Impulsively generated focused jets play a significant role in various applications, including inkjet 9 printing, needle-free drug delivery, and microfluidic devices. As the demand for generating jets 10 and droplets from medium- to highly viscous liquids increases, understanding the role of viscosity in 11 jetting dynamics becomes crucial. While previous studies have examined the viscous effects on walls, 12 the impact on free surfaces has not been thoroughly understood. This study aims to bridge this gap 13 by integrating experiments with numerical simulations to investigate the viscous effects on focused 14 jet formation. We demonstrate that mass and momentum transfer along the tangential direction of 15 the free surface contribute to focused jet formation, and viscosity plays a key role in this transfer 16 process. The viscosity-induced diffusion of the shear flow and vorticity near the free surface reduces 17 the jet speed. Based on experimental observations and simulation results, we propose an equation to 18 predict the viscous jet velocity. These findings offer new perspectives on viscous interface dynamics 19 in advanced manufacturing and biomedical applications
