Figure 10 . Scaled bubble size versus scaled specific input power using results from the literature in addition to the current study.
In the rest of this section void fraction measurements and scaling in heterogeneous regime are discussed. The same parameter space for producing Equation (11) was employed for scaling the void fraction and finding the function form of G() . Here, it was assumed that the bubbles are traveling at terminal velocity (see Figure 11); therefore, the drag force (FD \(\propto\)ρLd322Ub2 ) was balanced with buoyancy force (FB = ρLgd323 ). This assumption establishes a relationship between bubble size and bubble velocity (Ub2 ~ gd323 ). It is known that the void fraction is the ratio of gas superficial velocity to the bubble velocity (ε = USG/Ub ); therefore, the void fraction is proportional to bubble Froude number (Fr = USG/[gd32]0.5 ). Assuming that void fraction scales as a power law function of Froude number (Equation 5), Archimedes number (Equation 9), and Eötvös number (Equation 10), then Equation (17) gives the general form of G() . The exponents in Equation (17) (i.e. Χ , Ψ , and Ω ) were calculated from Equation (18) (Χ= 1.117, Ψ= 0.1, andΩ= -0.032). Figure 12 shows that the proposed coordinates (see Equation 19) were able to successfully scale the void fraction within the heterogeneous regime. Equation (19) successfully predicts the void fraction within ±25% accuracy for the current data.