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Abstract

Microbubbles entrained in a piezo-driven drop-on-demand 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 number of bubbles is studied through theoretical modeling and experiments. The system is modeled
as a set of two coupled harmonic oscillators: one corresponds to the compliant ink channel and the other corresponds
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. It is shown 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 into the coupled dynamics of a compliant ink channel with an entrained microbubble.