Dynamics of flow, particles and bubbles in a piezo-acoustic inkjet channel
Yogesh Jethani is a PhD student in the department Physics of Fluids. (Co)Promotors are prof.dr. D. Lohse, prof.dr. M. Versluis from the faculty Science and Tecnology and dr. T.J. Segers from the faculty Electrical Engineering, Mathematics and Computer Science.
Piezo-acoustic drop-on-demand inkjet printing technology is used for high-end graphics printing applications and in manufacturing processes of various components such as electronic displays and printed circuit boards. It continues to find growing usage for its high reliability, precision and versatility. However, air bubble entrainment and particle trapping just upstream of the nozzle impedes the reliability and reproducibility of an inkjet printing system. Furthermore, an ink channel with an entrained bubble will face acute nozzle failure if that specific nozzle continues to be actuated after the bubble entrainment event. The research presented in this thesis is motivated by this event and the related processes. The work was carried out at the Physics of Fluids group within the Faculty of Science & Technology at the University of Twente, in close collaboration with our industrial partner Canon Production Printing.
In Chapter 2, we characterized the unsteady and time-averaged flow inside the ink channel. This part of the thesis was motivated by the aim of understanding the separation of the boundary layer during the inward flow and the subsequent formation of the recirculation region in the time-averaged flow, which supposedly plays an essential role in the trapping of dirt particles. Characterizing the flow, especially close to the nozzle, is crucial in understanding particle and bubble motion inside the ink channel, which are coupled to the fluid flow itself. To characterize the unsteady flow, the flow field inside the ink channel was measured using fluorescent micro-particle tracking velocimetry at various instants during an actuation cycle. The flow was also simulated numerically by solving the Navier-Stokes equations for two-phase flow in ANSYS Fluent, along with a simplified single phase flow calculation. The computed two-phase flow fields and axial displacement profiles show good similarity to the flow measurements, indicating that the computed numerical simulations provide a crucial framework that can be used to study particle and bubble translation inside the ink channel.\\
The results of the flow characterization study indicate that while the topology of the flow remains similar when a small tapering (~10º) is introduced to the nozzle, the size of the vortex ring is inversely related to the taper angle. Furthermore, the size of the vortex ring for a given taper angle is robust, with respect to the driving conditions -- the underpressure in the feedthrough chamber and pulse amplitude.
In chapter 3, a comprehensive analysis of particle translation inside the ink channel was carried out in order to unravel the counter-intuitive particle trapping inside the vortex ring just upstream of the nozzle. Particle motion for rigid, homogeneous and spherical particles was modeled using point particle approach, applying the Maxey-Riley equation of motion for spherical particles. The ANSYS Fluent simulations described in chapter 1 were used as a base flow to compute trajectories for various particle sizes and densities, and for two different nozzle geometries -- a straight and a (~10º) tapered nozzle. To validate the results from this model, trajectories of 6 μm silica particles were experimentally measured using high-speed imaging. For the same initial conditions as the experimentally measured trajectories, the numerically computed trajectories exhibited good agreement with the measured trajectories.
The particle translation study starts with classifying whether a particle of given size and density would have a centrifugal (moving away from the center) or centripetal (moving toward the center) trajectory in the vicinity of the vortex ring. The numerical calculations show that the particles that are heavier than the fluid follow centripetal trajectories while the particles lighter than the fluid follow centrifugal trajectories. Additionally, the rate of trapping of particles is directly related to their size and density. In the next segment of this study, we focused on understanding the particle interaction with the vortex ring to evaluate the relative chances of particle trapping. The results indicated that the particle trapping chances increase with both the particle size and their density. Furthermore, it is also observed that the ink channel with a straight nozzle almost always has higher chances of particle trapping as compared to a channel with a tapered nozzle. The study concluded that due to higher relative chances of particle trapping, a straight nozzle is more susceptible to bubble entrainment-induced jetting instability, as compared to a tapered nozzle.
Chapter 4 of the thesis focused on investigating the acoustic response of the ink channel when an air bubble is entrained inside. The resonance behavior of a compliant piezo-driven inkjet channel with an entrained microbubble was explored by solving the eigenfrequencies of a coupled system comprising two harmonic oscillators: one representing the compliant ink channel and the other representing the microbubble. It was observed that when the compliance of the bubble dominates over that of the actuator, the resonance frequency of the coupled ink channel-bubble system converges to a constant value. Furthermore, in the presence of multiple entrained bubbles, the total gas volume becomes distributed, resulting in a reduced effective inertance of the bubbles due to increased bubble surface area to volume ratio. Consequently, the resonance frequency of the coupled system decreases under these conditions.
Additionally, a simple potential flow approach was employed to accurately determine the inertance of both the confined bubble and other geometries, such as a nozzle. This approach is crucial for considering the relative change in inertance between an entrained microbubble and a bubble in the free field. As a result, this chapter provides valuable physical insights into confined bubble dynamics, offering a straightforward tool for modeling the inertance of confined bubbles, nozzles, and other complex geometries. The implications of this work extend beyond inkjet printing, encompassing research areas like microfluidics, cavitation, and biomedical acoustics.
