3.3.4 Modeling of bubble average diameter
According to the Weber number and the flow ratio of the gas phase (QG)to the liquid phase (QL), a prediction model of the bubble size is proposed:
\begin{equation} \frac{d_{\text{av}}}{d_{m}}=k\times W^{a}\times\ \left(\text{\ \ }\frac{Q_{G}}{Q_{L}}\ \right)^{b}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (5)\nonumber \\ \end{equation}
After fitting the experimental data, the equation for the bubble size of the dispersed gas generated by the ceramic membrane is obtained:
\begin{equation} \frac{d_{\text{av}}}{d_{m}}=6818.48\times W^{0.11675}\times\left(\text{\ \ }\frac{Q_{G}}{Q_{L}}\ \right)^{-0.00357}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (6)\nonumber \\ \end{equation}
Figure 13 suggests that the theoretical data is basically consistent with the experimental data, and the relative error is 30% positive deviation and 15% negative deviation. In fact, the size of the bubbles is also affected by many factors, such as the wettability of the membrane, the pore size of the membrane, and the physical properties of the liquid. The next research will consider building a more complete model.
FIGURE 13 Prediction and verification of average diameter model of microbubbles produced by ceramic membrane

3.4 Bubble Behavior Characteristic