(178k) Effect of Liquid Surface Tension on the Initial Bubble Size in Molten Metal Bubble Reactors

Gas-liquid reactors containing molten metals find several different applications, including metallurgical processes, nuclear processes, and, more recently, methane cracking. The performance of these systems is strongly influenced by the size of the gas bubbles formed, which affect their rise velocity, but also the surface area-to-volume ratio, with consequent effects on the rates of heat and mass transfer. Although numerous correlations exist in the literature to estimate the size of gas bubbles, most of these concern gas-water systems. Occasionally, studies investigate the effect of the physical properties of the liquid media by studying systems making use of high-viscosity liquids but with similar surface tensions as water, such as glycerol. On the other hand, literature on bubble size estimation in liquids with higher density and surface tension, such as molten metals, is lacking. To date, many studies make use of Tate's law, which often leads to significant errors. In effect, such an approach is reasonable because using more complex equations would still not guarantee accuracy of the results, having been developed for systems with significantly different physical properties and being difficult to validate when using non-transparent liquids at high temperatures, for which optical measurements are extremely difficult. Yet, the need for a more accurate estimate of bubble size persists.

This work aims to determine the effect of the physical properties of the liquid medium, more specifically of surface tension, on the initial bubble size, i.e., right after its detachment from the inlet orifice. This, in turn will have an effect on the average bubble size in the bulk of the liquid. The work is founded on the following premises:

• in their study on bubble swarms in liquid metals, Sano and Mori [1] found a dependence of the average bubble diameter on liquid density and surface tension;
• in the present work, we find that this finding is in agreement with the average size of methane bubbles in a molten SnNi alloy at 1000°C, as experimentally determined in [2];
• a completely predictive model for the determination of the initial bubble size based on elementary force balances has been reported by Geary and Rice [3] and validated experimentally in air-water systems [4];
• when compared to the findings of Sano and Mori [1], Geary and Rice's model [3] underestimates the effect of liquid surface tension, as shown in Figure 1.

Here, we attempt to reconcile the results found in [1] and [3], by modifying the dependence of the initial bubble size on the liquid surface tension, taking into account the early onset of coalescence and break-up phenomena, as well as detachment time.

Figure 1 caption. Bubble volume after detachment as predicted by Geary and Rice [3] for different sparger orifice radii, r_h, and liquid viscosities, σ.

References

1. Sano, M., Mori, K., Dynamics of Bubble Swarms in Liquid Metals, 1980, Transactions ISIJ, 20, 669.
2. Kim, J., Oh, C., Oh, H., Lee, Y., Seo, H., Kim, Y.K., Catalytic methane pyrolysis for simultaneous production of hydrogen and graphitic carbon using a ceramic sparger in a molten NiSn alloy, 2023, Carbon, 207, 1-12.
3. Geary, N.W., Rice, R.G., Bubble Size Prediction for Rigid and Flexible Spargers, 1991, AIChE Journal, 37, 161.
4. Polli, M., Di Stanislao, M., Bagatin, R., Abu Bakr, E., Masi, M., Bubble Size Distribution in the Sparger Region of Bubble Columns, 2002, Chemical Engineering Science, 57, 197.