Abstract A Lagrangian model has been derived that describes the size, species composition and velocity of an individual gas bubble as it ascends through a vertical column with stagnant liquid and exchanges mass with the other phase. Various correlations for the liquid-side mass transfer coefficient for laminar flow have been implemented in the Lagrangian model and the predictions are compared with available experimental data in the literature. The predictability of the Lagrangian model is in general not acceptable due to the limitations of the available theoretical framework employed for deriving the existing correlations for the mass transfer coefficient. The various mass transfer coefficients give very different simulation results, and furthermore, the experimental data show a transient behavior in the change of bubble size due to mass transfer which is not captured by the Lagrangian model. An over- or underestimation of the interface mass transfer flux will give an erroneous change of bubble size, which may have significant influence on the predicted bubble rise velocity - in particular if the drag coefficient is very sensitive to the size of the bubble. It is emphasized that the cause of discrepancy between the simulation results and experimental data is not due to the Lagrangian model but mainly caused by the lack of good models for the mass transfer coefficient.

中文翻译：

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来自停滞液体中上升的单个气泡的传质的拉格朗日模型

摘要 拉格朗日模型已经推导出来，该模型描述了单个气泡的大小、种类组成和速度，因为它上升通过带有停滞液体的垂直柱并与另一相交换质量。层流的液体侧传质系数的各种相关性已在拉格朗日模型中实现，并将预测与文献中可用的实验数据进行比较。由于用于导出传质系数的现有相关性的可用理论框架的局限性，拉格朗日模型的可预测性通常是不可接受的。不同的传质系数给出了非常不同的模拟结果，此外，实验数据显示了由于传质引起的气泡尺寸变化的瞬态行为，拉格朗日模型没有捕捉到这种行为。对界面传质通量的高估或低估将导致气泡尺寸的错误变化，这可能对预测的气泡上升速度产生重大影响 - 特别是如果阻力系数对气泡的尺寸非常敏感。需要强调的是，造成模拟结果与实验数据不一致的原因并非拉格朗日模型，而主要是缺乏良好的传质系数模型。这可能会对预测的气泡上升速度产生重大影响 - 特别是如果阻力系数对气泡的大小非常敏感。需要强调的是，造成模拟结果与实验数据不一致的原因并非拉格朗日模型，而主要是缺乏良好的传质系数模型。这可能会对预测的气泡上升速度产生重大影响 - 特别是如果阻力系数对气泡的大小非常敏感。需要强调的是，造成模拟结果与实验数据不一致的原因并非拉格朗日模型，而主要是缺乏良好的传质系数模型。