A Model of Liquid-Drop Spreading for Electrohydrodynamic Jet Printing

Electrohydrodynamic jet (E-jet) printing is a recent technique for high resolution additive micromanufacturing. With high resolution comes sensitivity to small disturbances, which has kept this technique from reaching its industrial potential. Closed loop control of E-jet printing can overcome these disturbances, but it requires an improved understanding of ink droplet spreading on the substrate and a physical model to predict printed feature locations and geometries from process inputs and disturbances. This manuscript examines a model of ink droplet spreading that uses assumptions that are important to the e-jet process. Our model leverages previous energy balance models that were derived for larger length scale droplets. At the smaller length scale, we find that viscous losses are a significant portion of the energy budget and must be accounted for; this is in contrast to models at length scales two orders of magnitude larger. Our model predicts the droplet height, base radius and contact angle in time from an initial volume and E-jet printing control parameters. The model is validated with published droplet spreading data and new measurements of E-jet printed droplets of diameter 8 μm. The viscous friction calculated in the new model is found to be significant compared to surface energy.