Investigation of Discrete Population Balance Models and Breakage Kernels for Dilute Emulsification Systems

A novel in situ video probe with automated image analysis was used to develop a population balance model for a breakage-dominated liquid–liquid emulsification system. Experiments were performed in a 2 L tank, agitated by an axial flow propeller. The dispersed phase (ethylene glycol distearate) concentration was varied from 0.2 to 1.0% (w/w), and agitation rates were varied from 0.2 to 0.5 W/kg, in the presence of excess surfactant. Three numerical discretization methods were compared: fixed pivot, cell average, and finite volumes. The latter was then chosen for the subsequent simulations due to its rapidity and higher precision. An investigation of the different theories for bubble/droplet breakage was done and the frequencies (or breakage rate kernels) were compared. Four models were found applicable: the models developed by Coulaloglou and Tavlarides (Coulaloglou, C. A.; Tavlarides, L. L. Chem. Eng. Sci. 1977, 32, 1289); Sathyagal and Ramkrishna (Sathyagal, A. N.; Ramkrishna, D. Chem. Eng. Sci. 1996, 51, 1377); Alopaeus, Koskinen, and Keskinen (Alopaeus, V.; Koskinen, J.; Keskinen, K. I. Chem. Eng. Sci. 1999, 54, 5887); and Baldyga and Podgorska (Baldyga, J.; Podgorska, W. Can. J. Chem. Eng. 1998, 76, 456). The one by Sathygal and Ramkrishna included the daughter size distribution. A log-normal daughter size distribution was chosen for the models by Coulaloglou and Tavlarides and Alopeus et al. Also, a normal distribution was used in the model by Baldyga and Podgorska. These models were compared with the experimental data to allow parameter identification. The model by Baldyga and Podgorska was found to give the best prediction of the shape of the distribution, its mean diameter, and standard deviation.