## 3 Results and Discussions
### Flow Regime Mapping for Horizontal Flow
#### 3.1.3 Air/Newtonian Two-phase Flow  
The flow behavior of the air/Newtonian two-phase flow is shown in Figure 9. Figure 10 demonstrates that slug frequency increases with the increase of liquid superficial velocity for all studied combinations, while the superficial gas velocity was held constant for each set of data. Similar behavior was reported by [PERSON] and [PERSON] [22] for a Newtonian fluid (water). This happened due to the increase in liquid volume fraction. The liquid occupies more space in the liquid film region as the elongated bubble unit becomes smaller, which is why the slug unit increased in number. Figure 10 shows the effect of a superficial gas ratio on slug frequency. Results from Figure 10 reveal that, for a constant liquid flow rate, slug frequency decreases with increasing gas velocity. The slug frequency initially decreases with the gas velocity up to around 5 m/s gas velocity, and then increases again, indicating additional slug formation. Moreover, to provide further insight, Figure 11 represents the slug frequency vs. the mixture velocity for air/water flow. Figure 8: Comparison of the [PERSON] & Richardson [10] (adapted) flow regime map with experimental data obtained for horizontal gas/non-Newtonian flow. Copyright Canadian Journal of Chemical Engineering, 2020. Comparing Figures 9 and 11, it is evident that the slug frequency curves mainly depend on superficial gas velocity. Two of these graphs also show that in the range of 5 m/s to 6.5 m/s, the slug frequency reaches a minimum, and the slug frequency increases with increasing mixture velocity or gas superficial velocity. The sudden increase in slug frequency perhaps indicates the transition of the flow regime from slug to dispersed bubble flow. The higher gas flow rates induce more turbulence in the fluid flow, initiating the slug breakdown, which is attributed to the increase in the overall number of slugs in the system. It has also been observed that the number of dispersed bubbles increases in  
Figure 10: Effect of gas superficial velocity on slug frequency of air/water two-phase flow. Figure 9: Effect of liquid superficial velocity on slug frequency for air/water flow. the slug pocket and wet film area. This indicates the beginning of the transition of the flow pattern. These findings also agree with the experimental data of [PERSON] (2018) and [PERSON] (2018). Moreover, the slope of slug frequency vs. slug Froude number is reported in Figure 12.  
In Figure 12, the slope of slug frequency vs. slug Froude number yields an equation of \(f_{s}=0.0673\left( \begin{array}{c}N_{f_{s}}\end{array} \right)^{0.098}\). This equation shows a slight deviation from [PERSON] (2018), which is shown in Equation (5), perhaps due to the experimental conditions and the assumption (\(v_{m}=v_{s}\)) for the air-water flow of this experiment. To evaluate the standard deviation and experimental accuracy of this study, Figure 13 reports the regression analysis of slug frequency and Froude number. Figure 11: Slug frequency vs. mixture velocity for air/water flow. Figure 12: Slug frequency vs. Froude number for air/water flow. From Figure 13, the R\({}^{2}\) value was found to be 88.1%, which indicates that the slug frequency and Froude number have a good relationship. Since the experimental and modeled data are close to the regression line, the equation \(f_{s}=0.0673\left( \begin{array}{c}N_{f_{s}}\\ \end{array} \right)^{0.098}\) can explain the variability of the data around its mean. In order to further validate and test the reliability of the obtained experimental data, the results are reported with correlations with different model results reported in various previous studies. Figure 14 shows the experimental and modeled validation with the [PERSON] & Scott [41] correlation model for air-water two-phase flow. Figure 14: Experimental slug frequency for the air–water system compared with the prediction model of [PERSON] & Scott [41] correlation (R\({}^{2}\) = 73.8%).