A new mathematical model for nucleation of spherical agglomerates by the immersion mechanism

Initial wetting of crystals by binder droplets is a key rate process in spherical agglomeration, however there are no models to predict the kinetics and formation of agglomerate nuclei. Two new mathematical models are introduced for agglomerate nucleation by an immersion mechanism; immersion rate limited model and collision rate limited model. The agglomerate nucleation number developed in this work predicts different regimes; immersion rate limited, collision rate limited and intermediate. In an immersion rate limited regime, agglomerate size increases with square root of time. In a collision rate limited regime, size increases linearly with time if the bulk crystal volume fraction, φPb, is constant, or with an exponential decay rate for batch crystallisation with decreasing φPb. The timescale for nucleation is less than ten minutes for a broad range of conditions, significantly less than most crystallisation timescales. These models have great promise for population balance modelling and spherical agglomeration optimisation.