A model-based prediction of droplet shape evolution during additive manufacturing of aligned fiber-reinforced soft composites

The objective of this paper is to develop a mathematical model capable of predicting the temporal shape evolution of a droplet during the additive manufacturing of aligned fiber-reinforced soft composites. Given the ellipsoidal shape of the droplets encountered during the additive manufacturing process, the three time-dependent output parameters of interest include the height of the droplet (H), and its two relevant diameters D// and D⊥ that are measured in the directions parallel and perpendicular to the fiber axis, respectively. The model calculations start with a substrate parametrization step involving a characterization of the diameter of the fibers, fiber bundles and fiber spacing encountered in the printing zone. This coupled with the knowledge of the inkjet printing parameters and the fluid properties of the ink allow for the subsequent calculations. The droplet shape is parametrized as an ellipsoidal cap. For every discrete time-step calculation, the model uses the equations of energy and volume conservation as well as an experimentally calibrated relation for the ratio D//H. The model also involves a free energy barrier calculation at every time increment that checks for the pinning of the D⊥ diameter. The validation experiments involved single droplet impingement studies using three inks under distinctly different inkjet printing conditions and substrates profiles. In general, the model prediction errors are observed to be under 7%. The free energy barrier calculation is a critical component of the model. In some cases, it contributes to a >50% reduction in the model prediction errors.