Computationally, the phenomenon of bubble bursting is handled by comparing the bubble location and residence time near the surface to the rules that determine its immediate fate. When a bubble breaks the line of the undisturbed surface of the sample, its individual clock is initialized. The bubble is considered to burst when it has remained at the surface for a time period exceeding a specified drainage time, td, set to zero for instantaneous bursting. Due to the lack of information on drainage and erosion of a thin polymer film during pyrolysis, the parameter td is set to a constant value that allows for a crude investigation of surface effects that may result from the presence of surfactants.
All bubbles that have satisfied the requirements for bursting during the current timestep are removed from the computation. The mass loss rate is then computed by summing the masses of all bubbles that have burst since the end of the previous timestep and dividing by the timestep length:
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(38) |
Merging is assumed whenever the volumes of multiple bubbles overlap. The multiple bubbles are replaced by a single bubble whose volume is the sum of the volumes of the merged bubbles and whose center is at their center of mass. This simple approach is supported by the rapid coalescence of two bubbles in a clean fluid as determined by Li and Liu [44] and discussed in subsection 4.2.4. In this case the coalescence time was found to be shorter than the bursting time for a bubble at an initially flat interface by as much as a factor of five.