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Yield Stress Fluids, Meeting #1 Yield Stress Fluids, Meeting #1 1. Introduction to yield stress fluids understand definition/caveats of apparent yield stress fluids develop a feel for yield stress and viscosity values 2. Rheometry with yield stress fluids identify and avoid slip artifacts correct for parallel plate artifacts recognize LAOS response of yield stress fluids Randy H. Ewoldt June 26, 2009 Part of the summer 2009 Reading Group: Yielding, Yield Stresses, Viscoelastoplasticity Non-Newtonian Fluids (NNF) Laboratory, led by Prof. Gareth McKinley References • Barnes, H. A., "The yield stress - a review or `pi alpha nu tau alpha rho epsilon iota' - everything flows?," Journal of Non-Newtonian Fluid Mechanics 81(1-2), 133-178 (1999) • Bonn, D. and M. M. Denn, "Yield Stress Fluids Slowly Yield to Analysis," Science 324(5933), 1401-1402 (2009) • Brunn, P. O. and H. Asoud, "Analysis of shear rheometry of yield stress materials and apparent yield stress materials," Rheologica Acta 41(6), 524-531 (2002) • Yoshimura, A. S. and R. K. Prudhomme, "Response of an elastic Bingham fluid to oscillatory shear," Rheologica Acta 26(5), 428-436 (1987) 2 YieldYield Stress Stress Fluids: Fluids: Idealized example: Apparently solid at low stress, σ < σY Apparently solid at low stress, σ < σY linear scale Apparently fluid at high stress, σ > σY Apparently fluid at high stress, σ > σY e.g.e.g. paint, paint, toothpaste, toothpaste, hand hand lotion, lotion, concrete,concrete, snail snail slime, slime, nuclear nuclear waste waste sludge sludge Idealized example: log-log scale 3 Detailed experiments ApparentApparent yield yield stress stress fluids:fluids: Tomato puree 1.1. Initially Initially “high” “high” viscosityviscosity Toothpaste 2.2. Dramatic Dramatic viscosity viscosity dropdrop over over narrow narrow σ range of stress Viscosity, η = range of stress γ 3.3. Flows Flows Mayonnaise Carbopol 980, polymer microgel (0.2wt%) 4 Viscosity, η ≈ 108 Pa.s Ig Nobel Award, Physics (2005) - Presented jointly to John Mainstone and Thomas Parnell of the University of Queensland, Australia, for patiently conducting the so-called pitch drop experiment that began in the year 1927 — in which a glob of congealed black tar pitch has been slowly dripping through a funnel, at a rate of approximately one drop every nine years. Started: 1927 Drop #1: 1938 Drop #8: 2000 (12 years between drops #7 and #8) Drop #9: ???? 5 6 An estimated 5 to 8 percent of all human-generated atmospheric CO2 worldwide comes from the concrete industry. Concrete creep is caused by the rearrangement of particles at the nano-scale. The basic building block of cement paste at the nano- scale -- calcium-silicate-hydrates, or C-S-H -- is Professor Franz-Josef Ulm granular in nature. M.I.T. Dept. of Civil and Env. Eng. A more dense phase of C-S-H can be induced by additional smaller particles that fit into the spaces between the nano-granules of C-S-H, which greatly η≈1014 Pa.s hinders the movement of the C-S-H granules over time. The rate of creep is logarithmic, which means slowing creep increases durability exponentially. η≈1019 Pa.s A nano-indentation device allows them to measure in minutes creep properties that are usually measured in year-long creep experiments at the macroscopic scale. 7 Vandamme and Ulm, PNAS, 2009 Apparent yield stress fluids? Blood Hematocrit content Olivine (a rock), various grain sizes Plasticine (modelling material, like putty) 8 Barnes, JNNFM, 1999 Slime & simulant rheology: Flow Carbopol (polymer microgel) Laponite (particulate gel) Carbopol 940 in DIW, pH→7 with NaOH Laponite RD in DIW 9 Ewoldt et al., Soft Matter, 2007 Magnetorheological Fluid LORD Corp. MRF-132DG carbonyl iron particles (1-20µm) in silicone oil B α =⋅1.4 105-2 Pa.T no field field-activated 105 (a) 4 [Pa] 10 R σ Magnetic Field 3 10 0.462 T 0.221 T AR-G2 rotational rheometer, 2 0.100 T 10 parallel plates with 600 grit sandpaper, h=500µm 0.046 T 0.030 T D=40mm for ambient test 1 10 0.012 T D=20mm for magnetic field tests ambient Using MRF Rheometer Cell from Corrected Shear Stress, Stress, Shear Corrected 100 Murat Ocalan, Ph.D. Thesis (in progress), MIT 10-5 10-4 10-3 10-2 10-1 100 101 102 103 Rim Shear Rate [s-1] 10 Ewoldt, Ph.D. thesis, 2009 Magnetorheological fluid 108 7 Magnetic Field 10 (b) B=0.462 T B=0.221 T 6 10 B=0.100 T [Pa.s] B=0.046 T 5 η 10 B=0.030 T B=0.012 T 104 ambient 103 102 101 100 Corrected Viscosity, 10-1 100 101 102 103 104 105 Corrected Shear Stress, σ [Pa] R 11 Apparent Yield Stress Fluids Some quotes from Barnes, JNNFM, 1999 Yield stresses were usually only a ‘figment of peoples’ extrapolation The existence of an essentially horizontal region in a double-logarithmic plot of stress versus strain rate is the most satisfactory criterion for the existence of a ‘yield stress’ (quote from Evans [36]) [Barnes] is in substantial agreement with Evans in this view, especially if then term ‘yield stress’ is prefixed with the adjective ‘apparent’! Nguyen and Boger [38] reviewed experimental methods of measuring the flow properties of yield stress fluids in 1992: … the especial value of which is the emphasis on possible sources of error in measurement. [36] I. Evans, J. Rheol. 36 (7) (1992) 1313. 12 [38] Q.D. Nguyen, D.V. Boger, Ann. Rev. Fluid Mech. 24 (1992) 47. Despite the practical importance, there is no reliable way at present to predict the onset of flow. Perhaps the main difficulty with much of the literature on yield stress fluids is the prevailing presumption that the solid-liquid transition occurs at a single invariant stress. This assumption ignores the fact that the microstructure may adjust dynamically when flow begins. Foams, emulsions, and Carbopol gels (such as hair gel) are probably closest to “ideal” yield stress materials, because they do not usually show measurable rejuvenation or aging; in these cases, a yield stress may be a material property In the few direct comparisons between computed and experimental velocity fields for the falling sphere, the agreement is poor (14), probably because the yielding process in the experimental fluids is not adequately described by the models. Much fundamental work thus remains to be done. 13 Examples of “ideal” yield stress fluids (negligible thixotropy) • Nivea Lotion ~ 4 Pa • Gilette foamy shaving cream ~10 Pa • Aloe gel ~60 Pa • Nivea Cream, Toothpaste and Mayo ~200-300 Pa • Magnetorheological fluid 10 ~ 10,000 Pa 14 Experimental Issue: Slip 15 Sandpaper required to avoid slip NiveaNiveaLotion-0001f Lotion 100.0 NiveaLotion-S02-h1050-0001f, Steady state flow step NiveaLotion-S02-h450-0001f, Steady state flow step NiveaLotion-S02-h700-0001f, Steady state flow step NiveaLotion-S03-h1050-0001f, Steady state flow step NiveaLotion-S03-h450-0001f, Steady state flow step NiveaLotion-S03-h700-0001f, Steady state flow step NiveaLotion-S04-h1050-0001f, Steady state flow step FILLED) P/P w/ sandpaper, 3 different gaps 10.00 M shear stress (Pa) OPEN) P/P, NO sandpaper, 3 different gaps Sandpaper from 1.000 McMaster-Carr 1.000E-6 0.01000 100.0 Part #) 47185A51 Adhesive-back shear rate (1/s) 16 sandpaper, 8” dia. disc, 600 grit Flow curves: different perspectives NiveaLotion-0001f NiveaLotion-0001f NiveaLotion-S02-h1050-0001f, Steady state flow step 1.000E7 NiveaLotion-S02-h1050-0001f, Steady state flow step 1.000E7 NiveaLotion-S02-h450-0001f, Steady state flow step NiveaLotion-S02-h450-0001f, Steady state flow step NiveaLotion-S02-h700-0001f, Steady state flow step NiveaLotion-S02-h700-0001f, Steady state flow step NiveaLotion-S03-h1050-0001f, Steady state flow step NiveaLotion-S03-h1050-0001f, Steady state flow step NiveaLotion-S03-h450-0001f, Steady state flow step 1.000E6 NiveaLotion-S03-h450-0001f, Steady state flow step 1.000E6 NiveaLotion-S03-h700-0001f, Steady state flow step NiveaLotion-S03-h700-0001f, Steady state flow step NiveaLotion-S04-h1050-0001f, Steady state flow step NiveaLotion-S04-h1050-0001f, Steady state flow step 1.000E5 1.000E5 10000 10000 1000 1000 100.0 100.0 viscosity (Pa.s) viscosity (Pa.s) 10.00 10.00 1.000 1.000 0.1000 0.1000 1.000 10.00 100.0 1.000E-6 0.01000 100.0 shear stress (Pa) shear rate (1/s) 17 Parallel plate correction, steady flow 100 Nivea Lotion Parallel plates with sandpaper D=40mm OPEN: Apparent stress FILLED True stress [Pa] h=1050 µm σ h= 700 µm 10 h= 450 µm M Shear Stress, Shear 1 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 -1 Shear Rate [s ] 18 Parallel plate stress correction M R Torque balance M = 2()πσrrdr2 ∫0 Linear assumption σ ()rHr= 2M Apparent rim stress σ ()R = Correction formula A π R3 M dMln σ =+3 R 3 2lnπ Rd γ R Error for perfect plastic for σ (r ) = σY σ A 4 → σ A d lnσ A σ R =+3 σY 3 4ln d γ R 19 4/3 ratio mentioned by Brunn and Asoud, Rheol. Acta, 2002 Parallel plate stress correction, Nivea lotion steady flow 100 Nivea Lotion Parallel plates with sandpaper D=40mm OPEN: Apparent stress FILLED True stress [Pa] h=1050 µm σ h= 700 µm 10 h= 450 µm Shear Stress, Shear 1 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 -1 Shear Rate [s ] 20 Roughened Cone – Works! 100 Nivea Lotion on AR-G2 3 different samples to show repeatability (S02, S04, S05) all geometries with sandpaper P/P) D=40mm, with plate-plate correction o Cone) D=60mm, α=2 , no correction necessary [Pa] σ 10 S02, P/P, h= 1050µm (uncorrected, for reference) S02, P/P, h= 700µm S02, P/P, h= 450µm S04, P/P, h=1050µm Shear Stress, Shear S05, Cone 1 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 -1 Shear Rate [s ] 21 Nivea lotion flow curve 6 10 Nivea Lotion 3 different samples to show repeatability (S02, S04, S05) 5 S02, P/P, h= 1050µm
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