Rheophysics of 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 = V 1/3 -F 0 D0D0 h F cap Maugis model Pendular state Pair-wise interaction Surface tension  Contact angle θ (=0) Normal and tangential contact forces same as dry grains (Hertz and Coulomb) 2 / 12 Dense assembly of frictional spherical grains with capillary forces

Lees-Edwards periodic boundary condition Control - Average shear rate - Normal stress Parameters: - Friction coefficient μ = Number of grains N = Stifness number Κ = (E/P) 2/3 = / 12 Homogeneous steady shear flow Normal stress  yy = Pressure P Shear rate x y z

Inertial numberReduced pressure 4 / 12 Two dimensionless numbers diameter a mass m Pressure P Shear rate

range of validity Funicular  Roughness a = m  water = 7.3 × J/m 2 P* = 1  P = 2,5 kPa  H = 10 cm in gravity field Range of saturation / reduced pressure 5 / 12

6 / 12 Constitutive law:  * (I,P*) and  (I,P*)

Cohesion at contact 2D Rognon et al. JFM 2007 P * 7 / 12 Comparison with previous study  I I  0,1 0,03 0,02 0,015

h/a Contact (+85% to 20%) 8 / 12 Strong effect of distant interactions ! P* = 0,43 – D 0 = 0 P* = 

h/a 8 / 12 Strong effect of distant interactions ! P* = 0,43 – V = D 0 = 0,08 D 0 = 0,01 D 0 = 0 P* =  Distant (+40%) Contact (+85% to 20%)

9 / 12 small contribution of - distant interactions - capillary interactions Contributions to shear stress

Microstructure: Clustering effet F cap 10 / 12 Microstructure Coordination number zczc zdzd I = I = I = Contact duration

Approaching pairs Receding pairs x y z 11 / 12 Microstructure : anisotropy of contact network Contact interactions FabricDistant interactions  - 0,03F xy  0,14  0F xx -F yy F zz -1/3  0,01  0F xz,F yz  0 Average force Anisotropy Contact Anisotropy 20% 80% 2D Rognon et al. EPL 2006

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 force Large 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