The influence of air on period doubling motion in vertically vibrated grains beds

Han, Hong; Jiang, Ze; Zhang, Rui; Lyu, JrJung

doi:10.1016/j.physa.2014.02.045

Cited by 6 publications

(13 citation statements)

References 45 publications

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“…The IBBM cannot reproduce such a steady state in Γ > Γ 1 . Whereas the effect of intersticial gas is neglected in this study, it might play a role in the vibrated granular behavior 23 24 25 . Much more detail evaluation of the interstitial-air effect is one of the most important future problems.…”

Section: Discussionmentioning

confidence: 99%

Bottom pressure scaling of vibro-fluidized granular matter

Katsuragi

2015

Sci Rep

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Vibrated granular beds show various interesting phenomena such as convection, segregation, and so on. However, its fundamental physical properties (e.g., internal pressure structure) have not yet been understood well. Thus, in this study, the bottom wall pressure in a vertically vibrated granular column is experimentally measured and used to reveal the nature of granular fluidization. The scaling method allows us to elucidate the fluidization (softening) degree of a vibrated granular column. The peak value of the bottom pressure pm is scaled as Γ, where pJ, d, g, ω, H, and Γ are the Janssen pressure, grain diameter, gravitational acceleration, angular frequency, height of the column, and dimensionless vibrational acceleration, respectively. This scaling implies that the pressure of vibrated granular matter is quite different from the classical pressure forms: static and dynamic pressures. This scaling represents the importance of geometric factors for discussing the behavior of vibro-fluidized granular matter. The scaling is also useful to evaluate the dissipation degree in vibro-fluidized granular matter.

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Section: Discussionmentioning

confidence: 99%

Bottom pressure scaling of vibro-fluidized granular matter

Katsuragi

2015

Sci Rep

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“…Equation shows how two dimensionless parameters dictate the dynamics of the bed: Γ, which characterizes the energy injection and α. This parameter α is the frictional factor controlling energy dissipation via air drag, , closely related to coefficients previously defined in air-damped bouncing ball studies. , Also 1/α could be interpreted as the characteristic time needed for the column to reach a regime where its motion is governed by the viscosity of the fluid . In the context of vibrated beds moving in air, α has the significance of other dimensionless numbers such as Bagnold’s number used to characterize flow regimes of liquid–particle suspensions or Reynolds and Froude numbers used in fluid mechanics.…”

Section: Overview Of Kroll’s Modelmentioning

confidence: 96%

“…On a coarse approximation, we can see how studies where the IBBM has been reported to hold (without vacuum) ,, have α < 0.2. Recent works on the effect of air on vibrated bed dynamics ,, have been done for 0.1 < α < 0.5. Experimental studies on the motion of vibrated beds where there is a strong and notorious effect of interstitial air have α ranges that can reach 10 or more for the lowest frequencies and smaller grains.…”

Section: Overall Dependence Of Bed’s Flight Dynamics On Dissipative P...mentioning

confidence: 99%

“…(left) Isoperiodic map α–Γ with rectangles or lines indicating the range of parameters explored in some literature studies. (right) Zoom of the α–Γ isoperiodic map showing two data sets from experiments performed by Han et al who used stainless steel spheres of different sizes. White filled symbols correspond to the data set of Figure 4 from ref taken at different grain diameters at 60 Hz in air.…”

Section: Overall Dependence Of Bed’s Flight Dynamics On Dissipative P...mentioning

confidence: 99%

“…Following the interest aroused by the experimental studies of refs and and looking forward to achieve a theoretical understanding of the bouncing dynamics of a vibrated bed with a model that considers experimental characteristics of vibrated beds used for industrial application design, in this article, we explore Kroll’s model predictions over a wide range of parameters, inspired by configurations used in literature studies as well as in industrial applications. Still nowadays, apparently simple machinery like vibratory separators represent a challenge for resizing and rescaling, and manufacturers often rely on past experience .…”

Section: Introductionmentioning

confidence: 99%

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

Guerrero

Idler

Sánchez

2016

Ind. Eng. Chem. Res.

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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.

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