Coagulation and fragmentation: Universal steady-state particle-size distribution

A population balance model presented describes simultaneous coagulation and fragmentation during shear-induced flocculation. Given sufficient time, a floc-size distribution reaches steady state that reflects the balance between coagulation and fragmentation. The model agrees with experimental data for the evolution of the average floc size. Higher shear shifts the steady-state size distribution to smaller sizes. When the steady-state size distributions obtained at various shear rates are scaled with the average flee size, however, they collapse onto a single line. This indicates that the steady-state floc-size distribution is self-preserving with respect to fluid shear. This distribution is universal for the employed coagulation and fragmentation rates provided that less than 5% (by number) of the particles remain unflocculated. This result is supported with experimental data on shear-induced flocculation of polystyrene particles, although a detailed quantitative comparison is limited by the irregular structure of the flocs.