A binomial distribution function suitable for geometric grid was proposed and applied in population balance model (PBM) to simulate the particle size distribution (PSD) of activated sludge after flocculation. The results showed that the PSD and mean size simulated by using binomial distribution give better agreement with the experimental data than those simulated by using binary distribution. The accuracy of simulation of PSD and mean size can be improved by calibrating the value of parameter Cp of binomial distribution function. Different from other daughter particle distribution which can only describe one-type daughter particle distribution

the binomial distribution function shows a strong adaptability and can present more probable daughter particle distributions through adjusting the parameter Cp. Moreover

the value of parameter Cp might also characterize breakage behavior of particle:a smaller Cp value might imply that the particle display strong stability leading to large numbers of large daughter particle

whereas a larger Cp value might imply that the particle display weak stability and the large-scale fragmentation resulting in large numbers of small daughter particle.