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Rheology TA Instruments – US West Gkamykowski@Tainstruments.Com 4/2/2019 TA Instruments – Waters LLC Materials Characterization by Rheological Methods Gregory W Kamykowski PhD Senior Applications Scientist for Rheology TA Instruments – US West [email protected] ©2019 TA Instruments TAINSTRUMENTS.COM 1 Rheology: An Introduction Rheology: The study of the flow and deformation of matter. Rheological behavior affects every aspect of our lives. TAINSTRUMENTS.COM 2 1 4/2/2019 Rheology: The study of the flow and deformation of matter Flow: Fluid Behavior; Viscous Nature F F = F(v); F ≠≠≠ F(x) Deformation: Solid Behavior F Elastic Nature F = F(x); F ≠≠≠ F(v) 0 1 2 3 x Viscoelastic Materials: Force F Maxwell depends on both Deformation and Rate of Deformation and vice versa. Kelvin, F Voigt TAINSTRUMENTS.COM 3 Basic Material Behaviors Egg Polymer Ceramic Water Oil Soap Metal white Melt ? Flow Flow & Deformation Deformation Elastic Solids Viscous Liquids Visco elastic Stress Stress Modulus = Viscosity = Strain Strain Rate TAINSTRUMENTS.COM 4 2 4/2/2019 Rheological Testing - Rotational 2 Basic Rheological Methods 1. Apply Force (Torque)and measure Deformation and/or Deformation Rate (Angular Displacement, Angular Velocity) - Controlled Force, Controlled Rate Shear Angular Velocity, Velocity, Angular Stress Torque, Shear Stress 2. Control Deformation and/or Displacement, Angular Deformation Rate and measure Force needed (Controlled Strain Displacement or Rotation, Controlled Strain or Shear Rate) Torque, Stress Torque, TAINSTRUMENTS.COM 5 Steady Simple Shear Flow Top Plate Velocity = V 0; Area = A; Force = F H y Bottom Plate Velocity = 0 x vx = (y/H)*V 0 . -1 γγγ = dv x/dy = V 0/H Shear Rate, sec σσσ = F/A Shear Stress, Pascals . ηηη = σσσ/γγγ Viscosity, Pa-sec These are the fundamental flow parameters. Shear rate is always a change in velocity with respect to distance. TAINSTRUMENTS.COM 6 3 4/2/2019 Parallel Plate Shear Flow Stress σσσ Force or torque Strain γγγ Linear or angular displacement Strain ʖ Linear or angular velocity Rate TAINSTRUMENTS.COM 7 SHEAR RATE CALCULATIONS IN EXTRUSION . Extruder: γγγ = πππDN/(60*h) D = Diameter; N = rpm; h = gap . 3 Q = Output rate; Circular, Rod: γγγ = 32Q/( πππD ) D = orifice diameter compounding, cable . Rectangular, Slit: γγγ = 6Q/(wh 2) Q = Output rate; w = width cast film, sheet h = gap . Annulus: γγγ = 12Q/( πππ(D1+D2)h 2) Q = Output rate; D1 = Inner diameter blown film, blow molding D2 = Outer diameter h = gap TAINSTRUMENTS.COM 8 4 4/2/2019 Representative Flow Curve 1.E+05 Newtonian Pseudoplastic Region Behavior 1.E+04 0 < n < 1 (Newtonian) 1.E+03 Transition Power Law ηηη = ηηη0 Region Region 1.E+02 Viscosity Viscosity (Pa-sec) 1.E+01 . ηηη = m* γγγ (n-1) 1.E+00 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 M 3.4 -1 ηηη0 ∝∝∝ W Shear Rate (sec ) TAINSTRUMENTS.COM 9 Idealized Flow Curve Often we try to correlate our rheology data with actual applications. However, differences between similar materials are accentuated at the low shear 1) Sedimentation rates, where rotational rheometers excel. 2) Leveling, Sagging So, even if one does not get to high shear 3) Draining under gravity η rates, the rheology data are still useful. 4) Chewing and swallowing 5) Dip coating log 6) Mixing and stirring 7) Pipe flow 8) Spraying and brushing 9) Rubbing 10) Milling pigments in fluid base 11) High Speed coating 4 5 6 8 9 1 2 3 7 10 11 1.00E-5 1.00E-4 1.00E-3 0.0100 0.100 1.00 10.00 100.00 1000.00 1.00E4 1.00E5 1.00E6 shear rate (1/s) TAINSTRUMENTS.COM 10 5 4/2/2019 Simple Shear Deformation Top Plate Displacement = X 0; Area = A; Force = F H y Bottom Plate x Displacement = 0 x = (y/H)*X 0 γγγ = dx x/dy = X 0/H Shear Strain, unitless σσσ = F/A Shear Stress, Pascals G = σσσ/γγγ Modulus, Pa These are the fundamental deformation parameters. Shear strain is always a change in displacement with respect to distance. TAINSTRUMENTS.COM 11 Stress Relaxation Stress Relaxation of Soy Flour, Overlay 10 9 • Instantaneous Strain • Note the decrease in the modulus as a ) function of time. 10 8 G(t) ( G(t) [Pa] F G(t) T=20°C T=30°C T=40°C T=50°C 10 7 10 0 10 1 10 2 10 3 time [s] TAINSTRUMENTS.COM 12 6 4/2/2019 Rheological Parameters FLUIDS TESTING Parameter Shear Elongation Units . Rate γγγ ε Seconds -1 Stress σσσ τττ Pascals . Viscosity ηηη = σσσ/γγγ ηηηE = τττ/εεε Pascal-seconds SOLIDS TESTING Parameter Shear Elongation Units Strain γγγ ε Unitless Stress σσσ τττ Pascals Modulus G(t) = σσσ/γγγ E = τττ/εεε Pascals TAINSTRUMENTS.COM 13 Rheological Parameters CREEP TESTING Parameter Shear Elongation Units Stress σσσ τττ Pascals Strain γγγ ε Unitless Compliance J = γγγ /σσσ D = ε/τε/τε/τ 1/Pascals TAINSTRUMENTS.COM 14 7 4/2/2019 Creep Testing Stress is held constant. Strain is the measured variable. Compliance = Strain/Stress 3x10 -3 HDPE 2x10 -3 Viscoelastic 1x10 -3 Fluid Compliance (1/Pa) Solid 0x10 0 0 5 10 15 20 Step time (min) Viscosity = 1/Stress is held constant. Strain is Slope in steady flow regime. Intercept = non-recoverable Compliance TAINSTRUMENTS.COM 15 GEOMETRIES TAINSTRUMENTS.COM 16 8 4/2/2019 Geometry Options Concentric Cone and Parallel Torsion Cylinders Plate Plate Rectangular Very Low Very Low Very Low Solids to Medium to High Viscosity Viscosity Viscosity to Soft Solids Water to Steel TAINSTRUMENTS.COM 17 Converting Machine to Rheological Parameters in Rotational Rheometry Machine Parameters M x Kσ σ M: Torque = =η ΩΩΩ : Angular Velocity ΩxK γ• θθθ : Angular Displacement γ Conversion Factors Kσσσ : Stress Conversion Factor Kγγγ : Strain (Rate) Conversion Factor MxK σ Rheological Parameters σ σσσ : Shear Stress (Pa) • = =G γγγ : Shear Rate (sec -1) ηηη : Viscosity (Pa-sec) xK γγγ : Shear Strain θ γ γ G : Shear Modulus (Pa) The conversion factors, K σσσ and K γγγ, will depend on the following: Geometry of the system – concentric cylinder, cone and plate, parallel plate, and torsion rectangular Dimensions – gap, cone angle, diameter, thickness, etc. TAINSTRUMENTS.COM 18 9 4/2/2019 Shear Rate and Shear Stress Calculations Geometry Couette Cone & Plate Parallel Plates Conversion Factor Kγγγ Ravg /(R o-Ri) 111/βββ R/h 2 3 3 Kσσσ 1/(2* πππRi L) 3/(2 πππR ) 2/( πππR ) TAINSTRUMENTS.COM 19 Choosing a Geometry Size Assess the ‘viscosity’ of your sample When a variety of cones and plates are available, select diameter appropriate for viscosity of sample Low viscosity (milk) - 60mm geometry Medium viscosity (honey) - 40mm geometry High viscosity (caramel) – 20 or 25mm geometry Examine data in terms of absolute instrument variables torque /displacemen t/speed and modify geometry choice to move into optimum working range You may need to reconsider your selection after the first run! TAINSTRUMENTS.COM 20 10 4/2/2019 Geometry Options With the variety of cones, plates, cups and rotors available, select a geometry based on desired experimental parameters and the material properties Cones and Plates No Solvent Trap With Solvent With Solvent Trap (NST) Trap and Heat Break (HB) Smooth, Sandblasted, and Cross hatched Concentric Cylinders (or Cups) and Rotors (or Bobs) TAINSTRUMENTS.COM 21 When to use Cone and Plate Very Low to High Viscosity Liquids High Shear Rate measurements Normal Stress Growth Unfilled Samples Isothermal Tests Small Sample Volume TAINSTRUMENTS.COM 22 11 4/2/2019 Shear Rate is Normalized across a Cone The cone shape produces a smaller gap height closer to the inside, so the shear on the sample is constant ͬ͘ = h increases proportionally to dx , γ is uniform ͜ TAINSTRUMENTS.COM 23 Cone Diameters Shear Stress 20 mm 40 mm 60 mm 3 As diameter decreases, shear stress increases = ͇ 2 ͦͧ TAINSTRUMENTS.COM 24 12 4/2/2019 Cone Angles Shear Rate Increases 2 ° 1 ° 0.5 ° 1 As cone angle decreases, shear rate increases ʖ = Ω TAINSTRUMENTS.COM 25 Limitations of Cone and Plate Typical Truncation Heights: 1° degree ~ 20 - 30 microns 2° degrees ~ 60 microns 4° degrees ~ 120 microns Cone & Plate Truncation Height = Gap Gap must be > or = 10 [particle size]!! TAINSTRUMENTS.COM 26 13 4/2/2019 Correct Sample Loading × Under Filled sample: Lower torque contribution × Over Filled sample: Additional stress from drag along the edges Correct Filling TAINSTRUMENTS.COM 27 When to use Parallel Plates Low/Medium/High Viscosity Samples with long relaxation time Liquids Temperature Ramps/ Sweeps Soft Solids/Gels Materials that may slip Thermosetting materials Crosshatched or Sandblasted plates Samples with large particles Small sample volume TAINSTRUMENTS.COM 28 14 4/2/2019 Plate Diameters Shear Stress 20 mm 40 mm 60 mm 2 As diameter decreases, shear stress increases = ͇ ͦͦ TAINSTRUMENTS.COM 29 Plate Gaps Shear Rate 2 mm Increases 1 mm 0.5 mm ͦ As gap height decreases, shear rate increases ʖ = Ω ͜ TAINSTRUMENTS.COM 30 15 4/2/2019 Effective Shear Rate varies across a Parallel Plate For a given angle of deformation, there is a greater arc of deformation at the edge of the plate than at the center ͬ͘ = dx increases further from the center, ͜ h stays constant TAINSTRUMENTS.COM 31 When to Use Concentric Cylinders Low to Medium Viscosity Liquids Unstable Dispersions and Slurries Minimize Effects of Evaporation Weakly Structured Samples (Vane) High Shear Rates TAINSTRUMENTS.COM 32 16 4/2/2019 Peltier Concentric Cylinders TAINSTRUMENTS.COM 33 Geometry Information – Estimated Min and Max Shear Rates Sample Max Shear Rate Min Shear Rate Geometry Diameter (mm) Degree Gap (micron) Volume (mL) (approx) 1/s (approx) 1/s 0 1000 0.05 1.20E+03 4.00E-07 0 500 0.03 8 0.5 18 1.17E-03 1 28 2.34E-03 2 52 4.68E-03 4 104 9.37E-03 0 1000 0.31 3.00E+03 1.00E-06 0.5
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