ANALYSIS OF THE FOAM INJECTION MOLDING PROCESS USING A CHEMICAL
BLOWING AGENT
Sejin Han, *Franco Costa, *Edwin Klompen
Autodesk, 2353 North Triphammer Road, Ithaca, NY 14850, USA
* Autodesk, 259-261 Colchester Rd., Kilsyth, VIC. 3137, Australia
Abstract
This paper details the analysis of the foam injection
molding process which uses a foaming gas generated
from a chemical blowing agent. The analysis is done
using a numerical simulation program developed in this
study. The simulation analyzes the injection molding
process with the calculation of bubble nucleation and
growth. Some experiments were conducted to validate the
simulation results. The experiments performed include
viscosity measurement and molding experiments. The
experiment and simulation results compare reasonably
well.
generation will be made. Following this, the experiments
used for the validation of the simulation will be described
and comparisons between the simulation and experiment
will be shown.
Governing Equations for Flow Analysis
To analyze the flow of resin during foam injection
molding, we solve the following set of equations [2, 3]:

   ( v)  0
t
Dv
 p    τ  g
Dt
DT
DP
C p
   (kT )   2   eT
Dt
Dt

Introduction
The use of foam injection molding is becoming
popular because it can reduce the weight of molded parts
and achieve improved dimensional stability while
maintaining the structural integrity of the part. The
foaming gas used in the foam injection molding can be
either physical blowing agent or chemical blowing agent
(CBA) [1]. Physical blowing agent involves a change of
state but no change in the composition. On the other hand,
CBA involves some change of composition [1].
This paper is on the analysis of the foam injection
molding with chemical blowing agent. The reaction or
thermal decomposition of the CBA will generate the
foaming gas (such as carbon dioxide or nitrogen) which
will be used to create cellular plastics [1]. Chemical
blowing agent (CBA) is popular in the foam injection
molding process because it can be easily adapted to an
existing injection molding process without the need for
additional equipment. In this study, thermal
decomposition of sodium bicarbonate is used for the
foaming gas generation.
A numerical calculation is used for the analysis of the
foam molding process in this study. A simulation of the
process requires the analysis of the bubble nucleation and
growth as well as the flow calculations related to regular
injection molding simulation.
In the next sections, the simulation methods for the
flow, bubble nucleation and growth will be described.
Then, the description of the reaction for the foaming gas
(1)
(2)
(3)
Equation (1) is the mass continuity equation, (2) the
momentum equation and (3) the energy equation. A threedimensional finite element method is used to solve the
above set of equations as in [2]. Tetrahedral elements are
used in the current simulation.
Bubble Nucleation Model
A bubble nucleation model is needed to calculate the
generation of bubbles during foam injection molding. The
bubble nucleation model that will be used in this study is
the fitted nucleation model [4]. With this model, the
bubble nucleation rate can be calculated from the
following equation:
J  F1 N [
2 0.5
 16F2 3
] exp[
]
m
3KT [ Pb  Pl ]2
(4)
In this model, the parameters F1 and F2 are
determined by fitting the measured nucleation result from
a molding trial. The value of Pb was determined from
Henry’s law using the calculated gas concentration value.
SPE ANTEC™ Indianapolis 2016 / 1762
The number of gas molecules per volume was used as the
value of N in this study.
Bubble Growth Calculation
Along with the bubble nucleation calculation, the
bubble growth during the foam injection molding process
must also be calculated. For this, the following equations
are solved. The first equation describes the rate of change
of the radius of the gas-melt interface, R [5]:
4R / R  ( Pg  Pl )  2 / R
(5)
This needs to be solved with the following equation
to obtain the bubble radius and the bubble pressure
distribution during molding [5]:
3
6  2 D h Rg T ( Pg 0  Pg ) 2 R 4
d Pg R
(6)
(
)
3
dt Rg T
Pg R 3  Pg 0 R0
As for the viscosity, the values were measured using
an in-line viscometer installed on an injection molding
machine (at various shear rates and temperatures). The
measurement was done with and without chemical
blowing agent. A schematic of the typical viscosity
measurement results as a function of shear rate is shown
in Figure 1. Generally, the viscosity with CBA is lower
than the viscosity without CBA because of the
plasticization effect of the foaming gas.
The viscosity of the polymer/gas/bubble system can
be fitted to the following equation. The viscosity of the
pure resin is modified to account for the gas and bubble in
the system using the following equation [2]:
  r (1   )V exp(V2c  V3c 2 )
1
(9)
Where
is the viscosity of the resin without gas or
bubble. is the volume fraction of the bubble, and c is
the gas concentration. The value of V1 was assumed as 1.
The values of V2 and V3 were fit to match the measured
viscosity data.
Chemical Blowing Agent Thermal
Decomposition Kinetics
To use a CBA in the injection molding process
effectively, the CBA needs to completely react or
decompose within the residence time in the barrel. In this
section, the kinetics for the foaming gas generation will
be described. In this study, the thermal decomposition of
sodium bicarbonate (NaHCO3) is used for the generation
of foaming gas. The chemical reaction for this is as
follows [6].
2 NaHCO3  Na2CO3 + CO2 + H2O
(7)
The degree of reaction for this process can be
calculated from the following equation [6]:
d/dt = K0 exp(-E/RgT)( 1 – )
(8)
where  is degree of reaction, T is temperature, t is time
and K0 and E are constants, and Rg is the universal gas
constant (which has the value of 8.314 J/mol-K). In this
study, the values of K0 = 1.117x1011 / sec and E = 105800
J/mol will be used [6].
Material Properties
The simulation requires various material properties.
The required properties include viscosity, PVT (pressurevolume-temperature) data, thermal properties, mechanical
properties, surface tension, solubility, diffusivity and
bubble nucleation parameters.
Figure 1: A schematic of the typical viscosity
measurement results for a resin with chemical blowing
agent (CBA) and without CBA at a single temperature
and various shear rates (shown on logarithmic scales for
the viscosity and the shear rate).
The solubility of the gas in the polymer will be
represented by the following equation:
(10)
In this study, the values of h1 and h2 were determined
from the experimental data given in [7].
The diffusivity of the gas will be represented by:
(11)
SPE ANTEC™ Indianapolis 2016 / 1763
In this study, the values of D1 and D2 were determined
from the experimental data given in [8].
foaming gas generation only occurred in the barrel, and
no reaction occurred in the feed system or in the cavity.
An Example Case
In the next section, an example case of foam injection
molding will be presented.
1. Molding Trials
Molding experiments were conducted using a
rectangular plaque mold. The shape of the feed system
and the part are shown in Figure 2(a). The thickness of the
part was 2 mm with length of 200 mm and width of 40
mm. The resin used was polypropylene (PP). The mold
temperature was 50oC, and the initial melt temperature
was 225oC. The fill time was about 0.8 sec. Moldings
with two different packing pressure levels were
performed (5 MPa or 24 MPa), and the packing time was
12 sec. The cooling time was 15 sec resulting in the total
cycle time of about 30 sec. The chemical blowing agent
used in the experiment was sodium bicarbonate
(NaHCO3). The weight % of the CBA was 4%. About 10
MPa of back pressure was applied to prevent the
nucleation and growth of the bubbles inside the barrel.
Cavity pressure measurement was recorded during
molding. The location of the pressure measurement was
18 mm from the gate along the center of the part as shown
in Figure 2(b).
The shrinkage of the part after the molding was also
measured. The shrinkage determination was done by
measuring the distance between the reference marks on
the part formed by gauge lines inscribed on the mold
cavity surface at precise locations. The measurement was
done in the area shown in Figure 3. The shrinkage was
measured along the flow direction (which is the length
direction for this case) as well as perpendicular to the
flow direction.
(a)
(b)
Figure 2: (a) Rectangular plaque model used in the study
for the experiment and the simulation and (b) the location
of the pressure transducer.
Figure 3: The shrinkage measurement area.
2. Simulation and Experiment Results
To calculate the amount of foaming gas generated,
first, the kinetics of thermal decomposition of the CBA in
the barrel was analyzed. The thermal decomposition
kinetics of NaHCO3 was calculated using equation (8).
The calculation is done for 2 different temperatures (200
o
C and 225oC). The calculation results are shown in
Figure 4. As can be seen from this figure, the degree of
reaction reaches 99% after 20 sec at 200 oC, and after 5
sec at 225oC. For the molding used in this study, the
temperature of the resin in the barrel was 225oC. The
residence time of the resin in the barrel was estimated to
be more than 30 sec. From this, we assume that the
reaction of CBA in the barrel was 100% complete within
the residence time. Therefore, we will assume that the
Figure 4: Degree of reaction of the CBA with time at
temperature of 200oC and 225oC.
SPE ANTEC™ Indianapolis 2016 / 1764
From the chemical reaction formula (equation (7)),
we can see that the percentage CO2 gas generated from
NaHCO3 is 26.2% by weight. Since the weight % of CBA
for the current case is 4%, the amount of foaming gas
generated is 1.048 % by weight of the injected polymer
melt.
The thermal decomposition of NaHCO3 will produce
by-products such as Na2CO3 and H2O. H2O will be in
liquid or vapor form depending on the temperature and
pressure conditions in the barrel or cavity. The byproducts could have some effects on the molding. They
can also affect the foaming because Na2CO3 can act as a
nucleation site and H2O can act as a blowing agent.
However, these effects will be ignored in this study.
Also, the thermal decomposition of NaHCO3 will
absorb heat. However, the actual temperature
measurement of the resin during molding shows that the
temperature drop due to the endothermic reaction of CBA
can be neglected. Therefore, its effect in the simulation
will be neglected. Also, the pressure rise due to the
foaming gas generation in the barrel will be neglected
since the pressure in the barrel is usually regulated during
most stages of the injection molding cycle.
The effects of crystallization on the foaming will not
be directly accounted for in this study. Finally, the gas
generated from the chemical reaction will be assumed to
be completely dissolved in the melt prior to injection.
The simulation was conducted using the code
developed in this study. A heat transfer coefficient of
2500 W/(m2-C) for heat transfer between the mold and
the melt was used in the simulation. The threedimensional tetrahedral mesh used in the simulation is
shown in Figure 2.
Some simulation and experiment results are
compared in this section. Firstly, the pressure values
obtained from the simulation and the experiment at the
pressure sensor location are compared. The error in
pressure values obtained from the simulation and the
experiment during the filling stage is shown in Figure 5.
The error is defined as the difference in pressure values
from the experiment and the simulation divided by the
average of experiment and simulation values. As can be
seen, the average error between the experiment and the
simulation is around 8%.
Next, the effect of packing pressure on the bubble
morphology is studied from the simulation. The bubble
size (radius) and bubble number density calculated are
compared in Figures 6 - 8. These figures show the
distribution of the bubble radius and bubble number
density over a cross-section. Figure 6(a) shows the bubble
radius distribution during the filling stage. As can be seen,
the bubble can grow mainly near the melt front during
filling. Figure 6(b) is for the bubble number density
distribution during the filling stage.
Figure 5: The error between the measured and predicted
pressures during the filling stage.
(a)
(b)
Figure 6: (a) The bubble radius and (b) the bubble number
density calculated during filling stage.
Figure 7 shows the bubble radius at the end of
molding for a position near the end of flow (18 mm from
the part end). This location is chosen for this result
because the bubble nucleation and bubble growth at the
pressure sensor location are very small due to the high
pressure maintained near the gate during the packing and
cooling stages even for a case of 5 MPa of packing
pressure. On the other hand, the pressure near the end of
flow drops to a very low value during the packing and
cooling stages for 5 MPa of packing pressure, so that
significant bubble nucleation and growth can occur at that
location. Figure 7(a) is for the case where packing
pressure of 24 MPa is applied. Figure 7(b) is where 5
MPa packing pressure is applied. For the case in Figure
SPE ANTEC™ Indianapolis 2016 / 1765
7(a), because of the long application of high packing
pressure, the bubbles generated and grown during filling
are all removed, and almost no growth of bubbles occurs
during the packing and cooling stages. This is because the
packing pressure of 24 MPa is much higher than the
saturation pressure of the gas (which is about 2.5 MPa).
However, for the case in Figure 7(b), because low
packing pressure is applied, the pressure in this cavity
location is quite low. Therefore, the bubble can grow
during the packing and cooling stages of the molding. The
bubble radius in the core region is about 30 microns.
(a)
(a)
(b)
Figure 8: The bubble number density (in 1/cm3)
calculated at the end of molding where (a) 24 MPa and
(b) 5 MPa of packing pressure is applied for 12 sec.
(b)
Figure 7: The bubble radius (in mm) calculated at the end
of molding where (a) 24 MPa and (b) 5 MPa of packing
pressure is applied.
Figure 8 shows the bubble number density at the end
of molding near the end of the flow. Figure 8(a) is for the
case with 24 MPa of packing pressure, and 8(b) is for 5
MPa of packing pressure. For Figure 8(a), because of the
high packing pressure (24 MPa), most bubbles generated
during filling will collapse, and will not nucleate again
during the packing and cooling stages. No further
foaming is expected after the part has solidified and
cooled to room temperature. For 5 MPa of packing
pressure the bubbles can nucleate during the packing and
cooling stages.
The experiment to visualize the bubble morphology
in the molded sample is underway, and may be reported
in the future.
Finally, the shrinkage values obtained from the
experiment and the simulation are compared. Table 1
shows the error in shrinkage values between the
experiment and the simulation. The %error is defined as
the difference between the measured and the simulation
values divided by the average of experiment and
simulation values. The %error is of the order of 10%. For
this case, the error in the perpendicular-to-flow direction
is smaller than that in the flow direction. The case with 24
MPa of packing pressure produced parts with
approximately 20% less shrinkage on average than those
produced with 5 MPa of packing pressure.
Table 1: %Error in shrinkage values between the
experiment and the simulation.
Packing pressure
[MPa]
24
5
Flow direction
11.5
20.4
Perpendicular-toflow direction
2.1
6.4
Conclusion
In this study, the foam injection molding using a
chemical blowing agent was studied. The analysis of the
kinetics of thermal decomposition of the chemical
blowing agent shows that the reaction is 100% complete
inside the barrel before injection. Therefore, all the
foaming gas generated from CBA was used in the
SPE ANTEC™ Indianapolis 2016 / 1766
simulation. The simulation and experiment were
compared in terms of the molding pressure and the
shrinkage. They compared reasonably well.


References
Nomenclature
1.
c
CP
D
D 1, D 2
E, K0
F1, F2
g
J
K
k
m
N
p, Pl
Pb
Pg
Pg0
R
̇
R0
Rg
T
t
v
V 1, V 2, V 3
e
 


r
h
h1, h2

Gas concentration
Specific heat
Diffusivity
Diffusivity parameters
Chemical blowing agent reaction parameters
Parameters for the Fitted Nucleation model
Gravitational constant
Nucleation rate (per volume per time)
Boltzmann constant
Thermal conductivity
Molecular mass
Number of nucleation sites
Pressure
Gas Pressure
Pressure of the bubble
Initial pressure of the bubble
Radius of the bubble
Rate of change of radius of the bubble
Initial radius of the bubble
Universal gas constant
Temperature
Time
Velocity vector
Viscosity parameters
Expansivity
Bubble volume fraction
Shear rate
Viscosity of the gas and polymer system
Viscosity of the polymer (without gas)
Solubility
Solubility equation parameters
Density
Surface tension
Stress tensor
2.
3.
4.
5.
6.
7.
8.
S. T. Lee, C. B. Park & N. S. Ramesh, Polymeric
Foams: Science and Technology, Taylor & Francis
(2007).
S. Han, F. Costa and L. Kishbaugh, ―Numerical and
Experimental Studies on Bubble Nucleation and
Growth During Microcellular Injection Molding‖,
SPE ANTEC Paper (2014).
K. Talwar, F. Costa, V. Rajupalem, L. Antanovski
and C. Friedl, "Three-Dimensional Simulation of
Plastic Injection Molding", SPE ANTEC Paper
(1998).
K. Taki, ―Experimental and numerical studies on
the effects of pressure release rate on number
density of bubbles‖, Chemical Engineering
Science, v. 63, pp. 3643-3653 (2008).
M. Amon and C.D. Denson, ―A Study of the
Dynamics of Foam Growth: Analysis of the
Growth of Closely Spaced Spherical Bubbles‖,
Polym. Eng. Sci., 24, 1026-1034 (1984).
Y. L. Wu and S. M. Shih, ―Intrinsic kinetics of the
thermal decomposition of sodium bicarbonate‖,
Thermochimica Acta, 223, pp. 177 – 186 (1993).
Y. Sato, K. Fujiwara, T. Takikawa, Sumarno, S.
Takishima, H. Masuoka, ―Solubilities and diffusion
coefficients of carbon dioxide and nitrogen in
polypropylene, high-density polyethylene, and
polystyrene under high pressures and temperature‖,
Fluid Phase Equilibria, 162, 261–276 (1999).
S. Areerat, E. Funami, Y. Hayata, D. Nakagawa,
M. Ohshima, ―Measurement and prediction of
diffusion coefficients of supercritical CO2 in
molten polymers‖, Polymer Engineering and
Science, 44, 1915—1924 (2004).
SPE ANTEC™ Indianapolis 2016 / 1767