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 particles' relative motion, E_rel, and the particles' mean free path, λ. The layers' dissipative properties may be characterized by parameter D₁ = N(1-e₁) where N is the particle number, e₁ the particles' 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 E_rel is found to be independent of D₁, proportional to the square of vibrational amplitude and frequency, and inversely proportional to N^2/3. 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 layer's 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 layers' dissipative properties and proportional to N^5/3. The results of the simulation are compared with the experimental data obtained for 2-D vibrated granular layers.