# 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
Figure 4: A collection of experiments at different viscosity ratios (\(\beta\)) for different inclination angles (\(\theta\)), with the yellow fluid being the descending heavy fluid and the blue fluid being the ascending light fluid; the angle value marked in red is the critical angle at which the transitional flow regime changes to a side-by-side flow, with the viscosity ratios (\(\beta\)) of (**a**) \(\beta\) = 5.46; (**b**) \(\beta\) = 9.3; (**c**) \(\beta\) = 82.67; (**d**) \(\beta\) = 238.66; (**e**) \(\beta\) = 467.77. The enlarged plots in (**a–d**) show the flow of light fluid at \(\theta\) = 5\({}^{\circ}\) for the corresponding viscosity ratio for light fluid flow; the enlarged view in (**e**) shows the flow pattern of light fluid flow at \(\theta\) = 5\({}^{\circ}\) at its viscosity ratio and the flow pattern of the first half and the second half of the light fluid at \(\theta\) = 15\({}^{\circ}\). Figure 5: (**a**) Phase diagrams of flow classification at different inclination angles for each logarithm of viscosity ratio; CAF stands for axisymmetric core-annular flow, ECAF stands for eccentric core-annular flow, TSBS stands for transition side-by-side flow, and SBS stands for side-by-side flow; the reddish transparent region indicates that the flow pattern in this region is CAF, and the greenish transparent region indicates that the flow pattern in this region is TSBS. (**b**) The variation in the ratio of the light fluid width to the pipe width (\(\delta_{a}\)) with the \(\theta\) for different \(\beta\). The small figure in the figure illustrates a partially enlarged view of the yellow portion. The yellow part is the change rule of the  
3.1.2. Changes in the Flow Regime of Aqueous Maltose Solution (Heavy Fluids)  
We then investigated the changes in the flow pattern of the aqueous maltose solution, and for ease of observation, the pictures we show here are of the lower half of the pipe. The change in the viscosity ratio is mainly achieved by changing the magnitude of the inertial and viscous forces on the two fluids in the pipe to change the flow pattern. Based on our previous simulation results and the experimental results of [PERSON] et al. [1], we can classify the viscosity ratio range into three categories: The first category is for viscosity ratios less than 10 (\(\beta<\) 10), and we refer to this range as the low viscosity ratio range. Heavy fluids in this viscosity ratio range descend from the centre of the pipe in vertical pipes. The second category is viscosity ratios greater than 10 and less than 300 (10 \(<\beta<\) 300), and we refer to this range as the medium viscosity ratio range; heavy fluids in this viscosity ratio range separate during descent. The third category comprises viscosity ratios greater than 300 (\(\beta>\) 300); we refer to this range as the high viscosity range. Heavy fluids in this viscosity ratio range fall along the pipe wall. In our experiments, we found that the results for viscosity ratios of 5.46 and 9.3 are consistent. Because of this, here, we only show the experimental results for a viscosity ratio of 5.46. Figure 6a demonstrates the variation with time of the flow regime of aqueous maltose solution at different inclination angles (\(\theta\)) for \(\beta=\) 5.46. This is in the low-viscosity ratio range. We observe that when the \(\theta=0^{\circ}\), the aqueous maltose solution at this viscosity ratios will keep descending along the centre of the pipe, as shown in Figure 6a for A1 and A2. When \(0^{\circ}<\theta<45^{\circ}\), we can observe that the front section of the aqueous maltose solution has a very obvious flow away from the wall, as demonstrated in Figure 6a for B1 and C1.