Numerical simulations of the full ink-jet printing processes: From jetting to evaporation

Ink-jet printing requires to perfectly control both the jetting of droplets and the subsequent droplet evaporation and absorption dynamics. Considerable complexity arises due to the fact that ink is constituted of a mixture of different liquids, surfactants and pigments. Using a sharp-interface ALE finite element method, we numerically investigate the main aspects of ink-jet printing, both on the jetting side and on the drying side. We show how a short pause in jetting can result in clogged nozzles due to solvent evaporation and discuss approaches how to prevent this undesired phenomenon. Once the droplets have been jetted on paper and is evaporating, the print quality can be deteriorated by the well-known coffee-stain effect, i.e. the preferential deposition of particles near the rim of the droplet. This can be prevented in several ways, e.g. employing controlled Marangoni flow via surfactants or co-solvents or printing on a primer layer jetted in beforehand, thus creating a homogeneous deposition pattern for a perfect final printout

Regimes of bubble volume oscillations in a pipe

The effect of an acoustically driven bubble on the acoustics of a liquid-filled pipe is theoretically analyzed and the dimensionless groups of the problem are identified. The different regimes of bubble volume oscillations are predicted theoretically with these dimensionless groups. Three main regimes can be identified: (1) For small bubbles and weak driving, the effect of the bubble oscillations on the acoustic field can be neglected. (2) For larger bubbles and still small driving, the bubble affects the acoustic field, but due to the small driving, a linear theory is sufficient. (3) For large bubbles and large driving, the two-way coupling between the bubble and the flow dynamics requires the solution of the full nonlinear problem. The developed theory is then applied to an air bubble in a channel of an inkjet printhead. A numerical model is developed to test the predictions of the theoretical analysis. The Rayleigh-Plesset equation is extended to include the influence of the bubble volume oscillations on the acoustic field and vice versa. This modified Rayleigh-Plesset equation is coupled to a channel acoustics calculation and a Navier-Stokes solver for the flow in the nozzle. The numerical simulations indeed confirm the predictions of the theoretical analysi

Nonaxisymmetric Effects in Drop-On-Demand Piezoacoustic Inkjet Printing

Drop-on-demand (DOD) inkjet printing is well characterized and a well-studied problem, but nonaxisymmetric effects are typically ignored, while these effects can severely reduce the print-head performance and its stability. In this paper we first review nonaxisymmetric droplet formation originating from geometrical effects. We then focus on the possibility that observed nonaxisymmetry arises from surface instabilities of the meniscus by a Rayleigh-Taylor-like (RT) mechanism. It is shown theoretically that the meniscus can become RT unstable beyond a critical acceleration. A comparison with data extracted from high-speed recordings of the meniscus oscillations show that the critical accelerations are exceeded. Using the time duration that the critical acceleration is exceeded and the maximal growth rate, the extent of growth of the unstable wave is estimated

Secondary Tail Formation and Breakup in Piezoacoustic Inkjet Printing: Femtoliter Droplets Captured in Flight

The role of meniscus motion and ink viscosity in the formation of a secondary tail and its breakup are studied experimentally during the picoliter-droplet formation process of a MEMS piezoacoustic inkjet print head using laser-induced 8-ns single-flash stroboscopic imaging with a temporal resolution of 100 ns. It is found that the formation of the secondary tail is driven by meniscus motion and that the secondary tail forms reproducibly between the primary tail and the meniscus in the final microseconds before pinchoff. We demonstrate that the stability of the secondary tail can be controlled through the motion of the meniscus after the primary tail has formed. A 4 times increase in stretching rate results in a 2.2 times increase in the secondary-tail length and a 3 times higher number of femtoliter satellites. Furthermore, as expected for Rayleigh breakup, a 43% increase in ink viscosity is found to increase the secondary-tail length by 50%. Finally, it is found that, during inkjet printing, the secondary tail cascades into tertiary and quaternary tails. We show that the formation of higher-order tails is irreproducible and therefore driven by noise. The formation of thicker secondary and thinner higher-order tails results in a bimodal satellite size distribution, where the secondary satellites with a volume greater than or equal to 4fL are located closer to the primary-tail droplet, while satellites with a volume less than 4fL are located closer to the nozzle. The main findings of the present work, that the stability of the secondary tail decreases with a decrease in stretching rate and ink viscosity, can be employed in the inkjet-printing community for waveform design to minimize internal contamination of inkjet printers

Flows on the nozzle plate of an inkjet printhead

Flow patterns of ink layers on the nozzle plate of a piezo-driven printhead are investigated. Two different flow types are identified. First, a jet of droplets induces a radial airflow in the direction of the jet, which in turn causes a liquid flow towards the nozzle. Second, the movement of the meniscus in the nozzle causes an equally strong flow, but completely different flow patterns. The results are presented in a phase diagram with pulse amplitude and firing frequency as parameters

Selective evaporation at the nozzle exit in piezoacoustic inkjet printing

In practical applications of inkjet printing the nozzles in a printhead have intermittent idle periods, during which ink can evaporate from the nozzle exit. Inks are usually multicomponent where each component has its own characteristic evaporation rate resulting in concentration gradients within the ink. These gradients may directly and indirectly (via Marangoni flows) alter the jetting process and thereby its reproducibility and the resulting print quality. In the present work, we study selective evaporation from an inkjet nozzle for water-glycerol mixtures. Through experiments, analytical modeling, and numerical simulations, we investigate changes in mixture composition with drying time. By monitoring the acoustics within the printhead, and subsequently modeling the system as a mass-spring-damper system, the composition of the mixture can be obtained as a function of drying time. The results from the analytical model are validated using numerical simulations of the full fluid mechanical equations governing the printhead flows and pressure fields. Furthermore, the numerical simulations reveal that the time independent concentration gradient we observe in the experiments is due to the steady state of water flux through the printhead. Finally, we measure the number of drop formation events required in this system before the mixture concentration within the nozzle attains the initial (pre-drying) value, and find a stronger than exponential trend in the number of drop formations required. These results shed light on the complex physiochemical hydrodynamics associated with the drying of ink at a printhead nozzle, and help in increasing the stability and reproducibility of inkjet printing.Comment: For supplementary movie, see https://www.youtube.com/watch?v=a9PF8gOvAB

Flows on the nozzle plate of an inkjet printhead

Flow patterns of ink layers on the nozzle plate of a piezo-driven printhead are investigated. Two different flow types are identified. First, a jet of droplets induces a radial airflow in the direction of the jet, which in turn causes a liquid flow towards the nozzle. Second, the movement of the meniscus in the nozzle causes an equally strong flow, but completely different flow patterns. The results are presented in a phase diagram with pulse amplitude and firing frequency as parameters