Granular matter 2003. 6. 11 김종현. Contents What is granular matter? A study about granular...
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Transcript of Granular matter 2003. 6. 11 김종현. Contents What is granular matter? A study about granular...
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