# Exchange Flows in Inclined Pipes with Different Viscosity Ratios
## 3 Results and Discussion
### Exchange Flow Experiments in Pipes
#### 3.1.1 Changes in the Flow Regime of Light Fluids  
Subsequently, We investigate the effect of viscosity ratio (\(\beta\)) on fluid flow in an inclined pipe. Here, we collectively refer to fluids that flow upward as light fluids. The inclination of the pipe mainly affects the fluid flow by changing the inertia force of the fluid, as well as the shape of the fluid flow. In a vertical pipe, the rising flow is basically in the centre of the pipe, as shown in Figure 2, and we refer to this flow pattern as the axisymmetric core-annular flow (CAF). When the pipe is tilted, the flow pattern of the light fluid changes. In the following, we categorize the flow patterns according to whether they flow away from the wall or not, and we judge whether the fluid flows away from the wall on two bases: first, whether we can observe the existence of a continuous flow of maltose aqueous solution between the light fluid and the wall, and second, whether the front end of the light fluid forms a complete finger-like flow pattern, whereas the flow against the wall will only form a half-finger-like flow pattern. Figure 4a-e show the experimental images of flow regimes at different tilt angles (\(\theta\)) for a \(\beta\) of 5.46, 9.3, 82.67, 238.66, and 467.77, respectively. As this increases, we observe three flow regimes for the light fluid at all these \(\beta\). The first flow regime is that the light fluid flows away from the centre of the pipe but not along the wall, which we refer to as eccentric core-annular flow (ECAF), and we can observe this flow regime in Figure 4a-e at \(\theta\) = 5\({}^{\circ}\). The second flow regime is where the front end of the light fluid flows away from the wall while the back half of the fluid flows against the wall, and we refer to this flow regime as transitional side-by-side flow (TSBS), which we observe in Figure 4e with \(\theta\) = 15\({}^{\circ}\) and in Figure A1 in the Appendix A. The third flow regime is a light fluid that flows completely against the wall, which we refer to as a side-by-side flow (SBS), and we can observe this flow regime in Figure 4a-e at the angles after the red angle. Figure 5a shows the results of all experiments on the flow regime. In the phase diagram of Figure 5a, we summarize the light fluid flow regimes at different viscosity ratios (\(\beta\)) for different inclinations (\(\theta\)) so that we can divide the light fluid flow regime changes into  
Figure 3: Forces on the fluid in the inclined pipe; the blue solution is the light fluid, and the yellow solution is the medium fluid. (**a**) Force on light fluid; (**b**) force on aqueous maltose solution. four regions during the inclination of the pipe. The light fluid on the black dotted line in Figure 5a is CAF; because the pipe is vertical at this time, the direction of the force on the light fluid is parallel to the flow direction, and the direction of the light fluid flow will not be shifted, so the light fluid flows upward in the centre of the pipe. The light fluid in the light-red transparent region of Figure 5a is ECAF; because the \(\theta\) is small in this region, the direction is mainly dominated by \(F_{af}\), but due to the tilt of the pipeline, it will also produce \(F_{ar}\); at this time, the \(F_{ar}\), although small, will also change the direction of the light fluid flow with \(f_{a}\), resulting in light fluid in the upward flow of tilt in the process. In Figure 5a, the light-green transparent area of the light fluid flow state is TSBS.