Figure 5 . Probability density function of bubble size at different liquid viscosities andUSG =27.6 mm/s.
Transport coefficients determine the performance and efficiency of a bubble column and are sensitive to the bubble size and void fraction. Bubble size and void fraction are heavily depended on the operation regime, which sets the dominant fluidic mechanisms within a gas-liquid system. The rest of this paper is structured as such to study the bubble size and void fraction with respect to the operation regimes i.e., homogenous and heterogeneous.

3.2 Homogeneous regime

In this section bubble size and void fraction were studied in the homogenous operation regime, which features a linear trend between the void fraction and the gas superficial velocity as well as a direct correlation between bubble size and gas superficial velocity. Homogeneous bubbly flow is characterized by the absence of breakage and coalescence and a Gaussian BSD; therefore, any attempt to scale the bubble size should include the pore size (rp ) and the gas superficial velocity (USG ) in the parameter space. The present work also includes the liquid properties (i.e. surface tension σ , liquid viscosityμL , and liquid densityρL ), and gravity (g ) to scale the bubble size in the homogenous regime. Using dimensional analysis, the scaled bubble size was expected to be dependent on the Froude number (Fr ), Weber number (We ), and Reynolds number (Re ); see Equations (5)-(7).
Figure 6 validates the correlation for predicting bubble size (d32 ) in homogeneous regime (see Equation 8) against experimental bubble size data. Results show that in the homogenous regime the proposed correlation predicts the bubble size. In Equation (8) the power exponents were found following the recommendation from Kazakis et al.,40 which argues that the sparger material effects correlations of this type due to the sensitivity of bubble size to pore dimensions in homogeneous bubbly flow. The power law functional form between the aforementioned non-dimensional terms (see Equations 5-7) was first suggested by Akita and Yoshida;24 in addition, in Equations (5)-(7) the exponents were obtained empirically.40