Fractal theory study on morphological dependence of viscosity of semisolid slurries

A theoretical model is developed which enables the effect of particle morphology on the viscosity of semisolid slurries to be assessed. Hausdroff dimensionality is introduced as a means of characterising the morphology of a solid particle. The effective solid volume fraction, defined as the volume fraction of actual solid plus the entrapped liquid, is derived analytically. The viscosity of semisolid slurries is calculated by the adaptation of Thomas's empirical approximation. The viscosity of a semisolid slurry is found to be a non-linear function of the Hausdroff dimensionality. Slurries with particle morphologies of lower Hausdroff dimensionality have a higher viscosity for a given solid fraction. The external variables, such as shear rate and cooling rate, affect the flow behaviour of semisolid slurries primarily by changing the Hausdroff dimensionality and the linear size of solid particles. The effect of particle size on the viscosity is also discussed.