Simulation of buble coalescence in bubble column using the least-squares method

The population balance equation (PBE) has been combined with a steady-state gas phase momentum equation to model the operation of an air-water bubble column. Instead of solving a bubble number density constitutive equation, a population balance equation with coalescence term has been solved. The system of equations has been linearized by successive iteration and solved by the least-squares method with high accuracy and fast convergence. The bubble size distribution along the column axis has been investigated and compared to the corresponding experimental data, showing good agreement.