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Rheology of Slurries


Title: PowerPoint Author: Last modified by: KS Created Date: 12/4/2001 12:37:01 AM Document presentation format: (4:3) – PowerPoint PPT presentation

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Title: Rheology of Slurries

Rheology of Slurries
Che5700 ??????
  • Review briefly interactions between polymer
    stabilized colloid systems

Schematic Interaction Energy
Che5700 ??????
Schematic calculation, taken from J. Colloid
Interface Sci., 6492, 1951. Small size polymer,
less effective rigid better than flexible polymer
Batch Consistency
Che5700 ??????
  • 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

DPS degree of pore saturation volume of
liquid / volume of pore
Plastic body
More Comments
Che5700 ??????
  • 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

Che5700 ??????
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
Batch Calculation
Che5700 ??????
  • Mostly by weight sometimes by vol
  • Mostly based on total weight, sometimes based on
    weight of major ceramic powders

Some properties of suspension
Che5700 ??????
  • 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

Osmotic Pressure
Che5700 ??????
  • 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
  • A simplified equation for polymer solution?11/2
    makes second virial coefficient zero called
    Flory point, or theta point ? theta temperature

Osmotic Pressure in Colloidal Suspension
Che5700 ??????
  • 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

Che5700 ??????
  • basically Newtonian fluid and non-Newtonian fluid
  • Viscosity constant for Newtonian fluid for
    non-Newtonian power law fluid model, shown as
  • 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
Shear thinning
Shear thickening
??TA Ring, 1996
Comparsion of Instruments
Che5700 ??????
  • 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

Che5700 ??????
  • 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
Relative Indices
Che5700 ??????
  • 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

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

Che5700 ??????
  • Dilute suspension Einstein equation for
    spherical particles, ?2.5 limited to ?lt0.02
    (volume fraction) ?s solvent viscosity
  • Electro-viscous effect by Smouluchowski? zeta
    potential is included

Generalized Casson eq.
Effect of Polymers on Viscosity
Che5700 ??????
  • 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)

Dilute, Slightly Aggregated Suspension
Che5700 ??????
  • 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

Che5700 ??????
  • Cross equation characteristics, and its
    corresponding particle structure (in suspension)
    shear rate stopped, Brownian motion will bring
    particle back to its network
  • ??TA Ring, 1996

Two limiting viscosities
Percolation Threshold
Che5700 ??????
  • 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 (??????)
    because one bond involves two sites only if site
    percolation, then each site can have z
  • One can estimate percolation threshold for
    specific structures
  • Critical percolation volume fraction 16

Theoretical prediction of percolation threshold
for various geometries ??TA Ring, 1996
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
Around PZC, high viscosity after adding HEC, pzc
shift ? highest viscosity point also shift due
to HEC, value of viscosity also increase ??JS
Reed, 1995
Concentrated Slurries
Che5700 ??????
  • 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
  • Concentrated suspension often time dependent
    rheology ? thioxtropy ? due to particle structure
    may change with shear stress ? different stress
    lead to different steady state

Time Dependent Behavior
Che5700 ??????
After rest for a while, a gel strength developed
due to particle structure formation With yield
stress, coating can resist creep flow
Monodisperse System
Che5700 ??????
  • 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

Taken from TA Ring, 1996
Shear thinning ? 3 body interaction
General Equation
Che5700 ??????
  • 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

Doughtery-Krieger equation ??JS Reed, 1995 ?cr
KH are two fiited parameters
Anisotropic Particles
Che5700 ??????
  • E.g. rod, plate-like particles (clay) and its
    rheology still use Cross equation to describe
    rheology with one extra parameter r b/a
    (aspect ratio)
  • For clay different face, different charge, hence
    different behavior (structure) under different pH

For clay particles
??TA Ring, 1996
Different particle structure, different rheology
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