A Dynamical Model of Drop Spreading in Electrohydrodynamic Jet Printing

Electrohydrodynamic jet (e-jet) printing is a microscale additive manufacturing technique used to print microscale constructs, including next-generation biological and optical sensors. Despite the many advantages to e-jet over competing microscale additive manufacturing techniques, there do not exist validated models of build material drop formation in e-jet, relegating process design and control to be heuristic and ad hoc. This work provides a model to map deposited drop volume to final spread topography and validates this model over the drop volume range of 0.68–13.4 pL. The model couples a spherical cap volume conservation law to a molecular kinetic relationship for contact line velocity and assumes an initial contact angle of 180 deg to predict the drop shape dynamics of dynamic contact angle and dynamic base radius. For validation, the spreading of e-jet-printed drops of a viscous adhesive is captured by high-speed microscopy. Our model is validated to have a relative error less than 3% in dynamic contact angle and 1% in dynamic base radius.