The non-dimensional form of Equation (13) was produced using dimensional analysis on the given parameter space, which results in a single non-dimensional term equal to proportionality constant (k ). If this is repeated with the addition of viscosity (μL ) into the parameter space, then Equation (14) relates the bubble size (d32 ) with the input power (Pm = gUSG ) and liquid properties (surface tension, liquid viscosity, and liquid density). Equation (14) suggests that the unknown functional formf () needs to be found experimentally from bubble size (d32 ) data. Detailed inspections show that at lower specific input powers the bubble column is still operating in the homogenous regime; consequently, in the absence of shear breakage bubble size cannot be predicted from Equation (13). Figure 9 also shows that the d32 from conditions tested in water increase with increasing gas superficial velocity (specific input power), this is due to homogenous operation regime. The non-dimensional terms in Equation (14) are well established dimensionless terms; the scaled bubble size (left hand side) is the Ohnesorge number (Oh ), which is the ratio of the product of the inertia and surface tension forces to viscous forces. The scaled specific input power, which is related to the shear breakage, is the product of the Morton number\(\left(Mo=\frac{g\mu_{L}^{4}}{\rho_{L}\sigma^{3}}\right)\) and the Capillary number\(\left(Ca=\frac{\mu_{L}U_{\text{SG}}}{\sigma}\right)\); here the scaled Pm term is a combination of viscous, inertia, surface tension, and gravitational forces.