# Study on Siphon Drainage Capacity of Slopes with Long-Horizontal Pipe Sections
## 4 Discussion
### Critical Lift Variation at Siphon Restart
In addition, the increase in the average bubble length with the tube diameter can be seen in Figure 11a,b since the resistance to motion of the bubbles decreases with the increase in the tube diameter. When the bubbles are subjected to the thrust generated by the fluid motion in the vertical section, the slug bubbles will move and push the movement of the liquid slug, while the upward floating wall bubbles will remain stationary or move slowly and merge with the slug bubbles. Figure 11: Distribution of bubble lengths in the horizontal section of a long-distance siphon drain: (**a**) low Ca flow; (**b**) early stationary phase; (**c**) late stationary phase. The main hydrodynamic characteristic behaviors of gas-liquid two-phase flow originate from viscous forces, inertial forces, interfacial forces, and gravity. When the scale range changes, the effects of the different forces become entirely different. While gravity plays a significant role in defining the flow characteristics at conventional sizes, it tends to be negligible at the millimeter/micron scale, and interfacial forces play a more prominent role. Using the Eotvos number, it is possible to set a boundary criterion between these two scales [21,22]. By definition, it can be used to quantify the equilibrium relationship between gravity and interfacial forces. This is the hydrodynamic phenomenon reflected by the Eotvos number as the relevant characteristic number, and the defined equation is shown below. \[E\delta=\frac{g(\rho_{L}-\rho_{G})D^{2}}{\sigma} \tag{4}\]  
where \(g\) is the acceleration of gravity, \(\rho_{L}\) and \(\rho_{G}\) are the liquid density and gas density, respectively, \(D\) is the tube diameter, and \(\sigma\) is the surface tension. Removing the catchment tank before the end of the stop-flow period can compare the ability of different diameter siphons to retain water. The results showed that none of the D-3-5 tubes were affected when one end of the tube was not submerged in water, while water occasionally flowed out of the D-6.5 tube and almost all of the D-8 tube failed to retain water. In siphons with diameters no larger than 5 mm, surface tension plays a significant role due to the wall effect. Surface tension forms a gas-liquid-solid three-phase contact line or a gas-liquid two-phase contact surface through wall adhesion, which generates additional pressure more significant than the effect of gravity and forms a curved moon-shaped gas-liquid interface, where the central axis of the interface is parallel to the axis of the tube or forms a slight angle. In large-diameter siphons, the effect of gravity is dominant, and the liquid squeezes the bubbles in the horizontal tube to float upward and form a closed cavity with the tube wall. Similarly, the vertical section of the siphon tube has gas precipitated in the liquid due to changes in air pressure to form bubbles. The bubble movement in the small-diameter circular tube is mainly dependent on the buoyancy and the wall resistance, and before reaching a critical value to slip, the interaction force between the liquid and solid having exponential growth, which can be analogous to the principle of maximum static friction between adjacent solids. Correspondingly, the buoyancy effect on the middle section of the large-diameter circular tube slug bubble is much more significant than the surface tension and the frictional resistance of the three-phase contact line. Hence, the bubble converges to the highest horizontal section under the effect of buoyancy. Under the combined effect of the above conditions, the bubble length statistics are formed, as shown in Figure 11.