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Injection moulding of thermoplastics. I. Freezing-off at gates

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Abstract

The injection moulding of thermoplastics involves, during mould filling, flow of a hot molten polymer into a mould network, the walls of which are so cold that the polymer freezes on them. During the constant pressure drop part of the filling stage, but not during the preceding constant flow-rate part, freezing-off, that is premature blockage of the mould network by frozen polymer, is possible. A semi-quantitative analysis of such freezing-off at a gate is presented here. The length-scales and time-scales of all the relevant physical processes occurring during freezing-off are identified and a criterion is obtained which enables the occurrence of freezing-off to be predicted, at least crudely.

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Abbreviations

a j :

constant

b jk :

constant

Br :

Brinkman number

Br 0 :

initial Brinkman number

Gz :

Graetz number

Gz 0 :

initial Graetz number

h c :

half-height of flat cavity

h g :

half-height of flat gate

h * g :

half-height of polymer melt region in flat gate

L c :

length of cavity

L f :

filled length

L g :

length of gate

m :

viscosity shear-rate exponent

P :

pressure drop

Q :

volumetric flow-rate

r :

radial coordinate in round gate and cavity

R c :

radius of round cavity

R g :

radius of round gate

R * g :

radius of polymer melt region in round gate

Sf :

Stefan number

t :

time

t f :

freeze-off time

T :

temperature

T i :

inlet polymer melt temperature

T m :

melting temperature of polymer

T w :

gate wall temperature

u r :

radial velocity in round gate

u x :

axial velocity in flat gate

u y :

transverse velocity in flat gate

u z :

axial velocity in round gate

w c :

width of flat channel

w g :

width of flat gate

x :

axial coordinate in flat gate and cavity

y :

transverse coordinate in flat gate and cavity

z :

axial coordinate in round gate and cavity

α :

thermal conductivity of molten polymer

\(\hat \alpha \) :

thermal conductivity of frozen polymer

γ :

heat capacity of molten polymer

\(\hat \gamma \) :

heat capacity of frozen polymer

ε h :

ratio of half-height of flat gate to that of flat cavity

ε R :

ratio of radius of round gate to that of round cavity

ε w :

ratio of width of flat gate to that of flat cavity

ζ :

dimensionless axial coordinate in round gate and cavity

η :

dimensionless transverse coordinate in flat gate and cavity

η * :

dimensionless half-height of polymer melt region in flat gate

θ :

dimensionless temperature

θ i :

dimensionless inlet temperature

θ j :

j-th term in power series expansion of dimensionless temperature

ϰ :

thermal diffusivity ratio

λ :

dimensionless filled length

\(\hat \Lambda \) :

latent heat of fusion of polymer

µ :

viscosity

µ 0 :

unit shear-rate viscosity

v j :

j-th eigenvalue

\(\tilde v_j \) :

j-th zero of zeroth-order Bessel function of first kind

ξ :

dimensionless axial coordinate in flat gate and cavity

∏ c :

dimensionless pressure drop in cavity

∏ g :

dimensionless pressure drop in gate

ϱ :

density of molten polymer

\(\hat \varrho \) :

density of frozen polymer

σ :

dimensionless radial coordinate in round gate and cavity

σ * :

dimensionless radius of polymer melt region in round gate

τ :

dimensionless time

τ f :

dimensionless freeze-off time

τ 0 :

dimensionless time at start of final phase of freezing-off

\(\tilde \tau \) :

rescaled dimensionless time

\(\tilde \tau _f \) :

rescaled dimensionless freeze-off time

\(\tilde \tau _0 \) :

rescaled dimensionless time at start of final phase of freezing-off

ϕ :

dimensionless similarity variable

χ :

dummy variable

ψ :

scaled dimensionless axial coordinate in gate

References

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Authors and Affiliations

  1. Department of Chemical Engineering and Chemical Technology, Imperial College, Prince Consort Road, SW7 2BY, London, UK

    S. M. Richardson

Authors
  1. S. M. Richardson
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Richardson, S.M. Injection moulding of thermoplastics. I. Freezing-off at gates. Rheol Acta 24, 497–508 (1985). https://doi.org/10.1007/BF01462497

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  • DOI: https://doi.org/10.1007/BF01462497

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