Low-frequency oscillations and convective phenomena in a - - PowerPoint PPT Presentation

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Feb 23, 2024 119 likes •470 views

Nicols Rivas (n.a.rivas@ctw.utwente.nl) Physics of glassy and granular materials Multi Scale Mechanics Kyoto, Japan, July 2013 Low-frequency oscillations and convective phenomena in a density-inverted vibrofluidised granular system S.

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Low-frequency oscillations and convective phenomena in a density-inverted vibrofluidised granular system

Multi Scale Mechanics

Nicolás Rivas (n.a.rivas@ctw.utwente.nl) Physics of glassy and granular materials Kyoto, Japan, July 2013

S. Luding, A.R. Thornton,

C.R.K. Windows-Yule, D.J. Parker, N. Rivas

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MOTIVATION

When/how do granular materials flow? Discrete to continuum transition Collective dynamics of many-particle systems

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Asin(ωt) LX = 50d

SYSTEM GEOMETRY

Wide Column LX = 5d N = 3000 N = 300 control parameter S ≡ A2ω2/gd ∈ (20,400)

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SIMULATIONS

Event-driven algorithm Perfect hard spheres Collisions modeled by ˦˧˧N, ˦˧˧T and µS, µD, Solid walls boundary conditions (no top) Bi-parabolic sine interpolation

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LX = 50d Leidenfrost state (A = 1.0d, ω = 7.0(d/g)1/2) *color corresponds to granular temperature

PHASES

dense gas

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Convection state (A = 1.0d, ω = 12.0(d/g)1/2) LX = 50d

PHASES

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Container Length (LX) Oscillation Frequency (ω) Dimensionless Velocity (S) A = 1.0

PHASES

Ê Ê Ê Ê Ê Ê ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡

Ï Ï Ï Ï Ï Ï Ï Ï Ï

Ú Ú Ú Ú Ú Ú Ú Ú Ù Ù Ù Ù Ù Ù Ù Ù Ù

Bouncing Bed Leidenfrost Convection

One Roll Two Rolls

5 10 15 20 25 30 35 40 45 50 4 8 12 16 20 16 64 144 256 400

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Ê Ê Ê Ê Ê Ê ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡

Ï Ï Ï Ï Ï Ï Ï Ï Ï

Ú Ú Ú Ú Ú Ú Ú Ú Ù Ù Ù Ù Ù Ù Ù Ù Ù

Bouncing Bed Leidenfrost Convection

One Roll Two Rolls

5 10 15 20 25 30 35 40 45 50 4 8 12 16 20 16 64 144 256 400 Oscillation Frequency (ω) Dimensionless Velocity (S) A = 1.0

PHASES

?

Container Length (LX)

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LOW-FREQUENCY OSCILLATIONS

A = 1.0d, ω = 14.0(d/g)1/2

(40 Hz for 5mm particles)

5d

Bouncing Bed

Leidenfrost Convection 5 10 20 30 40 50 5 10 15 20 25 100 225 400

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Time Vertical Centre of Mass (zcm)

S = 16 S = 400 5 10 15 20 25 5 10 15 20 25

LOW-FREQUENCY OSCILLATIONS

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Frequency P.S.D.

S = 16 S = 400 0.03 0.1 0.3 3 10 25 0.01 0.1 1 10 100

LOW-FREQUENCY OSCILLATIONS

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S = 144 S = 256 S = 400 S = 16 S = 64 0.03 0.1 0.3 3 10 25 0.01 0.1 1 10 100

Frequency P.S.D.

LOW-FREQUENCY OSCILLATIONS

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ω0 ω0

S = 144 S = 256 S = 400 S = 16 S = 64 0.03 0.1 0.3 3 10 25 0.01 0.1 1 10 100

Frequency P.S.D.

LOW-FREQUENCY OSCILLATIONS

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S wC

A = 4.0 A = 1.0 A = 0.4 016 64 144 256 400 0.2 0.3 0.4 0.5 0.7 0.8 0.9 1. Dimensionless Velocity (S) LFOs Frequency (ω0) 0.6

LOW-FREQUENCY OSCILLATIONS

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Cauchy’s equations Forced harmonic oscillator

LFO’s MODEL

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0 15 30

ρg ρs

Density (ρ)

Cauchy’s equations Forced harmonic oscillator

LFO’s MODEL

zcm ξ

15 30 0 5 10 15 20 25

Density (ρ)

Afmsin(ωfmt) ρshs k = 4gρg

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LFO’s MODEL

S wC

A = 4.0 A = 1.0 A = 0.4 016 64 144 256 400 0.2 0.3 0.4 0.5 0.7 0.8 0.9 1. Dimensionless Velocity (S) LFOs Frequency 0.6

Dashed lines come from the model

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EXPERIMENTS

We use PEPT (Positron Emission Particle Tracking) to track ONE particle Submilimeter, milisecond resolutions

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EXPERIMENTS

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EXPERIMENTS

Red = Simulations
Blue = Experiments

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EXPERIMENTS

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EXPERIMENTS

Observed convection phenomena

Inverse convective state

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EXPERIMENTS

Observed convection phenomena

“Crystalline convection”

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Vertically driven granular matter in density inverted states present low-frequency oscillations (LFOs). A forced oscillator model, obtained from considering a two phases continuum medium, agrees with simulation and experimental measurements.

LFO’s Conclusions

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Expand the model: Consider energy equation Solve full non-linear equation Study relevance of LFOs in wider systems