Rheophysicsof wet granular

materials

S. Khamseh, J.-N. Roux & F. Chevoir

IMA Conference on Dense Granular Flows - Cambridge - July 2013

Liquid bridge - constant volume V- forms once particles touch- disappears for h > D

0 = V1/3

-F0

D0 h

Fcap

θ

h

R

2

0

0

1( ) [1 ]

2

0

1cap

h D

F h FVRh

0 2 cosF R

Maugis modelPendular statePair-wise interactionSurface tension

Contact angle θ (=0)

Normal and tangential contact forces same as dry grains (Hertz and Coulomb)

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Dense assembly of frictional spherical grains

with capillary forces

Lees-Edwards periodic boundary conditionControl

- Average shear rate- Normal stress

Parameters:- Friction coefficient μ = 0.3- Number of grains N = 4000- Stifness number Κ = (E/P)2/3 = 8400

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Homogeneous steady shear flow

Normal stress yy = Pressure P

Shear ratex

y

z

mI

aP

2

0

PaP

F

Inertial number Reduced pressure

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Two dimensionless numbers

diameter a mass m

*effective frictiondependence on and ?

solid fractio

=

n

μ /P*I P

Pressure P

Shear rate

3 103

10 10V

Da

3

3saturation s ( , *)

(1 )

z Vs I P

a

210

110310 range of validity

Funicular

0

2

( ) /

1 exp( / )

Halsey-Levine 1

998

capF V F

V a

Roughness

a = 10-4 m water = 7.3 × 10-2 J/m2

P* = 1 P = 2,5 kPa H = 10 cm in gravity field

Range of saturation / reduced pressure

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Significant effect of capillary force for P* 1

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Constitutive law: * (I,P*) and (I,P*)

Cohesion at contact 2D Rognon et al. JFM 2007

P *

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Comparison with previous study

I I

0,1

0,030,02

0,015

Significant effect of cohesion for P* 1

h/a

Contact (+85% to 20%)

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Strong effect of distant interactions !

P* = 0,43 – D0 = 0P* =

h/a

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Strong effect of distant interactions !

P* = 0,43 – V = 10-3

D0 = 0,08 D0 = 0,01 D0 = 0P* =

Distant (+40%)

Contact (+85% to 20%)

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small contribution of- distant interactions

- capillary interactions

Contributions to shear stress

Microstructure:

Clustering effet

Fcap

Fcap

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Microstructure

Coordination number

zc

zd

I = 10-2

I = 10-2.5

I = 10-3

Contact duration

0

* 10

1,1

P

0

* 0,43

1,7

P

0

( ) exp ccP

Approaching pairs

Receding pairs

all pairs

1

pairs

F n nN

x

y

z

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Microstructure : anisotropy of contact network

Contactinteractions

Fabric Distantinteractions

- 0,03 Fxy 0,14 0 Fxx-Fyy

Fzz-1/3

0,01

0 Fxz ,Fyz 0

2

3NC NCcxy xy xy

zF F f

a

Average force

Anisotropy

ContactAnisotropy

20% 80%

2D Rognon et al. EPL 2006

*

0

( )sin(2 )N N d

Large effect of capillary forces on macroscopic behavior - already for P* 1

Strong influence of distant interactions : clustering effect

Shear stress dominated by anisotropy of average forceLarge fabric anistropy of distant interacting pairs

Shear localization for small P*

Include viscous force

Describe liquid transfer

Describe larger saturation range

Comparison with experiments

Conclusions

Perspectives