# 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
This is because under the action of pressure (\(F_{dr}\)), the aqueous maltose solution should flow down along the wall, but at this time, due to \(\beta\) being small and the viscous force (\(f_{d}\)) being large, the viscous force (\(f_{d}\)) and axial inertia force (\(F_{df}\)) are dominant during the movement of the front end of the aqueous maltose solution, which forces the maltose aqueous solution to move away from the wall. The \(F_{dr}\) of the rear section of the aqueous maltose solution overcomes the \(f_{d}\) and \(F_{df}\), so it will make the rear section of the aqueous maltose solution flow downward along the wall, as demonstrated in Figure 6a for B2 and C2. As the \(\theta\) becomes larger, the \(F_{df}\) will slowly become smaller, and the \(F_{dr}\) will slowly become larger, meaning the larger the effect from \(F_{dr}\), the smaller the fraction of the aqueous maltose solution that moves away from the wall; when comparing Figure 6a B1 and C1, we can observe this. When the part that starts to produce movement away from the wall reaches the bottom of the pipe, the subsequent aqueous maltose solution will all flow down the wall under the action of \(F_{dr}\). When \(\theta>45^{\circ}\), the effect of \(F_{dr}\) is so great that no aqueous maltose solution flowing away from the wall will be produced, which is illustrated in Figure 6a (D1). Figure 6b,c show the variation with time in the aqueous maltose solution at different tilt angles (\(\theta\)) for \(\beta\) = 82.67 and 238.66, respectively. This is in the medium-viscosity ratio range. We observe that when \(\theta\) = 0\({}^{\circ}\), the aqueous maltose solutions at the two viscosity ratios will continuously produce separated aqueous maltose solutions, as shown in Figure 6b for A3, A4, and A5, and Figure 6c for A6, A7, and A8; this is because, at this time, the viscosity of the water is not affected by the water. Figure 6: Variation in heavy fluid flow regimes in the range of three viscosity ratios (\(\beta\)), with the yellow fluid being an aqueous solution of falling maltose. (**a**) Variation in the heavy fluid flow regimes with time at different tilt angles (\(\theta\)) when \(\beta\) = 5.46; this viscosity ratio is in the low viscosity ratio range; the blue fluid is an aqueous 80 wt% glycerol-syrup solution; A1 and A2 are the heavy fluid flow regimes at \(\theta\) = 0\({}^{\circ}\), t = 20 s, and t = 30 s, respectively; B1 and B2 are the heavy fluid flow regimes in the first and second half of the \(\theta\) = 15\({}^{\circ}\), t = 20 s, respectively; C1 and C2 are the heavy fluid flow regimes in the first and second half of the \(\theta\) = 30\({}^{\circ}\), t = 20 s, respectively; D1 is the heavy fluid flow regime at \(\theta\) = 45\({}^{\circ}\), t = 20 s. (**b**,**c**) are the changes in the heavy fluid flow regimes with time for different inclination angles (\(\theta\)) in the range of medium viscosity ratios (\(\beta\)); the blue fluid is Dil.syrup. (**b**) \(\beta\) = 82.67. A3, A4, and A5 are heavy fluid flow states at \(\theta\) = 0\({}^{\circ}\), t = 2 s, 7 s, and 13 s, respectively, and B3, C3, D2, and E1 are heavy fluid flow states at \(\theta\) = 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), t = 2 s, respectively. (**c**) \(\beta\) = 238.66. A6, A7, and A8 are heavy fluid flow regimes at \(\theta\) = 0\({}^{\circ}\), t = 2 s, 7 s, and 10 s, respectively, and B4, C4, D3, and E2 are heavy fluid flow regimes at \(\theta\) = 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), t = 2 s, respectively. (**d**) Variation in heavy fluid flow state with time at different tilt angles when \(\beta\) = 467.77, the blue fluid is v.dil.syrup. the light fluid is small, and the viscous force (\(f_{d}\)) on the aqueous maltose solution is small. At this point, the axial inertia force (\(F_{df}\)) is greater than the sum of the viscous force (\(F_{dr}\)) and the viscous force of the aqueous maltose solution itself. Thus, a separated maltose aqueous solution is produced.