1. No category

B. Andreotti
M. Bouzid
P. Claudin
E. Clément
M. Trulsson
Nonlocal rheology of granular flows
Homogeneous shear flow of rigid particles
1
1.5
1
0
0.5
0
-30
0
30
Normal stress profile
Order parameter:
-1
-30
0
Velocity profile
Inertial number
30
Flow characteristics
0.5
0.9
3.5
0.8
2.5
0.6
-30
1.5
-30
0.4
0.3
0.2
0.1
0
-30
0
Shear stress profile
30
0
30
Volume fraction profile
0
Coordination number
What is the parameter controlling the transition from solid to liquid states ?
Solid
Liquid
30
Local rheology
0.34
0.815
0.32
0.30
0.805
0.28
0.26
0
Solid
Liquid
0.02
0.04
0.06
0.795
0
0.04
0.1
0
0.04
0.1
Can one create a solid/liquid interface?
(liquid)
(solid)
Can one create a solid/liquid interface?
Can one create a solid/liquid interface?
20
10
0
-10
-20
0.21
0.32
0.37
E pur si muove!
20
10
does not control the
solid-liquid transition.
0
-10
Linear relaxation:
-20
-0.4
0
0.4
Relaxation length of the shear rate
35
30
25
20
15
10
5
0
0
0.13
0.67
0.8
c
Above yieldingµconditions
20
20
10
10
0
0
-10
-10
-20
-20
0.21
0.32
0.37
-0.4
0
10
0.4
Relaxation length of the shear rate
40
30
20
10
0
0
0.13
0.4
A single liquid phase: the divergence is NOT the signature of change of state.
Fluidity
• Order parameter: fluidity
Solid
Liquid
• Fluidity must depend on state
variables only
• Relative environment fluidity
X
Non-local rheology
Non-local rheology
Relaxation length (i)
20
Linearisation around the base state:
10
0
-10
-20
-0.4
0
0.4
40
30
20
10
0
0
0.13
0.4
Relaxation length (ii)
Linéarisation around the fluid marginal state I = 0+
40
30
20
10
0
0
0.13
Agreement without any adjustable parameter
0.4
What is the origin of non-locality?
Are there localised plastic events ?
-
Local contribution of a region to the mean shear rate
Rigid vs soft particles
Rigid particles
Soft particles
• No localized plastic events
• Localized plastic events
• Permanent spatial heterogeneities
• Very intermi=ent dynamics
Generalised isostaticity
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
0
10
1
10
2
10
3
The isostatic limit gives the cross-over between:
• non-locality controlled by localized plastic events
• non-locality controlled by non-affine motions
10
4
10
5