QMOM-based population balance model involving a fractal dimension for the flocculation of latex particles

An experimental and computational study of agglomeration and breakage processes for fully destabilized latex particles under turbulent flow conditions in a jar is presented. The particle size distribution (PSD) and the fractal dimension of flocs of latex particles were monitored using an on-line laser diffraction technique. A population balance equation (PBE) was adapted to our problem by including the fractal dimension in its formulation as well as in the aggregation and breakage kernels. The quadrature method of moments was used for the resolution. The adjustment of 4 model parameters was then conducted on the first 6 moments of the PSD for various mean shear rates. The model correctly predicts the evolution of the first 6 moments calculated from the experimental PSD. The experimental results were adequately simulated by a single set of adjusted parameters, proving the relevance of the dependency on the fractal dimension and mean shear rate. A sensitivity analysis was performed on two main adjusted parameters highlighting the major roles of (1) the power to which the mean shear rate is raised in the breakage kernel and (2) the sizes of the colliding aggregates in the collision efficiency model. Finally, analytical relations between the sink and source terms of the breakage or aggregation of the PBE were derived and discussed, highlighting interesting features of the PBE model