# Effects of Tube Radius and Surface Tension on Capillary Rise Dynamics of Water/Butanol Mixtures
## 3 Results and Discussion
### Effect of Surface Tension of the Fluids on Capillary Rise Dynamics  
Experiments were performed in a single capillary tube (\(r\) = 0.4 mm) at room temperature (23 \(\pm\) 1 \({}^{\circ}\)C) to evaluate the effect of liquid surface tension on the capillary rise dynamics. Based on the measurement method shown in Figure 2, the \(\sigma\) values of the test materials for B0% (DW), B0.3%, B0.5%, and B0.7% were approximately 72, 64, 60, and 56 mN/m, respectively. The values of \(\sigma\) were consistent with the measurement results obtained from the pendant drop method [41; 42] with SmartDrop (SmartDrop Plus HS, Femtobioned Inc., Gyeonggi-do, South Korea). The measurement \(\sigma\) values for B0% (DW), B0.3%, B0.5%, and B0.7% in the pendent drop method were 72.32 \(\pm\) 0.42, 64.25 \(\pm\) 0.73, 60.02 \(\pm\) 0.67, and 56.19 \(\pm\) 0.57 mN/m, respectively. The addition of n-butanol in a low concentration causes a considerable decrease in the interfacial tension of water/butanol mixtures. This phenomenon stems from the property of pure n-butanol that has a relatively low surface tension (24 mN/m) compared to DW (72 mN/m). For this reason, the surface tension of the butanol-added solutions sharply decreases with increasing butanol concentration until it reaches a critical concentration, after which the surface tension decreases monotonically. The critical mass concentrations of alcohol/water solutions with butanol, pentanol, and hexanol were 3%, 0.5% and 0.3%, respectively [43]. In general, the \(\sigma\) of n-butanol/water mixtures as well as other alcohol/water mixtures depend on their corresponding temperature and composition, and even at low n-butanol concentrations of 0 to 1 wt%, the \(\sigma\) value varies [43; 44]. Figure 8 shows the capillary rise dynamics for four different concentrations of n-butanol/water mixtures with different values of \(\sigma\). Generally, as shown in Figure 8, all measurements show that the height of rise increases with time; however, the velocity of rise at which the meniscus moves through the capillary decreases over time, as shown in Figure 8b. In addition, the height of rise decreased with an increase in the concentration of n-butanol. In particular, \(h_{\text{e}}\) was 35.9, 32.1, 28.7, and 26.6 mm at B0%, B0.3%, B0.5%, and B0.7%, respectively. The viscosity, which depends on the concentration of blends, can be one of the parameters that plays an important role in capillary dynamic parameter because the viscosity can be changed due to the blends during the rising period. To calculate the equilibrium capillary rise height (\(h_{\text{e}}\)) that is considered as steady state characteristics of blends, Equation (3), using the surface tension of the blends and well-established and widely used by the balance of gravity and capillarity, was used [45]. As shown in Figure 8b, the higher the \(\sigma\) of the mixtures, the lower is the maximum instantaneous rise velocity. At B0%, B0.3%, B0.5%, and B0.7%, the peak velocity values were 0.45, 0.41, 0.34, and 0.3 m/s, respectively. The peak velocity when comparing \(\sigma\) values was observed at the same position on time basis (0.005 s), as shown in Figure 8b, unlike the peak values observed at different positions when comparing the capillary radii shown in Figure 7b. In Figure 8b, the peak value decreases systematically with \(\sigma\) because there is no oscillation phenomenon, as shown in Figure 4.  
Table 2 shows the lengths of characteristic stages (as defined in Figure 5) of n-butanol/water mixtures at \(r=0.4\) mm. In each of Stage I, II, and III length, the overall trend was dependent upon the increase in n-butanol blending ratios. The length increases with the increase of n-butanol ratio in Stage II, whereas there was no similar trend observed in Stages I and III, for the same condition. In the comparison between Tables 1 and 2, the characteristic \(h\) in lengths of Stages I, II, III shows a clear trend with increasing \(r\) and \(\sigma\).