Tuning granular matter rheology using externally supplied vibrations

Transcription

1 Flowing Matter January 2017 PORTO Tuning granular matter rheology using externally supplied vibrations Laboratory : LEMTA, Nancy (France) Team «Rheophysics and hydrodynamics of complex fluids» Sébastien Kiesgen de Richter (LEMTA) Caroline Hanotin (LEMTA) Nicolas Louvet (LEMTA) Mathieu Jenny (LEMTA) Philippe Marchal (LRGP) Naïma Gaudel (LEMTA)

2 EXAMPLE o Role and influence of external vibrations on Nickel ore transport Influence of vibrations Nickel ore in New Caledonia, Noumea. «Union française des géologues», 2003 Influence of an external stress on nickel ore liquefaction. BIMCO News du 12/10/2010, UK P&I Club LP Bulletin 602, Nepia SIGNALS n 69 Liquefaction Liquefied lateritic nickel ore Photo UK P&I Club Ship sinking due to nickel ore liquefaction

3 GRANULAR MATTER? o Dry and fluid saturated dense gravitational dispersions Dry Wet Fluid Saturated Macroscopic scale (>10-2 m) Mesoscopic scale (10-4 à 10-3 m) Microscopic scale (< 10-5 m) F N -F N R r F T ~ µ F N 2h r 1 Frictional force F adh ~ gr+r 2 g(1/r 1-1/r) ~ Capillary force v 2 h R R v 1 h v2-v1 R F 2 lub (h-2r) viscous force

4 SAMPLES AND VIBRATIONS o Experiments with model granular dispersions Monodisperse Spherical Glass beads (Whitehouse Scientific) d = 335 ± 15 µm ρ grains = 2400 kg.m -3 Newtonian interstitial fluid : Polyalkylen-Glycol (PAG)- water mixture η f = 70 mpa.s ρ fluide = 1032 kg.m -3 o Vibrations properties accelerometer A f = 1/T «Vibration stress» t (s) Sinusoidal vibrations Amplitude: A frequency: f A~[10μm 1mm] f~[10hz 100Hz] σ v =1/2 ρ S A²( 2πf )² r r f + r ( 1-f) s = grains fluide Controller Power amplifier Closed-loop vibration device

5 RHEOLOGY OF VIBRATED GRANULAR MATTER o Flow curves Experimental conditions Experimental results Stationary state σ = [1; 1000 Pa] Shear rate vane σ = K σ γ! = K! γ C θ! σ v DRY Baffle vibrations accelerometer Shaker volume FLUID SATURATED σ v Ph. Marchal, N. Smirani, L. Choplin, Journal of Rheol. 53, 1 (2009)

6 RHEOLOGY OF VIBRATED GRANULAR MATTER o Mechanical spectroscopy Experimental conditions Experimental results σ = σ 0 cos(ωt) σ 0 = 5 Pa, ω = [0.01;100] rad.s -1 DRY Existence of 2 regimes Regime ω < ω R : G ~ ω ² G ~ ω Maxwellian behavior Regime ω > ω R : G =G ~ ω ½ Glassy behavior ω R =1/ τ R FLUID SATURATED τ R = typical reorganization time

7 RHEOLOGY OF VIBRATED GRANULAR MATTER o Link between η 0 and τr. Influence of vibrations Maxwell Model (Plateau viscosity) (Shear modulus) (P. Coussot, 2007) Critical strain : the onset of contact breaking Dry Fluid saturated 1 η o µ exp 1 f VFT law ( ) s V η 0 1/Pe lub The rheology of vibrated granular matter is controled by τ R Ph. Marchal et al. Journal of Rheol. 53, 1 (2009) Pe lub h f A( 2pf = s d f ) Ratio of lubrication to frictionnal stress C. Hanotin, S. Kiesgen de Richter, Ph. Marchal, L.J. Michot and C. Baravian, Phys. Rev. Lett. 108, (2012)

8 A «TWO-STATE» MODEL o Transition from the strong to the weak contacts network C. Hanotin, S. Kiesgen de Richter, L.J. Michot and Ph. Marchal, Journal of Rheology (2014) State (C) State (M) Weak contacts network P M (t) State(M) F. Radjai et al., Chaos 9, 554 (1999) Shear +vibrations Shear P C = N C / N p P C + P M = 1 (probability for state C) State (C) Strong contacts network P C (t) First order Kinetic equation Link between P C and σ?

9 A «TWO-STATE» MODEL o Transition from the strong to the weak contacts network σ C σ MC σ M σ M s + ( t ) = s CP (t ) P (t ) P (t )P C + s M M s C MC C C C M = s P ( t ) + h! g C C H (t ) M State(C) State (M) ( Equation 1) 4 parameters: G, shear modulus η H, viscosity at high shear rate (γ ) f b, reorganisation frequency, γ c, critical deformation Equation 1 predicts the influence of shear induced and vibration induced events on the rheology if g! ( t ) / g << f b Maxwell Jeffrey Model with C

10 A «TWO-STATE» MODEL o vibrated dry granular matter ( Equation 1) ( linear domain)

11 A «TWO-STATE» MODEL o vibrated and fluid saturated granular matter ( Equation 1) Régime maxwellien slope = 1 Glassy behavior slope = 2

12 MICROSCOPIC MEASUREMENTS o Link between the reorganization time and the rheology for fluid saturated systems «Micro-macro link» Multispeckle diffusing wave spectroscopy Local measurement of the reorganization time V. Viasnoff, F. Lequeux and D. J. Pine, Rev. Sci. Instrum., 2002, 73, Macroscopical measurement (applied shear) The maxwell time is related to the reorganization time extracted from MSDWS. which is the typical reorganization time of the contact network induced by vibrations.

13 CONCLUSION o Applying external vibrations allows to tune the viscosity of both dry and fluid saturated granular matter. The behavior is Newtonian at low shear rate. o Vibrations modify the typical reorganisation time, τ R. Both dry and fluid saturated granular systems presents viscoelasticity o A kinetic approach (2 states model, Maxwell equation) well captures the dynamics. See Phys. Rev. Lett., vol. 108, n o 19, p , mai Soft Matter, vol. 9, n o 39, p , sept J. Rheol., vol. 59, n o 1, p , janv THANK YOU