Evaluating inkjet printability of viscoelastic ink through Deborah number analysis

Digital inkjet printing has been developed as a pivotal technology for precise, scalable, and cost-effective deposition of functional inks, enabling significant advancements in flexible printed electronics and bioprinting applications. Analysis of Deborah number (De), defined as the ratio between relaxation time and capillary time, serves as a critical parameter for linking between ink rheology and inkjet printability. However, determining the relaxation time of polymer-containing weakly viscoelastic fluids remains challenging due to the need for high-frequency measurements of storage and loss moduli. In this work, we present a comprehensive Deborah number analysis to evaluate the printability of polymer-based inkjet fluids. Using a squeeze-flow rheometer with piezoelectric axial vibration, we measured the viscoelastic properties of the inks up to 104 Hz and extracted the elastic and viscous coefficients. The Maxwell viscoelastic model was then employed to simulate the inks' viscoelastic behavior for higher frequencies up to 106 rad·s−1 and to determine relaxation times and consequently the Deborah number. This analysis was performed for inks with varying polymer types and concentrations, and their jetting performances were examined using a custom-built drop watcher system. By correlating the Deborah number with inkjet printability, we developed a Deborah number–Weber number (We) map, identifying the optimal range of 0.1 < De < 1 and 2 < We < 15 for stable single-drop jet formation. Our approach provides a robust framework for characterizing and predicting the printability of various functional inks, facilitating their application in advanced printing technologies.