  A model for diffusion-controlled spherical particle growth is presented and
solved numerically, showing how, on cooling at sufficient rate from a given
fraction solid, growth velocity first increases, and then decreases rapidly
when solute fields of adjacent particles overlap. An approximate analytical
solution for the spherical particle growth velocity is then developed and shown
to be valid until the solute fields begin to overlap. A particle stability
model is next presented, building on the above analytic solution. This model
permits prediction of the maximum cooling rate at which a semi-solid slurry or
reheated semi-solid billet can be cooled while still retaining the spherical
growth morphology. The model shows that particle stability is favored by high
particle density, high fraction solid and low cooling rate. The predictions of
the stability model are found to be in good quantitative agreement with
experimental data collected for Al-4.5wt%Cu alloy. Engineering applications of
the results obtained are discussed.
