Rheology of concentrated hard-sphere suspensions

Transcription

1 Rheology of concentrated hard-sphere suspensions Complex behaviour in a simple system Wilson Poon School of Physics & Astronomy, The University of Edinburgh Rut Besseling Lucio Isa ( ETH, Zürich) Khoa Pham ( CSIRO) Pierre Ballesta ( Crete) Jon Singer (??) Peter Pusey Dimitris Vlassopoullos (Crete) George Petekedis (Crete) Eric Weeks (Atlanta)

2 What am I doing here?

3 New tool: single-particle, real time imaging of concentrated suspensions under flow used to study a zoo of complex behaviour, much of which is yet to be theoretically explained.

4 Experimental hard sphere system PMMA 1µm 10nm Stabilised by chemically-grafted polymer brush Rheology textbook: Shear-thinning fluid Yield-stress fluid fluid ~ 12% polydispersity or more f + c crystal ~ 0.58 Glass φ

5 Popular constitutive equations for yield-stress suspensions Bingham, E. C. Fluidity and Plasticity. New York: McGraw-Hill, Herschel, W.H.; Bulkley, R. (1926), Konsistenzmessungen von Gummi- Benzollösungen, Kolloid Zeitschrift 39: Casson N. (1959), A flow equation for pigment-oil suspensions of the printing ink type. In: Mill CC, editor. Rheology of disperse systems. London, U.K.: Pergamon.

6 Chocolate + molten cocoa butter + shear ( conching ) = 50% suspension of sugar in oil

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8 PMMA suspensions Fits H-B Slope = 1 MCT can predict such behaviour ab initio Mike Cates talk

9 Measuring the constitutive relation is not totally straightforward Cone: rough Plate: Filled = rough Open = smooth No difference when φ < 0.58

10 Bulk rheology: φ = 0.64 is a H-B yield-stress fluid HB fluid in pipe: plug flow; plug diminishes with flow rate Huilgol & You, JNFM (2005)

11 Od Flow rate Plug size (fraction of pipe size)

12 Fluorescent, indexmatched PMMA φ ~ 0.64, 2R ~ 2.6 µm Particle tracking under shear: Decompose image into strips Shift to maximise correlation between successive strips Average v of strips Subtract average motion Track (Crocker-Grier etc.) Constant P 20 d 170 frames/s Add back average motion Fast confocal

13 1. No dependence of shear zone size on flow speed 2. In any case Od ~ 0.02 Plug size should be 0 Plug size (fraction of pipe size) Od

14 1. Pouliquen: granular flow [PRE 1996] Yielding due to stress fluctuations ( σ) spreading from walls Coulomb friction dominates Flow speed stress friction yield stress constant shear zone (width controlled by strength of σ) 2. Bocquet [Nature 2008, PRL 2009] ( Dhont): non-local fluidity (STZ) Colin s talk

15 Confinement-induced flow instabilities ~20D ~40D ~30D

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17 Certainly doesn t tell the whole story for the pipe flow of concentrated hard sphere suspensions how about simpler, rheometric, geometries?

18 3D confocal imaging in rheometric geometries ~ 5 slices/particle 0.1 s / particle Vertical slice ACIS (2009) Home-built parallel-plate shear cell or AR2000 rheometer cone-plate

19 Genuine slip next to smooth plate, not shear localization r = 2.5 mm (in 20mm-radius plate)

20 But shear localization does occur in rough/rough cone/plate σ m (Pa) ϕ 63% 61% 59% 52% H-B bulk rheology?! 1E γ a (s -1 ) exponential fit v / v cone v / v cone z / z gap z / z gap

21 Bocquet [Nature 2008, PRL 2009] ( Dhont): non-local fluidity True bulk flow curve Finite size effects?? σ m (Pa) E γ a (s -1 ) ϕ 63% 61% 59% 52% v / v cone exponential fit z / z gap

22 Parallel-plate shear cell (rough walls) Analyse local regions with linear velocity gradient Measured shear rate > average imposed shear rate

23 Particle dynamics as a function of local shear rate x, velocity ~ x, z plane z, gradient 15 µm 1 µm 15 µm y,z plane Substract affine component of shear-induced motion ~ x,y plane t = 800 s ~ x, y plane Significant heterogeneity in shear-induced motions Shear-induced cage breakout long-range diffusion in all directions

24 Structural relaxation Cf. Time-density superposition of quiescent HS colloids at φ < φ g. (van Megen) Time-shear superposition Cf. Theory (Fuchs & Cates; Berthier) F s ( Q m, t ) 1.0. γ = γ ( s -1 ) τ α t (s) f s 0.6 Exponentiality cf. Varnik L-J simulations t / τ α

25 Scaling with shear rate

26 0.01., D = 0.9 D 0 (τ B γ ) 0.8 D y (µm 2 /s) 1E-3 1E-4 a=0.85 µm (ϕ~0.62) a=0.43 µm (ϕ~0.6) 1E-4 1E γ (s -1 ) 0.1 D y (µm 2 /s) E-3 1E-4 no shear a=0.85 µm φ = 0.62, n=0.8 φ = 0.55, n=0.77 1E-5 1E-5 1E-4 1E γ (s -1 )

27 Increasing stress Increasing φ Kobelev PRE 2005 Schweizer 2007

28 ?

29 Extreme shear thickening Norman Wagner s talk

30 Conclusions Concentrated suspensions of hard spheres show complex flow behaviour Real-time single-particle resolution imaging helps to reveal (and perhaps elucidate!) this zoo of complexity Method can be extended to other systems That s all, folks!