Numerical simulation of creaming and foam formation in aerated liquid with population balance modeling

A new approach for simulating the formation of foam in aerated liquid is proposed. Foam is considered as a separate phase which is comprised of a mixture of air and liquid. A computational fluid dynamic (CFD) model has been developed for the simulation of creaming and formation of foam in aerated liquid using the proposed approach. The model accounts for the formation of foam due to transformation of both air and liquid into foam and it is destruction due to liquid drainage and bursting of bubbles. The coalescence model of Prince and Blanch (1990. Bubble coalescence and break-up in air-sparged bubble columns. AIChE J. 36, 1485–1499.) was considered for air-liquid dispersion whereas for the foam layer, the bubble coalescence due to film rupture was modeled using the model developed by Tong et al. (2011. Drainage and stability of 2D foams: foam behavior in vertical Hele-Shaw cells. Colloid Surf. A 382, 42–49). A population balance method was used to track the number density of different bubble class and the fixed pivot method was used to discretize the population balance equation. The source term for coalescence in the scalar transport equation was updated using a rectified model of Hagesaether et al. (2002. A model for turbulent binary breakup of dispersed fluid particles. Chem. Eng. Sci. 57, 3251–3267). The results obtained are in reasonable agreement with the predictions of Narsimhan (2010. Analysis of creaming and formation of foam layer in aerated liquid. J. Colloid Interface Sci. 345, 566–572.). The discrepancies were mainly attributed to assumption of uniform size bubble in Narsimhan (2010).