Oscillatory countercentrifugation of particles in a piezoacoustic printhead

Inkjet printing is a highly reproducible and reliable droplet deposition technique. However, its stability can be compromised by the stochastic entrainment of an air bubble inside the ink channel, causing acute nozzle failure. Prior studies have linked bubble entrainment to the trapping of dirt particles, which are typically denser than the ink, inside the pulsating toroidal vortex formed above the jetting nozzle. While this seemingly counterintuitive trapping has been numerically studied in idealized unbound vortices, its behavior in realistic flows remains mostly unexplored. Here, we investigate particle trapping within a piezoacoustic inkjet channel by using two-phase flow simulations and by modeling particle translation using the Maxey-Riley equation. We compare two nozzle geometries, i.e., a straight nozzle and one tapered at 10^∘, and find that introducing this small taper significantly alters the oscillatory flow near the nozzle. For both nozzle types, particles in the relevant size range (4–8 μm) and particle-to-fluid density ratios (0.5–3) exhibit consistent trends: particles heavier than the fluid follow centripetal trajectories, spiraling inward within the vortex ring, while lighter particles follow centrifugal paths. Particles denser than the fluid can become trapped when the particles can no longer follow the high-frequency flow oscillations thereby limiting their kinetic energy, allowing the strong centripetal force from the pressure gradient in the vortex ring to pull them inward. The particle-trapping rate increases with both particle size and density ratio, and is similar for straight and tapered nozzles. However, in tapered nozzles, the vortex ring is smaller, resulting in fewer particles interacting with it, thereby reducing the number of particles trapped, and potentially mitigating dirt-induced bubble entrainment.