Predicting Extensional Behaviors of Colloidal Dispersions through Piecewise Power Law Models

Colloidal dispersions have great potential to be used as an ink for Direct ink writing 3D printing due to the ability to tune biological, mechanical, electrical, or optical properties via colloid selection, giving them a wide range of potential applications. However, such dispersions often have complicated rheological behaviors, and tuning one into a printable ink is a difficult process requiring balancing pumpability, extrudability, stability, and end use functionality. In this work, ink extrudability is characterized using the dripping on substrate method and compared to predictions derived from a piecewise power law model.

Silica particles of three different diameters (100 nm, 500 nm, 1 μm) are dispersed in Polyethylene Glycol (PEG) at high volume fractions to create model non-Newtonian inks. A rotational rheometer is used to measure viscosity as a function of shear stress, and then a piecewise power law model is fitted to thinning, thickening, and plateau regimes. During extension, filament diameters thin like power law fluids. However, experimental threads thin faster and with power law exponents different than those predicted by the shear based piecewise power law model. Although this model predicted flowrates effectively, disagreement in extension can be understood through examination of the Deborah number, which correlates particle residence time to thread lifetime.