## 3 Results
### Comparison of Various Modified Chisholm Parameters
They argued that the modified parameter is given by  
\[C=f(\beta,\psi,Re_{\rm LO})=A\beta^{q}\psi^{r}Re_{\rm LO}^{s} \tag{16}\]  
\[\beta=\frac{\mu_{\rm L}^{2}}{\rho_{\rm L}\sigma D_{\rm h}} \tag{17}\]  
\[\psi=\frac{\mu_{\rm L}j}{\sigma} \tag{18}\]  
where dimensionless parameters \(\beta\) and \(\psi\) are the effects of the surface tension \(\sigma\) (N\(\cdot\)m\({}^{-1}\)), the viscosity \(\mu\) and the velocity of the liquid slug \(j\) (m\(\cdot\)s\({}^{-1}\)), and constant \(A\) and exponents \(q\), \(r\), and \(s\) are determined by the flow regimes. Here, there are given numbers for exponents \(q\) and \(r\) in the laminar (liquid)-laminar (gas or vapor) regime (vv). On the other hand, in other flow regimes, the surface tension becomes insignificant, so exponents \(q\) and \(r\) are zero. Thus, Equation (16) is merely a function of the all-liquid Reynolds number, \(Re_{\rm LO}\). A comparison of this parameter was reported with the measurements within an error of \(\pm 10\%\). [PERSON] et al. (2010) [15] used an advanced information processing technique, which can be utilized to carry out the input \"trial and error\" analysis to select non-dimensional numbers that could well correlate with the two-phase frictional multiplier. When the hydraulic diameter of the channel and the Weber number We are inputted, the information processing techniques can significantly improve the prediction of the two-phase frictional multiplier. Therefore, [PERSON] and Hibiki's correlation (Equation (15)) was modified using the non-dimensional Laplace constant. The non-dimensional Laplace constant Lo* is defined as  
\[Lo^{*}\equiv\left[\frac{\sigma}{g(\rho_{t}-\rho_{\rm g})}\right]^{0.5}/D_{\rm h} \tag{19}\]where g (m\(\cdot\)s\({}^{-2}\)) is gravity force. Consequently, [PERSON] and Hibiki's correlation was modified as shown below:  
\[C=f(Lo^{*})=21[1-exp(-0.358/Lo^{*})] \tag{20}\]  
This correlation is applicable for \(Re_{\rm L}\leqq 2000\), \(Re_{\rm G}\leqq 2000\), and \(0.014\leqq D_{\rm h}\leqq 6.25\) mm. The comparison of this parameter with seven items of reference data of the liquid-gas flow yielded 17.9%, while that with three items of reference data of liquid-vapor flow yielded 21.7%. For liquid-gas two-phase flow, it was recommended that Equation (20) may work better if the constant of \(-0.358\) is replaced with \(-0.674\), while for liquid-vapor flow, the constant of \(-0.142\) would work better. For adiabatic liquid-gas two-phase flow:  
Figure 16:0  
For adiabatic liquid-vapor two-phase flow:  
Figure 16:1  
[PERSON] and [PERSON] (2010) [16] collected the adiabatic two-phase pressure drop data in small channels from the literature. The collected database contains 12 different working fluids and a hydraulic diameter range of 0.148 to 3.25 mm. They noted that the Bond number Bo [-] and Reynolds number Re may have the potential to relate into a general correlation, because there are four forces related to two-phase flow in channels: gravitational, inertia, viscous, and surface tension forces. The Bond number and Reynolds number include these forces. The Bond number Bo is defined as  
Figure 16:2  
where the Bond number has the same meaning in the equation as in the non-dimensional Laplace constant \(Lo^{*}\) equation (Equation (19)), with the difference of the exponent. The relationship between [PERSON]'s parameter and the Bond number or liquid-phase Reynolds number \(Re_{\rm L}\) was investigated. [PERSON]'s parameter has a positive linear relationship with the Bond number when \(Bo\leqq 1.5\):  
Figure 16:3  
On the other hand, when 1.5 < \(Bo\leqq 11\), [PERSON]'s parameter depends on  
Figure 16:4  
It was reported that when \(Bo\leqq 1.5\), Equation (24) could predict 80.6% of the data within \(\pm 30\)%, and when 1.5 < \(Bo\leqq 11\), Equation (25) could predict 72.6% of the data within \(\pm 30\)%.