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Manystudies have been made about the behaviors of single gas bubbles ascending in various liquids, that is, the rising velocities or the shapes of single bubbles2'4'8)9). Single bubbles rise in a straight line when the bubble diameter is very small, and with increase of the bubble diameter, the path of the gas bubble turns to be zigzag or spiral. On the condition of onset of zigzag or spiral motion, Saffman6) and Hartunian and Sears3) carried out experimental and theoretical work. Saffman6) suggested that the zigzag motion was caused by the interaction between a periodic oscillation of the wake and the instability of the motion near the front of the bubble, and deduced that the value of the critical Weber number WeGat which instability appeared was 1.03. But this criterion does not agree with experimental results. Hartunian and Sears3) suggested that the interaction between surface tension and hydrodynamic pressure could result in instability of the bubble motion, and on a basis of the existing data and their ownexperimental results, they proposed that there

An improved two-stage model is proposed to predict bubble volume and to explain the phenomena of bubble formation whenbubbles are formed from a submerged single orifice accompanied by pressure fluctuations in a gas chamber.The following conclusions are reached by comparing the calculated results based on the proposed model with the experimental results :(1) The calculated bubble volumes agree well with the experimental results over a wide range of experimental conditions. (2) The change of bubble volume with bubbling time and the phenomena of pressure fluctuations in the gas chamber are well described by the model.

Crystallization experiments with calcium carbonate by three liquid-liquid reaction systems from a MSMPR crystallizer were conducted to makeclear the characteristics of reactive crystallization kinetics. As it was confirmed that the crystal growth obeys the ALlaw from the CSDobtained, the nucleation rate and growth rate wereobtained. The effects of the operating factors and the reaction systems on the crystallization kinetics were studied. It was clarified that the nucleation rate and the growth rate are correlated by the power law model, and that the kinetic orders in the power law model are correlated with carbonate alkah'nity irrespective of reaction system.

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