Inkjet Analysis

An ink jet system basically consists of three fundamental components: inks, a print engine (printhead) and an imaging medium (e.g. paper). Inks produce color by selectively absorbing and scattering light and  can be broadly categorized into 3 groups based on their colorant, i.e. organic dye, polymeric dyes, and pigments. The printhead generates and projects droplets of ink under digital control onto the imaging medium (paper) to form an image. Modern inkjet systems utilize micromachined printheads that contain hundreds to thousands of integrated micro-nozzles and can produce millions of droplets of ink per second. The droplets are generated with unprecedented uniformity and projected onto the imaging medium with remarkable precision to render high resolution images. While traditional printing has been the dominant impetus for the advancement of inkjet systems, this technology is rapidly evolving towards applications in emerging fields such as the printing of functional materials, deposition of biomaterials, production of pharmaceutics and 3D rapid prototyping. Inkjet systems broadly fall into two categories, continuous inkjet (CIJ) and drop-on-demand (DOD) as shown in Figure 1.

The development of an inkjet application involves numerous diverse yet coupled efforts. These include the rational development of ink formulations, the analysis of droplet generation, the precise deposition of droplets onto a medium and the analysis of ink media interactions, e.g. spreading, coalescence and absorption of droplets. Research in the Furlani group is focused on the use of computational fluid dynamics (CFD) to broadly facilitate the development of current and emerging inkjet applications. Dr. Furlani has over 10 years of industrial experience in the development of microfluidics and especially inkjet technology, which he acquired as a senior principal scientist in the Eastman Kodak Research Labs before joining the faculty at UB. His group currently uses CFD to advance fundamental understanding of inkjet processes, determine proof-of-concept, design and optimize system components and generally guide experimental efforts. This modeling competency is demonstrated in the following examples from research projects.

In CIJ, continuous jets of ink are produced at each nozzle by applying sufficient pressure to a common ink reservoir. The jets are inherently unstable (Rayleigh instability) and can be modulated using a periodic signal at the nozzle to break-up into a stream of uniform droplets that have a well-defined volume and velocity (10-20 m/s) and that form at a consistent distance downstream from the nozzle. The most common mechanism for modulating the jets is mechanical vibration, usually provided by a piezoelectric transducer as shown in Figure 1a. When the jets are properly modulated a steady stream of droplets is produced from each nozzle at rates of hundreds of kilohertz. However, only select droplets are allowed to reach the imaging medium to form the image. The unused droplets are deflected in flight and recycled to the ink reservoir that feeds the printhead. In electrostatic-based CIJ the nozzle is held at a potential and a small charge is imparted to each drop as it forms. Individual droplets in the stream are steered (deflected) using voltage-driven deflection plates as shown in Figure 1a. Figure 2 show a CFD simulation of a transducer-driven CIJ nozzle wherein a periodic pressure pulse is applied as a boundary condition at the inlet of a nozzle to modulate the jet to break into a stream of identical droplets.

A different method of CIJ printing has recently been developed by the Eastman Kodak Company. This is called Stream technology and has been commercialized in Kodak’s Prosper Imprinting Systems. In Stream CIJ a pressurized reservoir feeds a micromachined printhead manifold that contains hundreds of nozzles (~10-20 microns in diameter). Each nozzle produces a continuous jet of ink. The jets are individually modulated using a thermal pulse that induces the formation of uniform droplets with well-defined volumes and velocities. To modulate a jet, a periodic voltage pulse is applied to ring-like polysilicon heater element that is integrated into the nozzle surrounding the orifice, which causes a diffusion of thermal energy from the heater into the jet (Figure 3). Thus, the temperature of ink and hence its temperature dependent fluid properties, density, viscosity and surface tension, are modulated near the orifice. The dominant cause of jet instability and drop formation is the modulation of surface tension. The pulsed heating modulates the surface tension at a wavelength λ=v0τ, where v0 is the jet velocity and τ is the period of the heat pulse as shown in Figure 3. The down-stream advection of thermal energy gives rise to a spatial variation (gradient) of surface tension along the jet. This produces a shear stress at the free-surface, which is balanced by inertial forces in the ink, thereby inducing a Marangoni flow from regions of lower to higher surface tension (from warmer regions towards cooler regions). This causes a deformation of the free-surface (slight necking in the warmer regions and ballooning in the cooler regions) that ultimately leads to instability and drop formation. The drop volume can be adjusted on demand by varying the voltage pulse width τ, i.e. Vdrop=πr02v0τ, . Thus, longer pulses produce larger drops, shorter pulses produce smaller drops, and different sized drops can be produced from each orifice as desired. For printing applications two different sized drops are produced from each nozzle. In one mode of operation, the larger drops are projected onto a substrate to form an image while the smaller sized drops are deflected using air flow and recycled as shown in Figure 3. 

The Stream CIJ process has been modeled by Dr. Furlani using CFD analysis. Figure 4 shows Stream CIJ droplet formation: the experimental imaging of thermally induced droplet formation from a single nozzle is shown in Figure 4a and a corresponding CFD simulation is shown in Figure 4b. Dr. Furlani has performed extensive CFD analysis of this process and te results of a typical simulation are shown in Figure 5. The predicted drop formation is compared with corresponding experimental data in the form of a strobed image during pinch-off. Note that the CFD analysis is able to accurately predict the details of pinch-off and drop formation.

In DOD systems, droplets are produced as needed (on demand) to form an image. The droplets are generated by applying a pressure pulse within an ejection chamber connected to a nozzle orifice.  The pressure profile is tuned to eject a droplet with a desired volume and velocity, usually 15-55 mm in diameter and between 3 and 15 m/s, respectively. DOD printheads can be categorized according to mechanism used for drop ejection. The vast majority of commercial DOD printers utilize either piezoelectric or thermal droplet generation. Piezo DOD printheads use voltage-induced deformation of a piezoelectric transducer to produce a pressure pulse that ejects a droplet. In thermal inkjet (TIJ), a resistive element is used to superheat ink and generate a homogenous vapor bubble, which expands rapidly and provides a pressure pulse that ejects a droplet. Figure 6 shows a CFD simulation of piston-driven droplet ejection wherein a piston first moves upward rapidly to eject a droplet and they downward to facilitate pinch-off.  Figure 7 shows a cut-away view of a 3D CFD simulation of TIJ droplet ejection wherein an expanding  vapor bubble is generated within a nozzle chamber to eject a droplet.

In order to form an image, ink droplets are deposited onto a medium, usually some form of paper in traditional printing. The droplets travel from the printhead to the paper at a speed of several meters per second and then impact the paper, which is usually translating relative to the printhead. Upon impact, the droplets spread, coalesce and absorb into the paper and eventually dry to render the image. In order to model this process, the interaction of the ink with the paper, i.e. ink media interaction, must be known. However, paper is a complex material with a random network of fibers that define a complex porous medium with a 3D network of pores into which the ink absorbs (Figure 8). The Furlani group has used CFD analysis to simulate ink media interactions at both mesoscopic and microscopic length scales.  In mesoscopic analysis the medium is treated as a continuum with effective bulk properties, notably porosity and permeability as shown in Figure 9. The Navier-Stokes equations are adapted to account for flow resistance inside the medium. A CFD simulation of a drop impacting a porous medium is shown in Figure 10. By way of contrast, in the microscopic models, the media is represented by its constituent materials. Since the geometry of the media is fully described, there is no need to specify a bulk porosity or permeability. A CFD analysis can be performed to understand fundamental ink-media interactions as shown in Figure 11.

Porous Media Model: Many commercial CFD packages have a porous media model that can be used to predict ink media interactions. In this approach, the fluid dynamic equations are adapted to account for flow inside the medium. For example, in the FLOW3D program (www.flow3d.com ) the Navier-Stokes equation is modified to account for a distributed flow resistance. An example of an analysis using this approach is shown in Figure 10. Here, a 30 mm drop of water is incident on a porous media at a velocity of 10 m/s. Upon impact, the droplet initially spreads and then absorbs into the medium. Figure 10 and 11 show the pressure distribution after impact and during absorption.