Capillary breakup of liquid jets in the dripping regime and successive drop impacts on a solid surface

Purpose The aim of this paper is to present a fully encompassing numerical simulation of a spatially developing capillary jet emanating from a nozzle, followed by sequential pinch-off, free fall and successive drop impacts onto a solid surface, and to quantify energy exchanges during these stages. Design/methodology/approach Axisymmetric laminar air-water flow is described with a fully coupled, fully implicit Cahn−Hilliard−Navier−Stokes phase-field formulation within the Multiphysics Object-Oriented Simulation Environment finite element framework. Adaptive mesh refinement and adaptive time-stepping, together with a degenerate mobility, resolve multiscale interfacial dynamics while preserving the mass of the main jet and satellite drops. For a fixed nozzle-to-substrate distance, the inlet velocity is varied to obtain periodic dripping and dripping-faucet regimes. The jet and drop flow stages are examined through energy transfer pathways among kinetic, surface, gravitational and dissipative modes. Findings In periodic dripping, breakup periods and detached-drop volumes agree closely with Tate’s law. Successive impacts reveal rapid interface swelling, a pinned-to-unpinned contact-line transition driven by capillary waves and renewed spreading. The periodic-regime energy budget indicates repeatable energy pathways across detachment, impact and spreading. In the dripping-faucet regime, pinch-off is chaotic with strongly varying drop volumes; overlap of rebound and impact phases generates stronger capillary waves and sequential bubble entrapments, and the energy budget reveals destructive momentum interference and enhanced dissipation after impacts. Originality/value This work delivers a mass-conservative phase-field simulation from jet formation to multiple impacts and a time-resolved energy budget across all stages, providing new physical insights into the mechanisms governing drop-train processes relevant to inkjet printing.