Bubbles in inkjet printheads : analytical and numerical models

The phenomenon of nozzle failure of an inkjet printhead due to entrainment of air bubbles was studies using analytical and numerical models. The studied inkjet printheads consist of many channels in which an acoustic field is generated to eject a droplet. When an air bubble is entrained, it disrupts the droplet formation process. This phenomenon is called nozzle failure. A very simple analytical model of a bubble in a nozzle was shown to qualitatively capture the dependence of the droplet velocity on the bubble volume. A more advanced model in which the two-way coupling between the channel acoustics and the bubble volume oscillations is taken into account, is shown to quantitatively agree with experimental data. The two-way coupling between bubble volume oscillations and channel acoustics is essential in this case. To determine when two-way coupling can be neglected, a complete set of dimensionless groups is derived. This set of dimensionless groups yields sharp criteria for the significance of two-wat coupling and for nonlinearity in the volume oscillations. A fully nonlinear numerical model is developed to test the predictions from the dimensionless groups. The predictions are confirmed by the results from the numerical model. This model is extended to also calculate the translational motion of the bubble and its growth by rectified diffusion. The effects that cause air entrainment were also studied. The outside of the printhead is coated by a thin ink film. This ink film flows whenever the printhead is actuated due to Marangoni stress. This flow is the first link in a chain of events that causes air entrainment. A careful analysis of the governing equations shows that these thin Marangoni flows satisfy potential flow. This result is used to analytically calculate the evolution of a moving droplet and a fingering instability, and the theoretical predictions are confirmed by the observations

Lattice Boltzmann method to study the contraction of a viscous ligament

We employ a recently formulated axisymmetric version of the multiphase Shan-Chen (SC) lattice Boltzmann method (LBM) [Srivastava et al, in preparation (2013)] to simulate the contraction of a liquid ligament. We compare the axisymmetric LBM simulation against the slender jet (SJ) approximation model [T. Driessen and R. Jeurissen, IJCFD {\bf 25}, 333 (2011)]. We compare the retraction dynamics of the tail-end of the liquid ligament from the LBM simulation, the SJ model, Flow3D simulations and a simple model based on the force balance (FB). We find good agreement between the theoretical prediction (FB), the SJ model, and the LBM simulations

Stability of viscous long liquid filaments

We study the collapse of an axisymmetric liquid filament both analytically and by means of a numerical model. The liquid filament, also known as ligament, may either collapse stably into a single droplet or break up into multiple droplets. The dynamics of the filament are governed by the viscosity and the aspect ratio, and the initial perturbations of its surface. We find that the instability of long viscous filaments can be completely explained by the Rayleigh-Plateau instability, whereas a low viscous filament can also break up due to end pinching. We analytically derive the transition between stable collapse and breakup in the Ohnesorge number versus aspect ratio phase space. Our result is confirmed by numerical simulations based on the slender jet approximation and explains recent experimental findings by Castrejon-Pita et al., PRL 108, 074506 (2012).Comment: 7 page

Structural neuroimaging correlates of allelic variation of the BDNF val66met polymorphism.

BACKGROUND: The brain-derived neurotrophic factor (BDNF) val66met polymorphism is associated with altered activity dependent secretion of BDNF and a variable influence on brain morphology and cognition. Although a met-dose effect is generally assumed, to date the paucity of met-homozygotes have limited our understanding of the role of the met-allele on brain structure. METHODS: To investigate this phenomenon, we recruited sixty normal healthy subjects, twenty in each genotypic group (val/val, val/met and met/met). Global and local morphology were assessed using voxel based morphometry and surface reconstruction methods. White matter organisation was also investigated using tract-based spatial statistics and constrained spherical deconvolution tractography. RESULTS: Morphological analysis revealed an "inverted-U" shaped profile of cortical changes, with val/met heterozygotes most different relative to the two homozygous groups. These results were evident at a global and local level as well as in tractography analysis of white matter fibre bundles. CONCLUSION: In contrast to our expectations, we found no evidence of a linear met-dose effect on brain structure, rather our results support the view that the heterozygotic BDNF val66met genotype is associated with cortical morphology that is more distinct from the BDNF val66met homozygotes. These results may prove significant in furthering our understanding of the role of the BDNF met-allele in disorders such as Alzheimer's disease and depression

Control of jet breakup by a superposition of two Rayleigh-Plateau-unstable modes

We experimentally, numerically and theoretically demonstrate a novel method of producing a stream of widely spaced high-velocity droplets by imposing a superposition of two Rayleigh-Plateau-unstable modes on a liquid jet. The wavelengths of the two modes are chosen close to the wavelength of the most unstable mode. The interference pattern of the two superimposed modes causes local asymmetries in the capillary tension. The velocity of the initial droplets depends on these local asymmetries. Due to their different velocities, the droplets coalesce to produce a stream of larger droplets spaced at a much larger distance than the initial droplets. We analytically derive the perturbations that robustly induce this process and investigate the influence of the nonlinear interactions of the two Rayleigh-Plateau-unstable modes on the coalescence process. Experiments and numerical simulations demonstrate that the jet breakup and the subsequent droplet merging are fully governed by the selected modes

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

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

Bubbles in piezo-acoustic inkjet printing (A)

Ink‐jet printing is considered as the hitherto most successful application of microfluidics. A notorious problem in piezo‐acoustic ink‐jet systems is the formation of air bubbles during operation. They seriously disturb the acoustics and can cause the droplet formation to stop. We could show by a combination of acoustical detection and high‐speed visualization that the air‐bubbles are entrained at the nozzle and then grow by rectified diffusion. Experimental results on the droplet velocity as a function of the equilibrium radius R0 of the entrained bubble are presented, too. Surprisingly, the droplet velocity shows a pronounced maximum around R0=17 micrometer before it sharply drops to zero around R0=19 micrometer. A simple one‐dimensional model is introduced to describe this counterintuitive behavior which turns out to be a resonance effect of the entrained bubble. We show that the bubble counteracts the pressure buildup necessary for the droplet formation. The channel acoustics and the air bubble dynamics are modeled. It is crucial to include the confined geometry into the model: The air bubble acts back on the acoustic field in the channel and thus on its own dynamics. This two‐way coupling limits further bubble growth and thus determines the saturation size of the bubble