FIGURE 6 Images of microbubbles formed at different pressures: (A) 0.2 MPa, (B) 0.3 MPa, (C) 0.4 MPa, (D) 0.5 MPa and (E) 0.6 MPa. Liquid flow rate: 1.0 ml/min and gas flow rate: 10 ml/min with 10 cm ceramic membrane
FIGURE 7 Effect of gas pressure on the average bubble diameter. Liquid flow rate: 1.0 ml/min and gas flow rate: 10 ml/min with 10 cm ceramic membrane

3.2 Flow Pattern

The flow patterns of gas-liquid in ceramic membranes mainly include bubble flow and slug flow, as shown in Figure 8. It can be seen that the shape of the bubble is closely related to the gas flow and liquid flow. Therefore, a prediction model based on the critical point bubble for flow pattern is proposed as Eq. (4):
\begin{equation} \left\{\begin{matrix}Q_{G}=45-26Q_{L}\text{\ \ \ }\left(0<Q_{L}\ <1,0<Q_{G}<20\right)\text{\ \ \ }R^{2}=0.94857\ \ \ \ \ \mathbf{\text{bubble\ flow}}\\ Q_{G}=16.5+2.5Q_{L}\text{\ \ \ \ \ }\left(Q_{L}\ \geq 1,\ Q_{G}\geq 20\right)\text{\ \ \ \ \ \ \ \ \ \ \ \ \ }R^{2}=0.85714\ \ \ \ \ \mathbf{\text{slug\ flow}}\text{\ \ \ \ \ }\\ \end{matrix}\right.\ (4)\nonumber \\ \end{equation}
When the liquid flow and gas flow are low, the gas phase is discontinuously distributed in the form of small bubbles in the liquid phase. The bubbles are spherical but the gas holdup is low, and the flow pattern at this time is mainly sparse bubble flow (Figure 9A). With the increase of gas flow, more small bubbles are generated and transferred to bubble flow (Figure 9B). As the gas flow rate continues to increase, the small bubbles gather and transform into large bubbles, which take on the shape of a convex front and a flat back, with the flow pattern transforming into the slug flow in Figure 9C. It has been found large bubbles have a small phase interfacial area, which is not conducive to mass transfer.28
FIGURE 8 Flow patterns with ceramic membrane of two phases. Liquid flow rate: 1.0 ml/min and gas flow rate: 10 ml/min with 10 cm ceramic membrane