Mass-Transfer Properties of Microbubbles. 2. Analysis Using a Dynamic Model

Abstract

Gas-to-liquid mass transfer is commonly the rate-limiting step in industrial fermentations. Microbubble sparging has been shown to give extremely high volumetric masstransfer rates, even for low power-to-volume ratios. Microbubbles are surfactantstabilized bubbles having a radius on the order of 25 µm. The extremely high surfacearea-to-volume ratios of microbubbles can result in rapid changes in their size, internal pressure, and gas composition. Consequently, an unsteady-state modeling approach is needed to adequately describe microbubble mass transfer. A dynamic model of a single microbubble immersed in an infinite pool of stagnant liquid was developed and solved numerically. The model accounts for mass-transfer resistances of the surfactant shell and surrounding bulk liquid, bubble shrinkage, changes in the gas pressure and composition inside the bubble, and changes in the liquid-phase concentration profile of the transferred gas surrounding the bubble. The model was used to explore a variety of dynamic phenomena associated with microbubble mass transfer. The presence of a nontransferred gas in the microbubble was predicted to significantly reduce the masstransfer rate, indicating that microbubble sparging is better suited to gases with a high consumable fraction. The instantaneous mass-transfer coefficient was predicted to change significantly with time, but the time-averaged coefficient was constant enough to justify the measurement of average mass-transfer coefficients for microbubbles. Average mass-transfer coefficients predicted by the model agreed well with values measured experimentally and calculated using literature correlations.

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