Chemical Engineering 584: Polymer Processing Lecture 7: Extrusion and Mixing

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Chemical Engineering 584 Polymer
ProcessingLecture 7 Extrusion and Mixing
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Extrusion

• Extruders are used for
• Mixing
• Pumping
• Reactions/polymer modification
• Key design parameters for extrusion
• Flow rate
• Pressure drop
• Residence time distribution

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Extruders

• How do we design a melt screw pump?
• Must generate pressure from viscous stresses but
  in drag flow, no pressure generated
• If close an end partially, fluid is still dragged
  and pressure is generated
• Take the infinite flat plate and twist it into a
  barrel and shallow channel by twisting and
  turning the screw inside the barrel.

Pressure build-up
Twist into a screw
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Extruders

W width of channel H channel depth df
flight clearance Vb velocity of
barrel qbbarrel surface angle
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Extruders
sinq L/z
e fight width

• Neglect flight clearance in our analysis so Db
  Ds

Velocity of barrel VbpDN where N is the
rotation rate (assume barrel is moving and not
screw)
Vbz Vbcosq pDsNcosq
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Extruders

• Model for fluid
• Newtonian
• Apply the flat plate geometry for the case of
  drag flow and an opposing pressure flow

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Extruders

• The final result for the volumetric flow rate in
  the pumping section is

L length of screw q helix angle Ds screw
diameter H channel depth N rotation speed m
viscosity (Newtonian equivalent)
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Extruders

• For the volumetric flow rate in the die section
  for a Newtonian Fluid (Hagen-Poiseuille equation)
  (assume the die is tubular)

• The expressions for Qdie and Qextruder must be
  equal. This relationship leads to the operating
  point for the extruder-die system.

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Mixing

• Extruders (single and twin-screw) are common
  mixers for polymeric materials but other mixers
  used
• Static mixers
• Roll mills
• Batch mixers
• How is mixing characterized?
• Uniformity, Texture, Scale, intensity of
  segregation
• How are mixing processes characterized?
• Residence time distribution
• Goal of mixing Uniform composition

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Mixing

• Laminar Mixing
• Example mixing of two viscous liquids.
• Interfacial area increases with strain applied.

At initial time to, the initial area Ao is
defined by two vectors r1 and r2
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Mixing
Initially, interfacial area Ao is given by
At a later time, interfacial area A is given by
Note change in position vectors
For large deformations,

• L length of cube side
• minor component volume fraction
• g total strain

Average striation thickness
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Mixing

• Characterization of Mixing
• Increase in interfacial area related to strain
• Strain distribution function (SDF) describes the
  strain histories in a flow field. SDFs can be
  determined from velocity distribution

Instantaneous strain distribution function
Cumulative strain distribution function
Mean strain
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Mixing

• Example determine the strain distribution
  function (SDF) f(g)dg, the cumulative SDF and the
  mean strain for drag flow of a Newtonian fluid
  between parallel plates as shown below.

(Hint determine the velocity profile and flow
rate first)
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Mixing

• Besides SDF, the residence time distribution
  (RTD) function is another important measure of
  mixing
• Determines time that material spends in the mixer

Instantaneous RTD
Cumulative RTD
Mean residence time
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Mixing

• Example Determination of the residence time
  distribution for laminar, pressure-driven flow in
  a tube for a Newtonian fluid (see Example 7.8,
  Tadmor Gogos)

(Hint Given the velocity profile, relate it to
the residence time to the given position and the
geometry of the tube.)
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Mixing

• Example Effect of shear-thinning behavior on
  strain distribution. Consider a power-law fluid
  between two concentric cylinders (Tadmor Gogos,
  Example 11.2). Determine the cumulative SDF
  F(g), the SDF f(g)dg and the mean strain and
  comment on the effect of the power-law parameter
  n on the SDFs and the mean strain.

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Mixing Types of Mixers

• Batch mixers
• Advantages
• Operations varied in a cycle
• Additives added at different times
• Good temperature control
• Disadvantages
• Blenders (simple operation but handling
  difficult)
• Fluidized beds (difficult to clean, static
  build-up, not suitable for sticky mixtures)
• Batch liquid mixers (impellers bladed mixers
  for low to medium viscosity materials, Banbury or
  Roll-mills for high viscosity materials)

• Continuous mixers
• Advantages
• Fast, continuous
• Product uniformity
• Quality control
• Reduced labour
• Disadvantages
• Low dispersive mix quality
• Less flexibility
• Examples Single-screw and twin-screw extruders

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Mixing Strain Distribution and Residence Time
Distribution in Screw Extruders

• Relevant sections
• Baird Collias, Chapter 8
• Tadmor Gogos, section 11.10
• Flow is in down-channel direction and is
  2-dimensional (vz(x,y)). Barrel surface has
  velocity component in x-direction to give
  circulatory flow in the cross-channel direction.
• Assumptions
• laminar
• Steady
• Fully-developed
• Isothermal
• Gravity and convection negligible

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Mixing Strain Distribution and Residence Time
Distribution in Screw Extruders
The equations of motion in the x and z directions
reduce to
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Mixing Strain Distribution and Residence Time
Distribution in Screw Extruders
The velocity profile is
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Mixing Strain Distribution and Residence Time
Distribution in Screw Extruders

• For transverse flows (i.e., in the x-direction),
  neglect leakage flows and assume zero flow rate.

• Given the flow condition above, the pressure
  gradient can be determined and the velocity
  profile is

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Mixing Strain Distribution and Residence Time
Distribution in Screw Extruders

• For flow in the down-channel direction (i.e.
  z-direction), the equation of motion in the
  z-direction is solved by separation of variables
  subject to the following boundary conditions

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Mixing Strain Distribution and Residence Time
Distribution in Screw Extruders

• The velocity profile in the z-direction is
  given by the following equation (see Tadmor and
  Klein, Engineering Principles of Plasticating
  Extrusion, Van Nostrand, NY, (1970), p. 194).

where uzvz/Vbz, c x/W and h H/W.
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Mixing Strain Distribution and Residence Time
Distribution in Screw Extruders

• As in the cross-channel direction, the velocity
  profile can be integrated to give the volumetric
  flow rate in the down-channel direction and the
  pressure gradient can be determined.

Fp and Fd are shape factors for pressure and
drag flow
drag flow
pressure flow
Qd
Qp
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Mixing Strain Distribution and Residence Time
Distribution in Screw Extruders

• The ratio of the pressure to drag flow components
  of the flow rates is

• The velocity in the axial direction is given by
  the components of the cross-channel and
  down-channel velocities. Note that the velocity
  cannot be lt 0 (no back-flow).

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Mixing Strain Distribution and Residence Time
Distribution in Screw Extruders
Velocity profiles in cross-channel, down-channel
and axial directions for various Qp/Qd values in
shallow, square pitched screws (i.e. q 17.65o)
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Mixing in Extruders (Cont.)
Qp/Qd -2/3
Qp/Qd -1
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Residence Time Distributions in Extruders

• Operating conditions, melt viscosity and channel
  depth affect down-channel but not cross-channel
  velocity profile
• Particle in x-direction re-circulates in upper
  part of channel (see Fig. 11.27 11.28 in Tadmor
  and Gogos). This is described as follows

Valid for shallow channels but ignores leakage
flows, non-Newtonian effects, thermal effects and
flight geometry
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Residence Time Distributions in Extruders
Residence time of fluid particle in upper part of
channel
Residence time of fluid particle in lower part of
channel
Fraction of time fluid particle spends in upper
part of the channel
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Residence Time Distributions in Extruders
The axial residence time is given by
The minimum residence time occurs when ux 0 (x
2/3)
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Residence Time Distributions in Extruders
From the volumetric flow rates and geometry, the
instantaneous RTD can be determined
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Polymer Blends

• Most polymers are sold as blends (gt 30 Utracki
  et al)
• Why blend polymers
• More economic than making a new polymer
• Combine synergistic properties
• Reduce cost of base material
• Commercial blends available
• HIPS (Shell) (poly(styrene)/poly(butadiene))
• Nylon ST (DuPont) (nylon/(ethylene-propylene)
  copolymer rubber)
• Xenoy (General Electric) (poly(phenyleneoxide)/pol
  y(styrene))

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Polymer Blends

• Consider mixing of liquid-liquid dispersions in
  Newtonian systems
• Taylor (1934) examined break-up of a single
  Newtonian drop in a Newtonian matrix

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Polymer Blends

• Consider mixing of liquid-liquid dispersions in
  viscoelastic systems
• Wu (1982) related drop size to rheological and
  interfacial properties using a semi-empirical
  relation for concentrated, non-Newtonian
  polymeric fluids

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Polymer Blends

• Drop break-up studied since 1930s (Tomotika,
  Mason, Grace, Stone Leal)

Distortion at break-up
Initial distortion
A breaking thread of poly(propylene) in a
poly(styrene) matrix. Oscillations at the
interface cause the thread to break-up into drops
(from Sundararaj, Ph. D. Thesis, University of
Minnesota, 1994).
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Polymer Blends
Morphology development along a twin-screw
extruder for a 20 wt dispersion of
poly(propylene) in poly(styrene) (Sundararaj et
al., Polym. Eng. Sci., 36,1812, (1992)
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Polymer Blends

• Morphology development in polymer blends (Macosko
  et al, Macromolecules, 29, 5590, (1996)).

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Polymer Blends

• Compatibilization of Polymer Blends
• Most polymers are immiscible with one another and
  phase-separate at higher temperatures
• Require compatibilization to prevent phase
  separation
• Necessary for mechanical or physical property
  enhancement

Definitions DGmix Gibbs free energy of
mixing DHmix enthalpy of mixing DSmix entropy
of mixing T temperature R gas constant V
volume V1, V2 partial molar volumes of polymers
1 2 c enthalpic interaction parameter f1, f2
volume fractions of polymers 1 2 d1, d2
solubility parameters of polymers 1 2
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Polymer Blends

• Methods to compatibilize polymer blends
• Pre-made block copolymer addition
• Reactive blending

Polymer A
Polymer B
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Polymer Blends

• Blend morphologies are tailored to application
• HIPS (high impact poly(styrene))
• PS/(polybutadiene) blend
• How is HIPS produced?
• Styrene monomer soluble in PB ( 10 wt styrene)

Dark regions poly(styrene)

• Intense agitation followed by graft copolymer
  formation (compatibilizer)
• Phase inversion once polystyrene homopolymer
  formation significant
• Cell-like structure stabilized by compatibilizer

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Polymer Blends

• Other blend morphologies dispersed domains
• Nylon ST (super-tough nylon)
• Nylon 6,6 blended with 20 maleated EP rubber
  produces blend with superior impact strength
  (Epstein et al. US Patent 4,174,358 4,174,859
  (1977)
• Reactive blending used to control particle size
  for optimal impact strength

EP-r-maleic anhydride
(reaction between amine and anhydride groups
makes graft copolymer at interface between nylon
and EP phases)
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Polymer Blends

• Rubber toughened nylons can have morphology
  controlled by varying level of reaction
• Many examples in literature see adjacent
  figure for example
• All blends in figure are 80 wt nylon 6 with 20
  wt dispersed poly(propylene) (PP) phase)
• Nylon 6 stained dark in micrographs PP is white
• More reactive rubber added, finer dispersion of
  EP in nylon

Taken from Gonzalez-Montiel et al. Polymer, 24,
4587, (1995).