Analysis of bubble growth on a hot plate during decompression in microgravity
Résumé
The focus of the present work is the modeling of bubble growth on a hot plate during decompression (depressurization) of a volatile liquid at temperatures close to saturation and in the presence of dissolved gas. In particular, this work presents an organized attempt to analyze data obtained from an experiment under microgravity conditions. In this respect, a bubble growth mathematical model is developed and solved at three stages, all realistic under certain conditions but of increasing physical and mathematical complexity: At the first stage, the temperature variation both in time and space is ignored leading to a new semi-analytical solution for the bubble growth problem. At the second stage, the assumption of spatial uniformity of temperature is relaxed and instead a steady linear temperature profile is assumed in the liquid surrounding the bubble from base to apex. The semi-analytical solution is extended to account for the two-dimensionality of the problem. As the predictions of the above models are not in agreement with the experimental data, at the third stage an inverse heat transfer problem is set up. The third stage model considers an arbitrary average bubble temperature time profile and it is solved numerically using a specifically designed numerical technique. The unknown bubble temperature temporal profile is estimated by matching theoretical and experimental bubble growth curves. A discussion follows on the physical mechanisms that may explain the evolution of the average bubble temperature in time.
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