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Injection moulding of thermoplastics: Freezing of variable-viscosity fluids.

I. Developing flows with very high heat generation

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Abstract

The injection moulding of thermoplastics involves, during mould filling, flows of hot polymer melts into mould networks, the walls of which are so cold that frozen layers form on them. An analytical study of such flows is presented here for the case when the Graetz and Nahme numbers are large and the Pearson number is small. Thus the flows are developing and temperature differences due to heat generation by viscous dissipation are sufficiently large to cause significant variations in viscosity (but the difference between the entry temperature of the polymer to a specific part of the mould network and the melting temperature of the polymer is not).

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Abbreviations

Br :

Brinkman number

Gz :

Graetz number

h :

half-height of channel or disc

h * :

half-height of polymer melt region in channel or disc

L :

length of channel or pipe

m :

viscosity shear-rate exponent

Na :

Nahme number

p :

pressure

P :

pressure drop

Pe :

Péclet number

Pn :

Pearson number

Q :

volumetric flowrate

r :

radial coordinate in pipe or disc

R :

radius of pipe

Re :

Reynolds number

R i :

inner radius of disc

R o :

outer radius of disc

R * :

radius of polymer melt region in pipe

T :

temperature

T ad :

adiabatic temperature rise

T e :

entry polymer melt temperature

T m :

melting temperature of polymer

T max :

maximum temperature

T 0 :

reference temperature

T w :

wall temperature

\(\bar T\) :

flow-average temperature rise

u r :

radial velocity in pipe or disc

u x :

axial velocity in channel

u y :

transverse velocity in channel or disc

u z :

axial velocity in pipe

w :

width of channel

x :

axial coordinate in channel or modified radial coordinate in disc

y :

transverse coordinate in channel or disc

z :

axial coordinate in pipe

α :

thermal conductivity of molten polymer

\(\hat \alpha\) :

thermal conductivity of frozen polymer

β :

scaled dimensionless axial coordinate in channel or pipe or radial coordinate in disc

β 0 :

undetermined integration constant

γ :

heat capacity of molten polymer

ζ :

viscosity temperature exponent

η :

dimensionless transverse coordinate in channel or disc

η * :

dimensionless half-height of polymer melt region in channel or disc

H * :

scaled dimensionless half-height of polymer melt region in channel or disc or radius of polymer melt region in pipe

θ :

dimensionless temperature

θ * :

dimensionless wall temperature

Θ :

scaled dimensionless temperature

λ :

numerical constant

µ :

viscosity of molten polymer

µ 0 :

consistency of molten polymer

π′ :

dimensionless pressure gradient

Π′ :

scaled dimensionless pressure gradient

ϱ :

density of molten polymer

σ :

dimensionless radial coordinate in pipe or disc

σ i :

dimensionless inner radius of disc

σ * :

dimensionless radius of polymer melt region in pipe

ϕ :

dimensionless streamfunction

Ф :

scaled dimensionless streamfunction

χ :

dummy variable

ψ :

streamfunction

ω :

similarity variable

Ω :

similarity variable

References

  1. Pearson JRA (1985) Mechanics of Polymer Processing. Elsevier Applied Science, London

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  2. Richardson SM (1983) Chapter 5 in: Pearson JRA, Richardson SM (eds) Computational Analysis of Polymer Processing. Applied Science, London

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  3. Richardson SM (1986) Chapter 4 in: Advances in Transport Processes 6

  4. Pearson JRA (1978) Polymer Eng Science 18:222

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  5. Richardson SM (1983) Rheol Acta 22:223

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  6. Richardson SM (1985) Rheol Acta 24:497

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  7. Richardson SM (1985) Rheol Acta 24:509

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  8. Richardson SM, Pearson HJ, Pearson JRA (1980) Plastics Rubber: Processing 5:55

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  9. Richardson SM (1986) Rheol Acta 25 (in press)

  10. Richardson SM (1986) Rheol Acta 25 (in press)

  11. Pearson JRA (1977) J Fluid Mech 83:191

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  12. Ockendon H (1979) J Fluid Mech 93:737

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Author information

Authors and Affiliations

  1. Department of Chemical Engineering and Chemical Technology, Imperial College, SW7 2BY, London, U.K.

    S. M. Richardson

Authors
  1. S. M. Richardson
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Richardson, S.M. Injection moulding of thermoplastics: Freezing of variable-viscosity fluids.. Rheol Acta 25, 180–190 (1986). https://doi.org/10.1007/BF01332137

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  • DOI: https://doi.org/10.1007/BF01332137

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