  Microbubbles entrained in a piezo-driven drop-on-demand (DOD) printhead
disturb the acoustics of the microfluidic ink channel and thereby the jetting
behavior. Here, the resonance behavior of an ink channel as a function of the
microbubble size and the number of bubbles is studied through theoretical
modeling and experiments. The system is modeled as a set of two coupled
harmonic oscillators: one corresponding to the compliant ink channel and one to
the microbubble. The predicted and measured eigenfrequencies are in excellent
agreement. It was found that the resonance frequency is independent of the
bubble size as long as the compliance of the bubble dominates over that of the
piezo actuator. An accurate description of the eigenfrequency of the coupled
system requires the inclusion of the increased inertance of the entrained
microbubble due to confinement. We show that the inertance of a confined bubble
can be accurately obtained by using a simple potential flow approach. The model
is further validated by the excellent agreement between the modeled and
measured microbubble resonance curves. The present work therefore provides
physical insight in the coupled dynamics of a compliant ink channel with an
entrained microbubble.
