Simulating ultrasonic decrosslinking of crosslinked high-density polyethylene
The management of crosslinked plastic waste is an ongoing major environmental problem. Indeed, recycling of crosslinked polymers is difficult because of their inherent 3D networks. Although various attempts have been made to recycle crosslinked polyethylene,1–4 most of these previous studies have been focused on crosslinked low-density polyethylene. Over the past two decades, we have therefore been developing ultrasonic-assisted extrusion methods to decrosslink crosslinked high-density polyethylene (XHDPE). In these methods, however, the dissipation of ultrasonic energy causes severe thermal degradation of the XHDPE and inferior properties of the decrosslinked material.5
In our more recent work, we have developed our updated twin-screw extrusion XHDPE process, with which we can obtain decrosslinked XHDPE that exhibits excellent mechanical properties and melt processability.6–8 To optimize and scale up this ultrasonic decrosslinking process for XHDPE, however, new technology (based on science results) is required. To that end, we have proposed a theoretical model (with four parts) for our ultrasonic decrosslinking approach.9 In the first part of our model, the imposition of ultrasound induces bubble cavitation in XHDPE and decrosslinked XHDPE. In the next stage, the propagation of ultrasound in the decrosslinked XHDPE causes ultrasonic dissipation. In the third part, ultrasonically induced bubble dynamics causes the crosslinked network to rupture. Lastly, we model the flow of decrosslinked XHDPE in the ultrasonic treatment zone (see Figure 1)—in the presence of the viscous and ultrasonic dissipation—as nonisothermal, which means that the shear viscosity of the decrosslinked XHDPE is greatly affected by its gel fraction and crosslink density.
In this work,10 we have continued our decrosslinking studies by conducting simulations of ultrasonic XHDPE decrosslinking under static conditions in a twin-screw extruder (with and without thermal degradation). In this way, we are able to predict how the ultrasonic decrosslinking conditions affect the gel fraction and crosslink density of the XHDPE, as well as the spatial distribution of various processing characteristics. In addition, we have made experimental measurements with which to validate our proposed process model. Unlike our earlier models for ultrasonic devulcanization of rubber vulcanizates—which required kinetic parameters, bubble radius, and bubble volume fraction—our current model requires only the bubble radius and bubble volume fraction.
The predicted gel fraction and crosslink density of our ultrasonically decrosslinked XHDPE are shown as a function of treatment time (for ultrasonic amplitudes of 5, 7.5, and 10μm) in Figure 2. We obtained these results for a hydrostatic pressure of 1MPa and for a bubble volume fraction of 0.67%. The initial gel fraction and crosslink density are 0.63 and 0.0117kmol/m3, respectively, and we observe that both parameters decrease with treatment time and ultrasonic amplitude. Moreover, we find that the effects of residence time, ultrasonic amplitude, and bubble volume fraction are significant, whereas the ambient pressure has little influence on the ultrasonic decrosslinking of the XHDPE under static conditions. In addition, a series of sigmoidal equations provide excellent fits to our gel fraction and crosslink density predictions.
Our predicted gapwise temperature distributions at different axial distances (i.e., from the entrance of the ultrasonic treatment zone) and ultrasonic amplitudes, for a flow rate of 6.5g/min, are given in Figure 3. These results indicate that the temperature increases substantially with both increasing distance from the entrance and increasing ultrasonic amplitude (e.g., there is a significant temperature increase of 50K at an ultrasonic amplitude of 10μm). This temperature increase is caused by both the ultrasonic and viscous flow dissipations. Similarly, we show the predicted gapwise distribution of the gel fraction as a function of axial distance from the ultrasonic treatment zone and ultrasonic amplitude in Figure 4. In this case we find that the the gel fraction decreases with distance from the ultrasonic treatment zone entrance and with ultrasonic amplitude. The asymmetric distribution of the data in all these profiles (see Figures 3 and 4) is caused by the asymmetric thermal boundary conditions, i.e., the asymmetric distribution of the velocity in the extrusion direction.
The ultrasonic power consumption during XHDPE ultrasonic decrosslinking, the gel fraction, and the crosslink density that we measured in our experiments and predicted in our models are shown as a function of ultrasonic amplitude (for flow rates of 3.75, 6.5, and 8.25g/min) in Figure 5. Although we observe a fair agreement between our predicted and measured ultrasonic power consumption at all the flow rates, our predictions for gel fraction and crosslink density do not match the measured values at flow rates of 3.75 and 82.5g/min. It may be possible to resolve the underprediction of the crosslink density and gel fraction by using a higher bubble volume fraction. However, the disagreement in the crosslink density slopes arises because we do not have a suitable model for ultrasonically induced bubble nucleation in our simulations. In addition, we can reduce the discrepancy between the simulated and experimentally measured gel fraction values by including thermal degradation in our modeling (see Table 1).
Figure 5.Table 1.
|Gel fraction||Crosslink density (kmol/m3)|
In summary, we have simulated ultrasonic decrosslinking of XHDPE under static conditions, and have validated our modeling with experimental twin-screw extrusion measurements. With our model we can calculate the pressure, velocity, temperature, gel fraction, and cross-link density of the decrosslinked XHDPE in the ultrasonic treatment zone of the twin-screw extruder. We obtain good quantitative agreement between our simulated and experimental results for the ultrasonic power consumption during the decrosslinking process, but only a qualitative agreement for the gel fraction and crosslink density. We also find that incorporating thermal degradation into our model improves its predictions at high amplitudes. In our future work, we aim to further improve our simulations by incorporating ultrasonically induced bubble nucleation effects.
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