Figure 7 . Void fraction measurement in water and different aqueous solutions of glycerin (G1 and G3).
A parameter space was identified via careful inspection of the experimental setup to formulate a correlation to predict the void fraction using dimensional analysis. It was concluded that the parameter space should be comprised of liquid properties (i.e. surface tension, viscosity, and density), external body force (i.e. gravity), bubble size (d32 ), and the gas flow rate (i.e. gas superficial velocity). The effect of gas superficial velocity, gravity, and liquid properties were accounted for using Froude number (Equation 5), Archimedes number (Equation 9), and Eötvös number (Equation 10) for scaling the void fraction. Equation (11) shows the resulting correlation for scaling the void fraction, where G ( ) is an unknown function. Following Akita and Yoshida,24 Mouza et al.,39Kazakis et al.,40 and Anastasiou et al.,50 a power law functional form was considered for the unknown function G . Figure 8 validates the correlation for predicting the void fraction (ε ) in homogeneous regime against experimental data showing that Equation (12) successfully predicts the void fraction within ±5% accuracy of the current measurements.