Granular matter

2003. 6. 11

김종현

Contents

What is granular matter?

A study about granular matter

Size segregation & Mixing

Conclusion & References

What is granular matter?

It consists of macroscopic particles of different size, shape, and surface properties

Granular flow A flow with grains A flow with powder in a vacuum(there is no fluid

to support the particles) A mixture of grains and fluid phase

Topics Environment

Material behavior

Etc…

Segregation and clustering

Environment

Sand dunes

Astrophysical rings

Sand dunes

Their shape depends on the distribution of wind directions and ground behavior

Modeling of the morphology of sand dunes Different time scales between wind field behavior and

sand flux -> the calculation can be separated The effect of perturbations of the wind field onto the

stability of a dune

Global perturbation of the wind field onto a dune The local interaction between the sand grains and the wind

near the ground Avalanches that maintains the sand transport due to gravity

on the slip face

Astrophysical rings

In simulation, viscosity increases with time How the kinematic viscosity is depending on time

and on the radial coordinate if there is some collisional dissipation

Material behavior

Non-spherical particles Shear band formation Hysteresis in the deformation of soils

Cohesion and sintering Cohesive forces in granulates Hydration kinetics of cement

Shear band formation

The deformations are not homogeneously distributed when apply pressure to confined granular materials They are concentrated in thin

layers of intensive shearing

Hysteresis in the deformation of soils

Cohesive forces in granulates

Particulate solids show sticky properties Adhesive/cohesive forces acting between the

particles Reason : solid bridges

Solid bridges Soluble particle material can form solid bridges itself

through partial dissolution and re-solidification Partial melting of particle with low melting point or

at higher temperatures(sintering)

Macroscopic cohesion is determined by the ability of the material to resist shear stress in static equilibrium without normal loading When exceding a maximum stress(yield loci), the

material begins to flow

Yield loci depend on the loading history

Hydration kinetics of cement

Ratio of hydrated and unhydrated numbers x / (1 - x) ~ (t / t x) y

t < t x

Accelerated hydration ( y=2.5 ) Hydrates catalyse the hydration process

t > t x

Parabolic behavior ( y=0.5 ) They inhibit further hydration

Etc…

Apollonian parking model

Shock waves in dense gases

Rheology of bi-disperse granular media Studies on granular materials are confined to mono

-disperse media A real system : poly-dispersity in size and/or mass

Apollonian parking model

Application High performance concrete Ceramics that have to endure extreme stress…

Segregation and clustering

Reverse size segregation and mixing BNP and RBNP

Clustering and segregation

Pattern formation in vibrated granular media

Reverse size segregation & mixing

Critical temperature Tc exist !!

Size segregation RBNPMixing

BNP and RBNP

BNP (Brazil Nut Problem) Hard spheres with large diameters segregate to the

top when subjected to vibrations or shaking

RBNP (Reverse BNP)

Percolation effect Smaller ones pass through the holes created by the

larger ones

Geometrical reorganization Small particles fill small openings below large

particles

Global convection Bring large particles up but not allow for reentry in the

down stream

Define some parameters

Critical temperature Tc

Mass m and diameter d

Initial layer thickness t (in units of d)

Thickness of fluidized layer h

In D dimension, mv2/2 = DT/2 ~ mgdh At Tc , h=t

Tc ~ mgdt / t0 ( t0 is spatial dimension term )

T > Tc The system is fully fluidized

T < Tc A fraction of particles condenses at the bottom

In binary mixture of hard spheres,

Tc(B) < T < Tc(A)

dA / dB =8 , mA / mB = 4 in 2D dA / dB =2 , mA / mB = 2 in 3D

Crossover from the BNP to the RBNP

Crossover from the BNP to the RBNP

dA / dB =2 , mA / mB = 4 in 2D dA / dB =2 , mA / mB = 6 in 3D

Crossover condition y(D-1)= x

2D 3D

After…

Does the RBNP exist? G.A. Canul-Chay et al. can not observe RBNP. Temperature gradient exists along the vertical in th

eir granular vibrating bed

Reply The mixture is in contact with a thermal reservoir

at a global temperature T (no temperature gradient) Granular temperature (mean kinetic energy per

particle) : balance between power input (vibration) and dissipation (inelastic collision)

A large, heavy grains rise, but equally large, light grains sink in a granular bed if the bed is deep and the amplitude of vibration is large

T. Shinbrot et al. “Reverse Buoyancy in Shaken Granular Beds”, PRL(1998)

Clustering and segregation

Clustering

Reason : energy loss associated with particle-particle collisions

Necessary condition : net dissipation is strong Example

Freely cooling bi-disperse mixture …

In freely cooling granular material, statistical fluctuations in density and temperature cause position dependent energy loss Homogeneous state Cluster growth Clusters have reached system size

Pattern formation

A typical pattern that appears of vibrated materials (or external temperature gradient) is that of convection rolls

Pattern formation is cluster formation in a granular matter by vibration

f = 50 Hz

Γ = ω2A / g = 4.5

Magnetized sphere vibrates

Conclusion

Study about granular matter is wide

RBNP is not yet completed

Reference

Reverse Brazil Nut Problem, Daniel. C. et al. PRL, 86, 3423

Does the RBNP exist?, G.A.Canul-Chay et al. PRL, 89, 189601

Comment on “RBNP : Competition between Percolation and Condensation”, H. Walliser PRL, 89, 189603

Cluster-growth in freely cooling granular media, S. Luding, Chaos, 9, 673

Ordered Clusters and Dynamical states of Particles in a Vibrated fluid, Greg. A. et al., PRL, 88, 234301