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 in a mould cavity 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. This criterion is shown to be corroborated by experimental data for the filling of a spiral mould cavity by three different polymers under a range of different operating conditions.
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Abbreviations
- a j :
-
constant
- b jk :
-
constant
- c :
-
constant
- Br :
-
Brinkman number
- Br † :
-
characteristic Brinkman number
- Gz :
-
Graetz number
- Gz † :
-
characteristic Graetz number
- h c :
-
half-height of flat cavity
- h * c :
-
half-height of polymer melt region in flat cavity
- L c :
-
length of cavity
- L f :
-
filled length of cavity
- m :
-
viscosity shear-rate exponent
- P :
-
pressure drop
- Q :
-
volumetric flow-rate
- r :
-
radial coordinate in round cavity
- R c :
-
radius of round cavity
- R * c :
-
radius of polymer melt region in round cavity
- 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 :
-
cavity wall temperature
- u r :
-
radial velocity in round cavity
- u x :
-
axial velocity in flat cavity
- u y :
-
transverse velocity in flat cavity
- u z :
-
axial velocity in round cavity
- w c :
-
width of flat cavity
- x :
-
axial coordinate in flat cavity
- y :
-
transverse coordinate in flat cavity
- z :
-
axial coordinate in round 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
- ζ :
-
dimensionless axial coordinate in round cavity
- ζ § :
-
dimensionless axial position of matching plane in round cavity
- η :
-
dimensionless transverse coordinate in flat cavity
- η * :
-
dimensionless half-height of polymer melt region in flat cavity
- θ :
-
dimensionless temperature
- θ i :
-
dimensionless inlet temperature
- θ j :
-
j-th term in power series expansion of dimensionless temperature
- \(\bar \theta \) :
-
dimensionless flow-average temperature
- ϰ:
-
thermal diffusivity ratio
- λ :
-
dimensionless filled length
- λ f :
-
dimensionless filled length at freezing-off
- \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\Lambda } \) :
-
latent heat of fusion of polymer
- µ :
-
viscosity
- µ 0 :
-
unit shear-rate viscosity
- v j :
-
j-th eigenvalue
- ξ :
-
dimensionless axial coordinate in flat cavity
- ξ § :
-
dimensionless axial position of matching plane in flat cavity
- ∏ c :
-
dimensionless pressure drop in cavity
- ϱ :
-
density of molten polymer
- \(\hat \varrho \) :
-
density of frozen polymer
- σ :
-
dimensionless radial coordinate in round cavity
- σ * :
-
dimensionless radius of polymer melt region in round cavity
- τ :
-
dimensionless time
- τ f :
-
dimensionless freeze-off time
- τ 0 :
-
dimensionless time at start of final phase of freezing-off
- ϕ :
-
dimensionless similarity variable in entrance region
- χ :
-
dummy variable
- ψ :
-
scaled dimensionless axial coordinate in cavity
- ω :
-
dimensionless similarity variable in melt front region
- ω * :
-
constant
References
Richardson SM (1985) Rheol Acta 24:497
Richardson SM (1983) Rheol Acta 22:223
Selopranoto JH (1982) MSc thesis. Imperial College, University of London
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Richardson, S.M. Injection moulding of thermoplastics. II. Freezing-off in cavities. Rheol Acta 24, 509–518 (1985). https://doi.org/10.1007/BF01462498
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DOI: https://doi.org/10.1007/BF01462498