# Resonance behavior of a compliant piezo-driven inkjet channel with an entrained microbubble

## TL;DR

This study investigates how entrained microbubbles affect the resonance behavior of piezo-driven inkjet channels, combining theoretical modeling and experiments to understand the coupled dynamics and inertance effects.

## Contribution

The paper introduces a coupled harmonic oscillator model for the ink channel and microbubble system, validated by experiments, revealing the independence of resonance frequency from bubble size when compliance dominates.

## Key findings

- Resonance frequency is independent of bubble size when bubble compliance dominates.
- Inertance of confined microbubbles can be accurately modeled using potential flow.
- Model predictions agree well with experimental resonance curves.

## Abstract

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.