Reverse buoyancy as a consequence of cyclic fluidization Gustavo Gutiérrez USB Oliver Pozo UNSA...

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

SEGREGATIONBrazil-nut problem

SEGREGATIONBrazil-nut problem

y o2 c

os

t

v

Intruso

Rosato et al, 1987Rosato et al, 1987

Intruder

SEGREGATIONReverse Buoyancy

SEGREGATIONReverse Buoyancy

y o2 c

os

t

v

IntrusoHeavy

Shinbrot and Muzzio 1998Shinbrot and Muzzio 1998

Light

Breu et al, 2003Breu et al, 2003

timetime

Reverse Brazil-nut effectReverse Brazil-nut effect

v

v

i m i m

y o2 c

os

t

y o2 c

os

t

ReverseReversebuoyancy buoyancy

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

Vertical DisplacementVertical Displacement

Heavy intruder Light intruder

Vertical velocity vs.

density ratio

Vertical velocity vs.

density ratio

(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

Cyclic fluidization

t

cost

Evesque, Rajchenbach and de Gennes 1998Evesque, Rajchenbach and de Gennes 1998

g

y 2

o

1

cos2 1

amFFF WB

vCF

gVF

gVF

m

IW

mB

)1tcos(gg

g

y 2

o

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

v

)(tang),(F

0

o

im

io ),(F)t(v

GAP

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)

Luding et al 1994Luding et al 1994

)1(NX

Column of spheres

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

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

;

PREDICTION OF THE MODELPREDICTION OF THE MODEL

),(F),(F)t(v o

m

io

)(tang

),(Fo

o

),(F),(F)t(v o

m

io

Comparison of the model with the experimental results

Comparison of the model with the experimental results

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.