Acoustics of a piezo inkjet channel with an entrained air bubble

Piezo-acoustic drop-on-demand (DOD) inkjet printing is widely applied in high-end digital printing due to its unprecedented precision and reproducibility. However, the stability of piezo-DOD inkjet printing can sometimes be compromised through the stochastic entrainment of bubbles within the ink channel. The acoustically driven air bubble modifies the ink channel acoustics, and conversely, the modified ink channel acoustics influences the bubble dynamics. Here, we measure the acoustic eigenfrequency of a MEMS based silicon ink channel as a function of the bubble size. The eigenfrequency was measured using a pulse-echo system and the bubble size using a short-wave infrared imaging setup. We show that the measured eigenfrequency increases when an air bubble is entrained. Surprisingly, the ink channel resonance frequency plateaus at total bubble volumes larger than 10 pl. Moreover, it was found that at a constant total bubble volume, the resonance frequency increases with the number of entrained bubbles. We show that both experimental observations can be quantitatively explained from a simple lumped element model (LEM) comprising the ink channel Helmholtz resonator coupled to the bubble mass-spring system. The results of the LEM model were validated using a full numerical model of the coupled ink channel—bubble system.