A Fractal Rheological Model for SiC Paste using a Fractal Derivative

The rheological property plays an important role in a free-form extrusion 3D printing process, no rheological model was available in open literature that could effectively take into account effects of both the non-Newtonian viscosity and the concentration of nano/micro particles in a paste. Here a fractal law for non-Newtonian fluids is suggested using a fractal derivative, the law can predict correctly the boundary effect of a viscous flow, and can model effectively the nonlinear velocity distribution across the section. A systematic derivation of a fractal rheological model is suggested using the basic laws in the fluid mechanics, which can provide a deep insight into the two-scale fractal interpretation of non-Newtonian fluids. An experiment was carefully designed to verify the model and to elucidate the relationship between the shear rate and viscosity of the SiC paste. 15wt.%, 25wt.%, 35wt.% and 45wt.% SiC pastes were prepared by using mixing, stirring and ball milling processes. The rheology of the paste can be controlled primarily through the SiC concentration, which affects the fractal order. The fractal model sheds a bright light on a simple but accurate approach to non-Newtonian fluids.