Fractal theory study on morphological dependence of viscosity of semisolidslurries

A theoretical model is developed which enables the effect of particle morph ology on the viscosity of semisolid slurries to be assessed. Hausdroff dime nsionality is introduced as a means of characterising the morphology of a s olid particle. The effective solid volume fraction, defined as the volume f raction of actual solid plus the entrapped liquid, is derived analytically. The viscosity of semisolid slurries is calculated by the adaptation of Tho mas'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 visc osity for a given solid fraction. The external variables, such as shear rat e and cooling rate, affect the flow behaviour of semisolid slurries primari ly by changing the Hausdroff dimensionality and the linear size of solid pa rticles. The effect of particle size on the viscosity is also discussed.