Instability-driven dynamic behaviors of micro-scale liquid jets

Abstract

Instability can endow liquid jets with dynamic behaviors that can be either constructive or harmful. For example, the liquid rope coiling effect that happens for a viscous liquid jet may be responsible for the fragility in glass sheets during fabrication due to the inhomogeneity caused by folding and coiling motion of jet. With a moving plate, a coiling jet could draw intricate patterns and been applied to addictive printings with the coiling shape. This instability, termed as buckling instability in a wider context, is an intrinsic tendency for a thin object and will manifest on not only jet, but also elastic rod, elastic rope, viscous liquid bridge, or geological architecture like folded rocks. This widely observed instability is of rich potential to be exploited for manipulating viscous liquid jets. By applying an electric field, a jet could become significantly thinner and would be accelerated, resulting in a buckling jet that otherwise would not buckle. However, the literature relating the electric coiling is limited to assuming a uniform and vertical distribution of the electric field for a needle-to-plate configurated electrodes setup. In our experiment, we found out that this needle-to-plate configuration of electrodes cannot be taken as a uniform and vertical electric field distribution, for a needle-to-plate (commonly used for electric coiling), and plate-to-plate (used as the model when analysis) configuration demonstrates completely different onset conditions for the electric coiling phenomenon. Therefore, we studied the factor of the shape of the electric field on the charged liquid jet and it successively explained the discrepancy observed between a needle-to-plate and plate-to-plate electrode configuration and demonstrate applications with its facile control over coiling onset. Like an electric field that stretches the jet to tens of micrometers thin and induced coiling, other applications relate to liquid rope coiling are mostly with micro or nanoscale jet, where surface tension is expected to be dominating. We found that if the liquid jet is dispensed from a tiny nozzle with hundreds of micrometers diameter, the onset height of coiling as a function of flow rate is opposite to existing theories. In the existing literature, researchers either ignore the surface tension or shows it only offers minor correction to the onset curve whose experiments are conducted with large orifice and thus surface tension does not play an important role. Nowadays, the most adopted coiling is the coiling in microscale, like high-resolution printing or microfluidic jet folding, where the surface tension becomes dominate and strong enough to alter the slope of an onset curve. Hence, we have identified an unexplored, yet very widely adopted a regime of liquid rope coiling that provides critical guidelines for buckling instability applied in microscale. Our experiments, numerical methods, and linear stability analysis to approach this problem and have obtained well-match results. In summary, motivated by the discrepancy between our observation and existing theories, we have made our attempts to reveal some new physics and successively accounted for our observation regarding the buckling of micro-scale jets and demonstrate applications initiated by these findings.