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Reverse buoyancy as a consequence of cyclic fluidization
Reverse buoyancy as a consequence of cyclic fluidization
Gustavo GutiérrezUSB
Oliver PozoUNSA
Leonardo ReyesUSB
Ricardo Paredes V.IVIC
James Drake and Edward Ott
UMD
Gustavo GutiérrezUSB
Oliver PozoUNSA
Leonardo ReyesUSB
Ricardo Paredes V.IVIC
James Drake and Edward Ott
UMD
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SEGREGATIONBrazil-nut problem
SEGREGATIONBrazil-nut problem
y o2 c
os
t
v
Intruso
Rosato et al, 1987Rosato et al, 1987
Intruder
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SEGREGATIONReverse Buoyancy
SEGREGATIONReverse Buoyancy
y o2 c
os
t
v
IntrusoHeavy
Shinbrot and Muzzio 1998Shinbrot and Muzzio 1998
Light
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Breu et al, 2003Breu et al, 2003
timetime
Reverse Brazil-nut effectReverse Brazil-nut effect
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v
v
i m i m
y o2 c
os
t
y o2 c
os
t
ReverseReversebuoyancy buoyancy
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t=0.0s
t=0.77s t=1.0st=0.0s
t=3.83s t=5.27s
light
heavy
Displacement of the intruderDisplacement of the intruder
timetime
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Vertical DisplacementVertical Displacement
Heavy intruder Light intruder
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Vertical velocity vs.
density ratio
Vertical velocity vs.
density ratio
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(The reference frame is located on the container)
F’B : Buoyancy force
F’W : Weight
F’ : Drag force
F’B
V’
F’W
F’m
The granular medium fluidizes in part of the cycle
The granular medium fluidizes in part of the cycle
MODELMODEL
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Cyclic fluidization
t
cost
Evesque, Rajchenbach and de Gennes 1998Evesque, Rajchenbach and de Gennes 1998
g
y 2
o
1
cos2 1
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amFFF WB
vCF
gVF
gVF
m
IW
mB
)1tcos(gg
g
y 2
o
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MODELMODEL
This equation is valid when the granular medium is fluidized, otherwise the medium behaves like a solid.
This equation is valid when the granular medium is fluidized, otherwise the medium behaves like a solid.
dt
dy)1tcos(g
dt
yd
I
mo
I
2
2
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v
)(tang),(F
0
o
im
io ),(F)t(v
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GAP
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Gap for different grains subjected to vertical vibrations(Amplitud 8.5 mm y frecuency 11.7 Hz )
Inelastic sphere Mustard seeds
RiceModelBlack spherica seeds
Sánchez et al, 2003
Glass spheres (diameter: 300 - 350m)
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Luding et al 1994Luding et al 1994
)1(NX
Column of spheres
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Acost
h
PkAQ
A= transversal area
P= pressure
= viscosity of air
k= permeability
s
Air flow
h
Q
Porouspiston
Kroll 1954 / Reyes et al 2003Kroll 1954 / Reyes et al 2003
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Comparison of the model with the experimental results
Comparison of the model with the experimental results
Heavy intruder Light intruder
t)(tang
)t(ymo
2
;
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PREDICTION OF THE MODELPREDICTION OF THE MODEL
),(F),(F)t(v o
m
io
)(tang
),(Fo
o
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),(F),(F)t(v o
m
io
Comparison of the model with the experimental results
Comparison of the model with the experimental results
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CONCLUSIONCONCLUSION
• Assuming that cyclic fluidization occurs, for a granular system subjected to vertical sinusoidal vibrations, we have formulated a simple quantitative model for reverse buoyancy.
• The model gives the rising and the sinking velocity of an spherical intruder as a function of the ratio between the density of the object and that of the medium.
• We obtain a very good qualitative and quantitative agreement between the theoretical model proposed and our experimental findings.