1. Rheophysics of athermal granular materials
P. Mills, J.-N. Roux & F. Chevoir
Assembly of non brownian hard particles (d>>1 mm)
- Dry granular materials
- Dense suspensions of particles in a viscous fluid
IMA Conference on Dense Granular Flows
Cambridge - July 2013

2. Homogeneous shear state Jammed state * = critical state
Shear stress
Pressure P
diameter d
mass density rp
liquid viscosity hl
friction coefficient mg
Shear rate
Solid fraction f
Jammed state * = critical state
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3. Dimensionless numbers
Two time scales : shear time and inertial / viscous time
Dry grains
Inertial number
Dense suspensions
« Viscous number »
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4. Dry grains SuspensionsIs Is
Peyneau D
Peyneau D mg =0,3 Is Is
exp : Boyer et al. 2011
Khamseh D
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5. Relaxation from shear state to jammed state
characteristic time t
cutting off the shear stress
while maintaining the normal stress
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6. Time evolution of solid fraction dissipative interactions
Diffusive flux
dissipative interactions
Relaxation
Steady state :
Equation of state
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7. Relaxation time m f
Da Cruz PRE 05
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8. Constitutive law : scaling laws ?
Depend on I range !
Dry grains
Suspensions mg a b
Ref 2D
0,67
0,52
Peyneau 08 3D
0,39
0,42
0,38
Khamseh 12
0,3
0,87
0,81
0,95
0,86 mg a b
Ref 2D
0,3
0,4 – 0,5
(hmin)
0,4 – 0,2
Peyneau 08 3D
0,6
(hmax) 0
0,5
Boyer 11
Influence of dimension ?
Influence of friction !
a close to b ?
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9. Consequence for shear stress
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10. Dry grains Dense suspensions
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11. Conclusions = Questions
Scaling laws for m and f ?
Relaxation of solid fraction related to viscosity ?
Microscopic interpretation of :
- equation of state : Boltzmann equation ?
- viscous shear stress ?
- strong influence of friction ?