Particulate granulation and rheology: towards a unifying perspective
Hodgson, Daniel James Matthew
The mixing of powders and liquids is a process ubiquitous to many industrial, research and household applications, from the production of foodstuffs, pharmaceutical and cosmetic products to the preparation of hot drinks or cement. The final mixed state of powders and liquids can be broadly split into two distinct regimes identified respectively as having low- and high volume fraction, ∅. Low-∅ systems are typified by flowing suspensions whereas samples prepared with high-∅, beyond some threshold value, produce solid agglomerates which are unable to flow. These two regimes are the focus of two separate scientific disciplines; suspension rheology and granulation. Within the field of suspension rheology there has been recent advances in the understanding of a phenomena known as shear thickening, which describes the increase in a suspension's viscosity with increasing applied stress. In this thesis we aim to unify the phenomena of shear thickening and granulation within this new theoretical framework. We study shear thickening and granulation using a well characterised model system developed for this purpose, comprising polydisperse glass particles with a mean diameter of ≃ 7 μm and a glycerol-water mixture (90:10 %vol). We measured the rheological behaviour as a function of applied stress, σ, of suspensions at various volume fractions. We observed shear thickening behaviour, with divergences in the low-stress viscosity, η1(∅), and the high-stress viscosity, η2(∅), at ∅RCP = 0:662 and ∅m = 0:572 respectively. These divergences mark the transition between continuous shear thickening, discontinuous shear thickening and a state in which flow is not possible, with increasing volume fraction. Using a recently developed theory of shear thickening (Wyart and Cates, 2014), we were able to fit our rheological data quantitatively. The WC theory predicts a stress-dependent crossover in the fraction of contacts which are frictional in nature, following a stretched exponential function. In order to improve numerical agreement between our data and the model, we developed a method taking into account the volume-weighted contribution of particle sizes in our polydisperse system. Bulk mixing of the same model system in a custom-built high-shear mixer also exhibited three different mixing regimes with the change in behaviour coinciding with the location of the viscosity divergences, ∅m and ∅RCP, measured in the rheology experiments. For ∅ < ∅m suspensions are formed at both high and low stress; for ∅ ≥ ∅RCP granules are formed at all stresses; for ∅m ≤ ∅ < ∅RCP transient granules are formed, which are solid at high stresses, but can relax to a flowing suspension state at low stress. This transient behaviour is reversible with the application of high stress. This coincidence of viscosity divergence in the rheology measurements and mixing behaviour change in the high-shear mixing strongly suggests that the two phenomena are related. Thus we used the stress-dependent jamming volume fraction, ∅J(σ), predicted by the WC theory, to define the transition between the formation of suspensions and granules. We were able to calculate a quantitative phase diagram, with which the regions of the ∅-σ phase space in which granules or suspensions are formed can be easily identified, in agreement with our high-shear mixer data. Thus, using small-scale rheological measurements, requiring relatively small volumes of sample, we are able to define the parameter space in which granules can be prepared, thus eliminating the need for trial and error granulation experiments in order to define this space. We measured the volume-weighted mean granule size as a function of ∅ in the range ∅m → ∅ ≃ 0:85. Based on our observations of granule structure and measurements of granule size distributions, we modelled the granules as an ensemble of core-shell agglomerates with a log-normal size distribution. The packing in the granule cores was assumed to be ∅J(σ ), i.e. ∅m at high stress and ∅RCP at low stress. Appealing to conservation of mass arguments, our model predicts that the mean granule size decreases with increasing volume fraction and stress, in quantitative agreement with experimental data.