Solano-Altamirano J M, Goldman Saul
Dept. of Chemistry, The Guelph-Waterloo Centre for Graduate Work in Chemistry and The Guelph-Waterloo Physics Institute, University of Guelph, Guelph, Ontario N1G 2W1, Canada.
Math Biosci. 2014 Jun;252:27-35. doi: 10.1016/j.mbs.2014.03.008. Epub 2014 Mar 21.
We solved both the Diffusion and Laplace equations which predicted very similar results for the problem of a dissolving small gas bubble suspended in a liquid medium. These bubbles dissolved both because of surface tension and solute concentration effects. We focused on predicting bubble lifetimes ("td"), and dissolution dynamics - radius vs time (R vs t) for these contracting bubbles. We also presented a direct comparison of the predicted results, obtained by applying either Dirichlet or Neumann boundary conditions, to the bubble/medium interface. To the best of our knowledge, this is the first direct comparison that has ever been published on the application of these different boundary conditions to a moving gas/liquid boundary. We found that the results obtained by applying either Dirichlet or Neumann boundary conditions were very similar for small, short-lived bubbles (R0<25 μ,td<40s), but diverged considerably for larger, longer-lived bubbles. We applied our expressions to the timely problem of Inner Ear Decompression Sickness, where we found that our predictions were consistent with much of what is known about this condition.
我们求解了扩散方程和拉普拉斯方程，对于悬浮在液体介质中的小气泡溶解问题，这两个方程预测的结果非常相似。这些气泡的溶解是由表面张力和溶质浓度效应共同导致的。我们重点预测了气泡寿命（“td”）以及这些收缩气泡的溶解动力学——半径与时间的关系（R与t）。我们还对通过应用狄利克雷或诺伊曼边界条件在气泡/介质界面处得到的预测结果进行了直接比较。据我们所知，这是首次发表的关于将这些不同边界条件应用于移动的气/液边界的直接比较。我们发现，对于小的、寿命短的气泡（R0<25 μ，td<40s），应用狄利克雷或诺伊曼边界条件得到的结果非常相似，但对于更大、寿命更长的气泡，结果有很大差异。我们将我们的表达式应用于内耳减压病这个实时问题，发现我们的预测与关于这种病症的许多已知情况是一致的。
