Influence of Air on the Bouncing Dynamics of Shallow Vibrated Granular Beds: Kroll’s Model Predictions

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• 作者：Bruno V. Guerrero ; Vladimir I. Idler ; Iván J. Sánchez
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2016
• 出版时间：May 11, 2016
• 年：2016
• 卷：55
• 期：18
• 页码：5287-5297
• 全文大小：872K
• 年卷期：0
• ISSN：1520-5045

文摘

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.