Designing working diagrams for electrohydrodynamic printing

Abstract Cone-jet is an important working mode that is critical to the accuracy of electrohydrodynamic (EHD) printing. This work considers the leaky-dielectric model and firstly proposes five independent dimensionless numbers, viz., the Ohnesorge number Oh, the Weber number We, the electric capillary number CaE, the relaxation parameter α and the relative electrical permittivity of ink er, to delineate the cone-jet mode. Theoretical and computational analyses on the regime of cone-jet mode depicted by property and operating diagrams are performed. Theoretical analysis suggests that a cone-jet occurs in wide ranges of these dimensionless numbers. Computational analysis based on the finite element method narrows down these ranges. Complete working diagrams for the EHD printing are described in Oh-α and We-CaE spaces, respectively. The theoretical and computational analyses well agree with previous experiments, which provides a general rule to optimize the EHD printing.