To study the potential effects of bubble bursting dynamics on pyrolysis of the spherical polymeric sample, bubbles are assigned individual drainage clocks. As each bubble approaches the surface, its velocity is slowed according to the factor discussed in section 4.2.3. When the bubble breaks the plane of the surface, drainage is assumed to begin, and the clock is started. When the clock exceeds the predetermined drainage time, which is provided as an input parameter to the problem, the bubble bursts and releases its gases.
Figures 21 and 22 show that a delay in bubble bursting on the order of tens of milliseconds has a considerable effect on the pyrolysis rate for the PMMA sphere. The plot of radius as a function of time shows that the additional retention of gases in bubbles causes swelling of the sphere after the initial preheating period. When the bubbles that gather at the surface early in the process finally burst, they release a large amount of gas at once, as seen in the spikes for time-averaged mass loss rate around time t=8 s for drainage times of 20 ms and 30 ms. After this event, a decrease in mass loss rate sets in due to the thermal insulation of the interior of the sample by the increased amount of gas at the surface.
The number of finite elements used for these runs was 41, with timesteps of duration 0.25 ms.
Figure 21: Sample radius vs. time for bubbling PMMA sphere with bursting occurring a time period td = 0 ms (orange), 10 ms (yellow), 20 ms (green), and 30 ms (blue) after a bubble touches the sample surface.
Figure 22: Mass loss rate vs. time corresponding to Figure 21. Mass loss rates are averaged over 0.5 s.
Thermal effects of the bubbles with time are demonstrated in Figures 23 through 25. Large fluctuations in the temperature of the outer surface with time reflect the formation and bursting of the bubbles. The size of the temperature fluctuations increases as drainage time, and therefore the amount of gas close to the surface, increases. In each of these plots the temperatures at the outer surface and the center of the spherical sample are compared to those for a sample whose bubbles burst instantly (zero drainage time). The thermal insulation effects of the bubbles undergoing drainage before bursting are apparent in the lowered temperatures at the surface after bubbles have burst (the minimum temperatures for the upper plots) and at the sample center.
Figure 23: Temperature vs. time at the sample center (lower lines) and on the outer surface for drainage times td = 10 ms (yellow) and 0 ms (orange).
Figure 24: Temperature vs. time at the sample center and outer surface for drainage times td = 20 ms (green) and 0 ms (orange).
Figure 25: Temperature vs. time at the sample center and outer surface for drainage times td = 30 ms (blue) and 0 ms (orange).
The effects of surface bubbles on the temperature profile within the spherical sample are shown more clearly in Figures 26 and 27, with profiles of temperature vs. radius plotted every 2 s. When each bubble bursts as soon as it reaches the surface, the thermal conductivity of the outermost element does not change significantly from that of the polymeric melt. However, when each bubble is held at the surface before bursting, as in Figure 27, the thermal conductivity of the outermost element may be much smaller than the melt, resulting in a large jump in temperature over a small distance near the surface.
Figure 26: Temperature vs. radius at intervals of 2 s for bursting time td = 0 s.
Figure 27: Temperature vs. radius at intervals of 2 s for bursting time td = 20 ms.
Figure 28 presents a sequence of views of the PMMA sample with thin-film drainage times of 20 ms. Note that many of the bubbles are clearly located along the sample surface preparing to burst.
Figure 28: Two-dimensional view of bubbling PMMA sample with drainage time of 20 ms. Frames are shown at 4 s intervals beginning at time t = 0.