Oscillatory instability in a driven granular gas Evgeniy Khain Baruch Meerson Racah Institute of Physics Hebrew University of Jerusalem • Granular gas: a simple model of a fluidized granular medium • Granular hydrodynamics • Phase-separation instability • Oscillatory instability • Summary
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Oscillatory instability in a driven granular gas Evgeniy Khain Baruch Meerson Racah Institute of Physics Hebrew University of Jerusalem Granular gas: a.
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Oscillatory instability in a driven granular gas
Evgeniy KhainBaruch Meerson
Racah Institute of PhysicsHebrew University of Jerusalem
• Granular gas: a simple model of a fluidized granular medium
• Granular hydrodynamics
• Phase-separation instability
• Oscillatory instability
• Summary
• Granular Materials are ubiquitous:
sand, sugar, flour, …
• GMs are important:
powder metallurgy, pharmacology, …
• GMs are interesting
Surface Waves Avalanches
Brazil Nut Effect
Size separation
Motivation
The simplest model of granular gas:
Inelastic Hard Spheres
inelastic binary collisionscoefficient of normal
restitution:
elasticcollisions
The energy loss in each collision
4/)v)(vr-(1ΔE 22n1n
2 =
1r0
Hydrodynamics of gases with inelastic collisions
Continuous approach:coarse-grained variables
• Granular temperature T
• Granular density ρ
• Granular pressure P
Works well for nearly elastic collisions
Kinetic theory
Constitutive relations
1r-1
Eqs. of Granular Hydrodynamics
. Γv:Pqdt
dTρ
, fPdt
dvρ
, 0vρdt
dρ
These equations and constitutive relations can be derived
from kinetic theory(for nearly elastic collisions)
Jenkins and Richman (1985), …
)r-(1Γ 2
• P - stress tensor• q - heat flux• rate of energy losses