Breakup dynamics of continuous liquid jets under radial velocity perturbations

This study investigates the breakup dynamics of continuous inkjet printing (CIJ) subjected to radial velocity disturbances. Based on energy conservation, a theoretical relationship between the jet breakup length and the amplitude of radial velocity disturbance is first derived. The influence of disturbance amplitude (ϵ0′) and wavenumber (k′) on the jet breakup characteristics is investigated through direct numerical simulations employing the volume-of-fluid (VOF) multiphase model. Numerical simulations reveal that for disturbance amplitudes in the range ϵ0′=0.001∼0.1, increasing ϵ0′ significantly reduces the breakup length, following the relation Lb′∼ ln (2/ϵ0′2). Furthermore, the disturbance wavenumber k′ is found to determine the size and spacing of the resulting droplets, following the scaling laws d/D0∼k′−1/3 and S/d∼k′−2/3, respectively. A phase diagram in the ϵ0′–k′ space is constructed to classify three distinct breakup regimes: uniform droplet formation, one-droplet merging and filament breakup with multiple satellite droplets. At the optimal wavenumber k′=0.7, the effects of the Weber number and disturbance amplitude on the pinch-off behavior are further examined, identifying three ligament pinch-off modes: backward-merging, uniform, and forward-merging modes. These findings provide theoretical guidance for droplet control and prediction in applications such as continuous inkjet, extreme ultraviolet lithography (EUVL) technology, and microfluidics.