derived in terms of a critical vibrational amplitude. This critical amplitude is independent of the layersʹ dissipative properties and proportional to N5/3. The results of the simulation are compared with the experimental data obtained for 2-D vibrated granular layers.