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

Suppression of Satellite Droplet Formation by Very Dilute Viscoelastic Solutions

The presence of satellite droplets during inkjet printing is extremely undesirable since it degrades the quality and reproducibility of the print. Existing strategies for the suppression of satellite droplet formation involve increasing the viscosity of the ink, thus increasing the stability of the jetted filament and suppressing satellite droplet formation. However, such a mitigation strategy is usually at the cost of the jetting velocity. In the present work, we demonstrate that very dilute viscoelastic solutions can suppress satellite droplet formation, without any appreciable loss of droplet velocity as compared to the case with pure water (where satellite droplet formation is observed). Furthermore, we show that, for a given driving condition, there exist upper and lower bounds of polymer concentrations within which satellite droplets are suppressed. Satellite droplets are formed at concentrations below the lower bound, while droplet formation ceases for concentrations above the upper bound. Finally, we attempt to present scaling arguments that shed light on the underlying interplay between inertia, capillarity, and viscoelasticity, which leads to the suppression of satellite droplet formation

A Quantitative Comparison of Physical Accuracy and Numerical Stability of Lattice Boltzmann Color Gradient and Pseudopotential Multicomponent Models for Microfluidic Applications

The performances of the Color-Gradient (CG) and the Shan-Chen (SC) multicomponent Lattice Boltzmann models are quantitatively compared side-by-side on multiple physical flow problems where breakup, coalescence and contraction of fluid ligaments are important. The flow problems are relevant to microfluidic applications, jetting of microdroplets as seen in inkjet printing, as well as emulsion dynamics. A significantly wider range of parameters is shown to be accessible for CG in terms of density-ratio, viscosity-ratio and surface tension values. Numerical stability for a high density ratio O(1000) is required for simulating the drop formation process during inkjet printing which we show here to be achievable using the CG model but not using the SC model. Our results show that the CG model is a suitable choice for challenging simulations of droplet formation, due to a combination of both numerical stability and physical accuracy. We also present a novel approach to incorporate repulsion forces between interfaces for CG, with possible applications to the study of stabilized emulsions. Specifically, we show that the CG model can produce similar results to a known multirange potentials extension of the SC model for modelling a disjoining pressure, opening up its use for the study of dense stabilized emulsions

Jetting of microdroplets: numerical simulations using the Lattice Boltzmann color-gradient model

Simulating the small scale fluid dynamics involved with inkjet printing can be challenging. We show validation of a numerical model that can accurately simulate the jetting process, alongside examples of full jetting simulations. This can be used in future research to, e.g., investigate imperfect jetting due to manufacturing errors of jetting nozzles

Drying water droplets: Suppression of the coffee-stain effect by letting them dry on a thin oil film

We systematically study the evaporation of a water microdroplet put on a thin oil film, both experimentally and theoretically. First, the absence of an intercalated film between droplets and substrates is demonstrated by interferometry. The interfacial energies between the droplet, the oil film and the solid surface are the key parameters to determine the wetting characteristics. During evaporation, we measure the flow field with μPIV, which shows that it is controlled by the contact line behavior and the wetting state of the film with the droplet. Once the microdroplet contains particles, they accumulate during the evaporation process. We experimentally find that the final deposit of the particles is determined by the flow and by the movement of the contact line. We derive an analytical expression for the radial velocity profile in the flow field near the substrate, which proves that the hindering of evaporation at the rim of the droplet by the non-volatile oil meniscus prevents the flow towards the edge, and therefore suppresses the ``coffee-stain'' effect. We finally demonstrate that the final particle deposition can be manipulated by tuning the surface energy of the droplet by adding a specific amount of a surfactant

Comparison of Lattice Boltzmann, Finite Element and Volume of Fluid Multicomponent Methods for Microfluidic Flow Problems and the Jetting of Microdroplets

We show that the lattice Boltzmann method (LBM) based color-gradient model with a central moments formulation (CG-CM) is capable of accurately simulating the droplet-on-demand inkjetting process on a micrometer length scale by comparing it to the Arbitrary Lagrangian Eulerian Finite Element Method (ALE-FEM). A full jetting cycle is simulated using both CG-CM and ALE-FEM and results are quantitatively compared by measuring the ejected ink velocity, volume and contraction rate. We also show that the individual relevant physical phenomena are accurately captured by considering three test-cases; droplet oscillation, ligament contraction and capillary rise. The first two cases test accuracy for a dynamic system where surface tension is the driving force and the third case is designed to test wetting boundary conditions. For the first two cases we also compare the CG-CM and ALE-FEM results to Volume of Fluid (VOF) simulations. Comparison of the three methods shows close agreement when compared to each other and analytical solutions, where available. Finally we demonstrate that asymmetric jetting is achievable using 3D CG-CM simulations utilizing asymmetric wetting conditions inside the jet-nozzle. This allows for systematic investigation into the physics of asymmetric jetting, e.g. due to jet-nozzle manufacturing imperfections or due to other disturbances