Modeling micro-droplet formation in near-field electrohydrodynamic jet printing

Near-field electrohydrodynamic jet (E-jet) printing has recently gained significant interest within the manufacturing research community because of its ability to produce micro/sub-micron-scale droplets using a wide variety of inks and substrates. However, the process currently operates in open-loop and as a result suffers from unpredictable printing quality. The use of physics-based, control-oriented process models is expected to enable closed-loop control of this printing technique. The objective of this research is to perform a fundamental study of the substrate-side droplet shape-evolution in near-field E-jet printing and to develop a physics-based model of the same that links input parameters such as voltage magnitude and ink properties to the height and diameter of the printed droplet. In order to achieve this objective, a synchronized high-speed imaging and substrate-side current-detection system was used implemented to enable a correlation between the droplet shape parameters and the measured current signal. The experimental data reveals characteristic process signatures and droplet spreading regimes. The results of these studies are then used as the basis for a model that predicts the droplet diameter and height using the measured current signal as the input. A unique scaling factor based on the measured current signal is used in this model instead of relying on empirical scaling laws found in literature. For each of the three inks tested in this study, the average absolute error in the model predictions is under 4.6% for diameter predictions and under 10.6% for height predictions of the steady-state droplet. While printing under non-conducive ambient conditions of low humidity and high temperatures, the use of the environmental correction factor in the model is seen to result in average absolute errors of 10.35% and 12.5% for diameter and height predictions.