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Rheology of Slurries

Che5700 陶瓷粉末處理. Rheology of Slurries. Review briefly interactions between polymer stabilized colloid systems:. Che5700 陶瓷粉末處理. Schematic Interaction Energy. Schematic calculation , taken from J. Colloid Interface Sci., 6:492, 1951.

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Rheology of Slurries

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  1. Che5700 陶瓷粉末處理 Rheology of Slurries • Review briefly interactions between polymer stabilized colloid systems:

  2. Che5700 陶瓷粉末處理 Schematic Interaction Energy Schematic calculation, taken from J. Colloid Interface Sci., 6:492, 1951. Small size polymer, less effective; rigid better than flexible polymer

  3. Che5700 陶瓷粉末處理 Batch Consistency • Chapter 14 in JS Reed book • 5 consistency state: • Bulk powder (no liquid) • Agglomerates (granules) • Plastic body • Paste • Slurry (dilute solution called suspension; slip: slurry containing clay) • Factors: • Amount, distribution and properties of liquid • Amount, size and packing of particles • Types, amount and distribution of additives • Interparticles forces: attractive or repulsive

  4. DPS = degree of pore saturation = volume of liquid / volume of pore Plastic body paste slurry granule

  5. Che5700 陶瓷粉末處理 More Comments • Plastic state : often during extrusion, plastic pressing etc. • Granule & plastic body may rearrange due to applied force, to become more dense • Paste : often used in printing (thick films in electronic ceramics) • Slip or slurry: for casting

  6. Che5700 陶瓷粉末處理 Springback For plastic material, DPS = 1, on decompression, due to small compressibi-lity of liquid, volume expansion accom-panying slight particle rearrange-ment occur  springback SB

  7. Che5700 陶瓷粉末處理 Batch Calculation • Mostly by weight%; sometimes by vol% • Mostly based on total weight, sometimes based on weight of major ceramic powders

  8. Che5700 陶瓷粉末處理 Some properties of suspension • Some related to solute conc. only, unrelated to its chemistry: vapor pressure lowering, freezing point depression, boiling point elevation • a1 = activity; TBP = normal boiling point

  9. Che5700 陶瓷粉末處理 Osmotic Pressure • Solute conc. produce chemical potential difference: 1o (T,P) = 1o (T, P+) + Rg T ln(a1); : osmotic pressure (membrane is capable to separate solvent and solute) • thermodynamics:  = c2 Rg T (similar to ideal gas law; osmotic pressure exerted by solute concentration c2) • Since c2 = w2/M2  can be used to determine MW • For non-ideal solutions, expressions for  can be complex • A simplified equation for polymer solution:1=1/2 makes second virial coefficient zero; called Flory point, or theta point  theta temperature

  10. Che5700 陶瓷粉末處理 Osmotic Pressure in Colloidal Suspension • One of source: electrical double layer of colloids; many complex equations, results as the right figure (TA Ring, 1996); • Affected by zeta potential, double layer thickness, solid volume fraction etc. • a,b,.. Different particle packing models

  11. Che5700 陶瓷粉末處理 Rheology • basically: Newtonian fluid and non-Newtonian fluid • Viscosity = constant for Newtonian fluid; for non-Newtonian power law fluid model, shown as follows • Necessary to know rheology to predict flow of suspension into mold;  predict velocity distribution, shear stress on wall, pressure distribution in mold, etc • Rheology important to – transport, mixing, forming etc. Apparent viscosity

  12. Shear thinning Shear thickening 取自TA Ring, 1996;

  13. Che5700 陶瓷粉末處理 Comparsion of Instruments • Capillary viscometer: simple to use, easy to change temp. and shear rate, similar to real fluid condition, can study extrudate behavior at the same time; drawback: rate of shear is not constant across capillary • Coaxial cylinder viscometer: all region under constant shear rate, easy to calibrate; drawback: high viscous material difficult to fill in, polymer may creep up along shaft • Cone and plate viscometer: also constant shear rate in all region, small sample, less heat build up; easy to fill in, easy to clean up; drawback: rate of shear limited to low rates

  14. Che5700 陶瓷粉末處理 Measurements • Double cylinder or cone-and-plate or capillary tube are three common methods; Eq. derived to calculate viscosity from data; T = torque; Measuring shear rate should be close to shear rate in use; left figure:shear rate varies with position, hence often use narrow annulus

  15. Che5700 陶瓷粉末處理 Relative Indices • Some simple relative index for viscosity: e.g. time of fluid to pass a small hole • Gel strength – related to history of sample, need to stir with high shear for some time, settled, then measurement • Index of structural buildup – B gel = (Y2 - Y1)/ln(t2/t1) t2, t1 = time to wait • Index of structural breakdown B thix = (Y2 - Y1)/ ln(t2/t1); or (p1 - p2)/ln(t1/t2) [after constant shear rate different time; or different shear rate, same time] • Elastic nature: memory effect, not ideal

  16. Four regimes of uniform rigid-sphere system: (I) Newtonian fluid; (II) shear thinning regime; (III) high shear Newtonian regime; (IV) shear thickening regime

  17. Che5700 陶瓷粉末處理 Equations • Dilute suspension: Einstein equation – for spherical particles, =2.5; limited to <0.02 (volume fraction); s = solvent viscosity • Electro-viscous effect by Smouluchowski: zeta potential is included Generalized Casson eq.

  18. Che5700 陶瓷粉末處理 Effect of Polymers on Viscosity • Polymer effect: (a) increase viscosity of solution; (b)adsorb on particle surface to increase its effective volumec [1 + (Ls/a)3]; Ls = span of polymer layer on particle surface • P = polymer volume fraction soluble in solvent (after deduction of adsorption; + dilation effect)

  19. Che5700 陶瓷粉末處理 Dilute, Slightly Aggregated Suspension • Colloidally unstable suspension; memory effect over long time scales  thixotropy • Cross equation: c and m are fitted parameters;o = low shear limit viscosity;  = high shear limit viscosity

  20. Che5700 陶瓷粉末處理 • Cross equation characteristics, and its corresponding particle structure (in suspension); shear rate stopped, Brownian motion will bring particle back to its network • 取自TA Ring, 1996; Two limiting viscosities

  21. Che5700 陶瓷粉末處理 Percolation Threshold • This concept occurs in many situations; here to unstable colloidal system, exist a minimum particle concentration, if higher than this value, particle form bridging network, showing yield strength; from Newtonian fluid to Cross equation or Bingham plastic fluid • percolation or bond percolation (後者數值較低) – because one bond involves two sites only; if site percolation, then each site can have z coordination • One can estimate percolation threshold for specific structures • Critical percolation volume fraction ~ 16%

  22. Theoretical prediction of percolation threshold for various geometries: fromTA Ring, 1996

  23. For electro-statically stabilized suspensions: when close to PZC, viscosity of suspension increase quickly; away from pzc, like a Newtonian fluid; but for much higher or lower pH, due to ionic strength, double layer thickness decrease, system unstable again

  24. Around PZC, high viscosity; after adding HEC, pzc shift  highest viscosity point also shift; due to HEC, value of viscosity also increase; 取自JS Reed, 1995

  25. Che5700 陶瓷粉末處理 Concentrated Slurries • Can be sub-divided into different systems, e.g. stable or unstable; polymer or not; mono-modal particle size distribution • Polymer may entangle together  pseudo-plastic flow  Cross equation; some of parameters may be estimated from theory, e.g. m = (Mn/Mw) 1/5 [Mn = number averaged MW; Mw = weight averaged MW; ratio of these two values = width of MW distribution] • Concentrated suspension often time dependent rheology  thioxtropy  due to particle structure may change with shear stress  different stress lead to different steady state

  26. Che5700 陶瓷粉末處理 Time Dependent Behavior After rest for a while, a gel strength developed due to particle structure formation; With yield stress, coating can resist creep flow (gravitation)

  27. Che5700 陶瓷粉末處理 Monodisperse System • Derivation rely on description of particle structure and their interaction • Still Cross equation, but for concentrated system, can be simplified to the following form: Pe = ratio between particle motion and diffusion; t for translational instead of rotational

  28. Taken from TA Ring, 1996;

  29. Shear thinning  3 body interaction

  30. Che5700 陶瓷粉末處理 General Equation • Cross equation: both low shear or high shear viscosity can be represented by following equation: wherem =maximum volume fraction  often a fitted value from experimental data 0.5 – 0.74; n = 2 – 3; often 2 • Doughtery-Krieger eq. similar; others include Mooney equation, Chong equation etc

  31. Doughtery-Krieger equation: 取自JS Reed, 1995 cr & KH are two fiited parameters

  32. Che5700 陶瓷粉末處理 Anisotropic Particles • E.g. rod, plate-like particles (clay) and its rheology; still use Cross equation to describe rheology; with one extra parameterr = b/a (aspect ratio) • For clay: different face, different charge, hence different behavior (structure) under different pH For clay particles

  33. 取自TA Ring, 1996

  34. Different particle structure, different rheology

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