A multi-dimensional population balance model for agglomeration
In this paper we present a multi dimensional population balance model (PBM) for the agglomeration of fine particles together with a very effective method to obtain a numerical solution to this model. A simple multi-dimensional population balance is proposed that incorporates physical observations of growth of agglomerates as a function of size, surface liquid and deformability. A simple function for the probability that a collision results in coagulation is proposed, categorising particles as small/large, wet/dry and soft/hard according to physical properties such as solid volume, liquid content, porosity and surface area. Depending on the deformability of coagulating particles, we propose conservation rules for the above properties when a coagulation step occurs. In addition, we characterise the aggregates with a fractal dimension, enabling us to relate surface area to solid volume and pore volume, thus reducing the problem to three independent variables. Stochastic simulation, whereby an array of stochastic particles approximates the behaviour of the real particle ensemble, enables preliminary validation of the model using experimental results from agglomeration of fine calcite particles with aqueous polyethylene glycol binder in a 20 litre ploughshare mixer.