We present a numerical study of the effect of interstitial air on a vertically vibrated granular bed within one period of oscillation. We use a three-dimensional molecular-dynamics simulation including air phenomenologically. The simulations are validated with experiments made with spherical glass beads in a rectangular container. After validation, results are reported for a granular column of 9000 grains and approximately 50 layers deep (at rest), agitated with a sinusoidal excitation with maximal acceleration 4.7g at 11.7 Hz. We report the evolution of density, granular temperature, and coordination number within a vibration cycle, and the effect of interstitial air on those parameters. In three-dimensional computer simulations we found that the presence of interstitial air can promote the collective motion of the granular material as a whole.

We have performed molecular dynamics simulations of an intruder in a vibrated granular bed including interstitial fluid effects to account for the phenomenon of reverse buoyancy. We show that our model is able to reproduce the overall behaviour observed by previous experimental works and is the first finite-elements simulation to show the sinking of intruders lighter than the granular bed. To further advance our comprehension of this phenomenon, we studied the motion of the intruders in a single vibration cycle with respect to the bottom of the granular column, finding a substantial qualitative difference for heavy and light intruders and we compare these results with experiments using fine-sized glass beads. We show that, though heavy intruders seem unaffected by the force due to the fluid, the effect on light intruders is remarkable.

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In the present work, we explore the modification of the periodicity of the motion of shallow granular columns in the framework of Kroll's one-dimensional model for the motion of a vibrated bed. Within the model, bed dynamics depend on two parameters, the dimensionless maximum acceleration, Γ, and a dissipative parameter, α, depending on air viscosity, grain density, bed static porosity, oscillation frequency and grain diameter. We show how the bifurcation diagram for the flight time of the bed as a function of Γ changes with α. For α = 0, Kroll's prediction equals that of the inelastic bouncing ball model. When α is increased, bifurcations shift to higher Γ up to a point where not even a single bifurcation is predicted in a range of Γ where an inelastic bouncing ball displays several bifurcations. We also illustrate how the flight time reduces nonlinearly with increasing α in a monotonic way. We introduce isoperiodic maps to illustrate regions of single, double, or more periodicities in the phase space. We also show and discuss the dependence of the flight time on the parameters entering the definition of α within ranges of those parameters that have been explored in the literature. Grain diameter, grain density and vibration frequency are the most determinant.