Abstract
The evolution of the capillary breakup of a liquid jet under large excitation amplitudes in a parameter regime relevant to inkjet printing is analysed using three-dimensional numerical simulations. The results exhibit a reversal of the breakup length of the jet occurring when the velocity scales associated with the excitation of the jet and surface tension are comparable, and an inversion of the breakup from front-pinching to back-pinching at sufficiently large excitation amplitudes. Both phenomena are shown to be associated with the formation of vortex rings and a local flow obstruction inside the jet, which modify the evolution of the jet by locally reducing or even reversing the growth of the capillary instability. Hence, this study provides a mechanism for the well-known breakup reversal and breakup inversion, which are both prominent phenomena in inkjet printing. An empirical similarity model for the reversal breakup length is proposed, which is shown to be valid throughout the considered range of characteristic parameters. Hence, even though the fluid dynamics observed in capillary jet breakup with large excitation amplitudes are complex, the presented findings allow an accurate prediction of the behaviour of jets in many practically relevant situations, especially continuous inkjet printing.
Highlights
The surface-tension-driven breakup of liquid jets has been a very active topic of research since Savart (1833) reported the first systematic experimental observations of this phenomenon
To facilitate the analysis and discussion of the results presented in Sect. 4, the capillary breakup of the liquid jet is described by the theoretical analysis of the dominating instability mechanism, i.e. the Rayleigh-Plateau instability, and based on its hydrodynamic energy balance
The presented cases focus on the parameter regime 0.01 ≤ Oh ≤ 0.2 and 20 ≤ We ≤ 200 where the breakup reversal and inversion are most prominent (McIlroy and Harlen 2019), for which the flow is laminar, with 22 ≤ Re ≤ 1000, and which is relevant for inkjet printing applications (Calvert 2001; Derby 2010)
Summary
The surface-tension-driven (capillary) breakup of liquid jets has been a very active topic of research since Savart (1833) reported the first systematic experimental observations of this phenomenon. Plateau (1873) identified surface tension as the driving mechanism of this instability, and Rayleigh (1879) was the first to predict the growth rate of the instability by means of a linear stability analysis. This linear stability analysis and its extensions to viscous flows (Weber 1931; Chandrasekhar 1961) have proven to be powerful tools to describe the capillary breakup of liquid jets. This operating range is very relevant to various engineering applications, including inkjet printing (Calvert 2001; Derby 2010)
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