Predicting Colloidal Ink 3D Printing Behavior Using Simple Piecewise Power Law Constitutive Model

Predicting “printability” of colloidal inks for direct ink writing is a difficult task, and often focuses only on final print stability. However, pumpability from reservoir to nozzle is an equally important criteria of printability and often at odds with stability. Furthermore, pumpability often has important ramifications on printer operation space by setting print head speeds and flow rates ranges. In this work, 7 model colloidal inks with low yield stresses were made using amorphous silica ranging in sizes from 100 nm to 1 µm at volume fractions ranging from 0.3 to 0.5. Using a rotational shear rheometer, the viscosity flow curves of these inks were characterized shown to exhibit shear thinning, Newtonian, and shear thickening behaviors over the applied stress range, which were then described using a piece wise power law constitutive model. Using this constitutive mode, a model to predict the flow rate of colloidal inks in a direct ink writing system was developed that incorporates transitions between rheological behaviors across nozzle cross sections. The model predicts the majority of inks’ flow rates in a pressure driven direct ink writing printer under a range of applied pressures and conditions; however, in the application tested, the inks were always driven at pressures over their yield stress and in region with significant shear thickening the model have more significant mismatch with experimental results. In addition, the model is compared to direct ink writing systems in which an auger is used in addition to pressure. In these cases, colloidal inks with significant shear thinning pose a problem for the predictive capabilities of the model.