Satellite formation in drop-on-demand printing of polymer solutions

High speed photographic images of jets formed from dilute solutions of polystyrene in diethyl phthalate ejected from a piezoelectric drop-on-demand inkjet head have been analyzed in order to study the formation and distribution of drops as the ligament collapses. Particular attention has been paid to satellite drops, and their relative separation and sizes. The effect of polymer concentration was investigated. The distribution of nearest-neighbour centre spacing between the drops formed from the ligament is better described by a 2-parameter modified gamma distribution than by a Gaussian distribution. There are (at least) two different populations of satellite size relative to the main drop size formed at normal jetting velocities, with ratios of about three between the diameters of the main drop and the successive satellite sizes. The distribution of the differences in drop size between neighbouring drops is close to Gaussian, with a small non-zero mean for low polymer concentrations, which is associated with the conical shape of the ligament prior to its collapse and the formation of satellites. Higher polymer concentrations result in slower jets for the same driving impulse, and also a tendency to form ligaments with a near-constant width. Under these conditions the mean of the distribution of differences in nearest-neighbour drop size was zero.

Improved models for drop-on-demand ink-jet shortening

A previous 1-D model for the shortening of an unbroken drop-on-demand ink-jet ligament has been extended to the case of an arbitrary attached tail mass, and can also include extensional viscosity (which has ∼ 2% effect) as well as linear elasticity in the fluid. Predictions from the improved model are shown to be very similar to results from 2-D axisymmetric numerical simulations of DoD ink-jet ligaments and also to the results of recent experiments on Newtonian fluids jetted without satellite formation.

Jetting behaviour of polymer solutions in drop-on-demand inkjet printing

The jetting of dilute polymer solutions in drop-on-demand printing is investigated. A quantitative model is presented which predicts three different regimes of behaviour depending upon the jet Weissenberg number Wi and extensibility of the polymer molecules. In regime I (Wi < ½) the polymer chains are relaxed and the fluid behaves in a Newtonian manner. In regime II (½ < Wi < L) where L is the extensibility of the polymer chain the fluid is viscoelastic, but the polymer do not reach their extensibility limit. In regime III (Wi > L) the chains remain fully extended in the thinning ligament. The maximum polymer concentration at which a jet of a certain speed can be formed scales with molecular weight to the power of (1-3ν), (1-6ν) and -2ν in the three regimes respectively, where ν is the solvent quality coefficient. Experimental data obtained with solutions of mono-disperse polystyrene in diethyl phthalate with molecular weights between 24 - 488 kDa, previous numerical simulations of this system, and previously published data for this and another linear polymer in a variety of “good” solvents, all show good agreement with the scaling predictions of the model.

Regimes of Polymer Behaviour in Drop-on-Demand Ink-Jetting

Three regimes of fast DoD jetting behaviour for solutions of mono-disperse linear polymers have been linked to the underlying polymer molecular chains and their fully extended length L in good solvents. This allows scaling laws in molecular weight to be predicted and applied to experimental jetting results from different DoD print heads. The higher extensional flows encountered in high speed jetting in viscous solvents can fully stretch linear molecules outside the nozzle, permitting jetting of higher polymer content than for purely elastic behaviour. These results are significant for DoD printing at raised jet speeds and will apply to any DoD print head jetting linear polymer solutions.

A simple criterion for filament break-up in drop-on-demand inkjet printing

Jets from drop-on-demand inkjet print-heads consist of a main drop with a trailing filament, which either condenses into the main drop, or breaks up into satellite drops. Filament behaviour is quantitatively similar to that of larger, free symmetrical filamentscan be predicted from the aspect ratio and Ohnesorge number. Symmetrical filaments generated from inkjet print-heads show the same behaviour. A simple model, based on competition between the processes of axial shortening and radial necking, predicts the critical aspect ratio below which the jet condenses into a single drop. The success of this simple criterion supports the underlying physical model. © 2013 American Institute of Physics.

Time-resolved particle image velocimetry within the nozzle of a drop-on-demand printhead

Time-resolved particle image velocimetry (PIV) has been performed inside the nozzle of a commercially available inkjet print-head to obtain the time-dependent velocity waveform. A printhead with a single transparent nozzle 80 μm in orifice diameter was used to eject single droplets at a speed of 5 m/s. An optical microscope was used with an ultra-high-speed camera to capture the motion of particles suspended in a transparent liquid at the center of the nozzle and above the fluid meniscus at a rate of half a million frames per second. Time-resolved velocity fields were obtained from a fluid layer approximately 200 μm thick within the nozzle for a complete jetting cycle. A Lagrangian finite-element numerical model with experimental measurements as inputs was used to predict the meniscus movement. The model predictions showed good agreement with the experimental results. This work provides the first experimental verification of physical models and numerical simulations of flows within a drop-on-demand nozzle. © 2012 Society for Imaging Science and Technology.

Drop speeds from drop-on-demand ink-jet print heads

Measured drop speeds from a range of industrial drop-on-demand (DoD) ink-jet print head designs scale with the predictions of very simple physical models and results of numerical simulations. The main drop/jet speeds at a specified stand-off depend on fluid properties, nozzle exit diameter, and print head drive amplitude for fixed waveform timescales. Drop speeds from the Xaar, Spectra Dimatix, and MicroFab DoD print heads tested with (i) Newtonian, (ii) weakly elastic, and (iii) highly shear-thinning fluids all show a characteristic linear rise with drive voltage (setting) above an apparent threshold drive voltage. Jetting, simple modeling approaches, and numerical simulations of Newtonian fluids over the typical DoD printing range of surface tensions and viscosities were studied to determine how this threshold drive value and the slope of the characteristic linear rise depend on these fluid properties and nozzle exit area. The final speed is inversely proportional to the nozzle exit area, as expected from volume conservation. These results should assist specialist users in the development and optimization of DoD applications and print head design. For a given density, the drive threshold is determined primarily by viscosity, and the constant of proportionality k linking speed with drive above a drive threshold becomes independent of viscosity and surface tension for more viscous DoD fluid jetting. © 2013 Society for Imaging Science and Technology.