Bubble shrinkage no longer unpredictable

A big step for foaming simulation

Figure 1 The core-back process

In the plastic foaming injection process, the supercritical fluid (N2 or CO2) and the melt are firstly mixed into a uniform single-phase fluid through the screw, and the homogeneous mixture leads to thermodynamic instability due to instantaneous pressure release during the injection process. It makes the supercritical fluid in the melt generate tens of thousands of tiny bubbles through phase change, and after the mold cooling and solidification, the products with cell structures are obtained.

By adopting the Han and Yoo model of bubble growth dynamics, we can simulate the process and dynamics of the bubble growth. However, when the product’s geometric appearance gets complicated, and various processes are applied, the in-mold pressure will not always be low. For instance, the melt pressure at the thin area is still very high, and even higher than the packing pressure. On the other hand, the core-back process (Figure 1) will also bring additional packing pressure. Thus, the in-mold bubbles will not continue growing due to pressure release but may shrink because of the increasing in-mold melt pressure. Under the circumstances, the Han and Yoo model has limitations and is not able to accurately simulate the bubble shrinkage phenomena.

To improve the prediction capabilities of the original model, Moldex3D has collaborated with the Kanazawa University to develop the Modified Han and Yoo model. According to the bubble dynamic model proposed by Prof Taki from Kanazawa and the batch’s experimental data [1], the bubbles will surpass the energy barrier to nucleate and grow as the pressure releases. If the pressure on the bubbles increases, the bubbles will gradually shrink until they dissolve back into the melt (that is, it is back to the initial state of the mixture of melt and gas). If the pressure is released again at this time, the bubbles will nucleate and grow at the same location. The experimental results also have a very close trend with the bubble dynamic model, verifying the process of bubble shrinkage caused by the pressure imposed (Figure 3).

Figure 2 The bubble shrinkage experiment


Figure 3 The comparison of the simulation and experimental results

In the past, when the Han and Yoo model was used to simulate the thin-part geometry, the process of bubble shrinkage could not be accurately predicted. Therefore, the number of bubbles that disappeared due to the increasing pressure was underestimated. Now, in the latest Moldex3D 2021 version, the option of the Modified Han and Yoo model has been added (Figure 4). Compared with the original Han and Yoo model, the modified one can predict the shrinking bubbles more accurately (Figure 5). Similarly, if we apply this modified model in the core-back process, the required packing time for all the bubbles to dissolve back to the melt will be obtained.

Figure 4 The Modified Han and Yoo model option has been added in Moldex3D 2021.
Figure 5 The comparison of the original and Modified Han and Yoo models

The foaming process is very diverse and complicated and is widely applied in various fields. Therefore, it is particularly important to control the changes during the whole process. If we can accurately predict the bubble size through the microscopic model, it will be helpful for further prediction of many macroscopic properties such as heat transfer, mechanical strength, sound absorption, and low dielectric constant. As a result, the product design and production efficiency will be significantly enhanced.


[1] K. Taki et al., “3D Numerical simulation and experimental observation of bubble growth and collapse in Nitrogen-gas saturated molten polymer for the core-back foam injection molding”, ANTEC® 2021 – SPE.

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