Solving the World’s Toughest CFD Problems

## Optimization of Magnetic Blood Cleansing Microdevices

a Department of Chemical and Biomolecular Engineering, University of Cantabria, Spain
b State University of New York at Buffalo, Buffalo (NY), USA

## Separation of toxins with magnetic particles. Why is it so important?

The use of magnetic particles has recently expanded for a process known as detoxification in which different toxins are extra-corporeally captured from the bloodstream of intoxicated patients. The detoxification of biofluids is the most conceivable treatment in a high number of clinical conditions, some of them associated with high mortality rates such as sepsis. This is a lethal disease caused by a microbial infection that spreads through the bloodstream to overwhelm the body’s defenses. It represents the primary cause of death in hospital intensive care units, afflicting 18 million people yearly and accounting for over 200,000 deaths annually in the United States alone. The mortality rate can increase as much as 9% for every hour before the administration of the correct therapy. Hence, rapid elimination of the toxins is of paramount importance even in state-of-the-art hospital intensive care units.

We found that the limitations of the current treatments require the development of novel strategies such as the use of magnetic beads as toxin sequestering agents. Due to the magnetic properties of the particles, once the capture of the pathogens is complete, their separation from the patient’s blood can be performed in a continuous process using an external magnetic field generated by a permanent magnet. From the multiple magnetic microseparators developed in the last decade, we proposed the use of two-phase continuous-flow systems. These systems may be the best alternative because any flow restrictions and any degradation of the biofluid (i.e., non-specific entrapment of cells in the capturing region) are avoided, thus maintaining the efficacy and capacity of the system over time [1]. However, the optimization of these processes has been less studied and rational design is often lacking because of the complexity associated with their mathematical description. Therefore, we modeled the separation of magnetic beads from flowing blood streams inside a multiphase system with FLOW-3D in order to optimize the design of extracorporeal detoxification processes. In the proposed separator design, shown in Fig. 1, the beads are continuously injected through the upper inlet, deflected by the application of a magnetic gradient and collected into a flowing buffer stream. In order to achieve the efficient separation avoiding the mixing of the fluid phases, magnetic and fluidic forces were carefully studied and optimized. A detailed study of particle-fluid interactions as the beads are deflected is also provided.

## Modeling approach with FLOW-3D

The model for predicting the magnetophoretic particle transport inside the bioseparator shown in Fig. 1 consists of a CFD-based Eulerian-Lagrangian approach. We used the Lagrangian framework to model the bead dynamics, whereas the fluid transport, which is predicted by solving the Navier-Stokes equations, is calculated with an Eulerian approach. According to the Lagrangian approach, particles were modelled as discrete units and the trajectory of each one was estimated by applying classical Newtonian dynamics. Although different force contributions act on the particles during separation, we considered only the dominant magnetic and fluidic forces for predicting the bead trajectories under magnetic gradients generated by permanent magnets. We obtained different particle trajectories and thus, separation efficacies, by varying the distance between the lower wall of the channel and the top of the magnet, while keeping the same inlet velocities of the fluids (0.035 m·s-1 for the buffer and 0.01 m·s-1 for blood solution). More details of the modeling effort we developed can be found in our published work [1, 2].

## Particle magnetophoresis results

By varying the position of the magnet, we demonstrated that variable magnetic field gradients are generated, and thus, different separation efficacies were obtained. Figure 2 shows where the trajectories of the particles under different distances “d” between the magnet and the channel: For distances between 0 and approximately 1 mm, all the particles are separated independently of their original position at the inlet. For larger distances, the separation is incomplete due to the low magnetic forces. Medium to high magnetic forces are necessary for achieving complete particle separation. However, we demonstrated that high magnetic forces are undesirable for detoxification purposes due to the extreme acceleration of the particles that leads to perturbations of the flow patterns and to disruption of the fluid interface, as seen in Fig. 3. Therefore, medium magnetic forces appear to be optimum for this kind of system, because complete bead separation can be achieved while maintaining  blood integrity.

## Conclusions

In this work, we introduced a novel FLOW-3D model for predicting and optimizing the process of magnetic bead separation from blood in a multiphase continuous-flow microdevice. This model takes into account the dominant forces acting on the particles and can be used to study critical details of the separation process, including the trajectories of individual particles, the time required for the separation, and the perturbation of the blood/buffer co-flows. A critical element of this work is that we studied the interaction between two fluids flowing simultaneously in the device while taking into account the effects of particle-fluid interactions in the flow field. These issues are very important since the solutions should flow independently along the length of the channel and be separated at their respective outlets, avoiding any possible blood loss or dissolution. The methodology followed here provides a rational design guide since it can be used to predict particle separation by taking into account key operational variables and parameters. It applies generally for parametric analyses and optimization not only for blood detoxification processes, but also for other studies that involve multiple confined liquid phases inside microfluidic devices. Our future work will focus on the experimental analysis of the process using whole blood and the integration of the magnetic separation stage with the removal of the toxins in order to design novel detoxification processes.

### Acknowledgements

Financial support from the Spanish Ministry of Economy and Competitiveness under the projects CTQ2015-66078-R (MINECO/FEDER) and CTQ2015-72364-EXP/AEI is gratefully acknowledged. Jenifer Gómez-Pastora also thanks the FPI postgraduate research grant (BES-2013-064415). Edward P. Furlani gratefully acknowledges financial support from the U.S. National Science Foundation, through Award CBET-1337860.

### References

[1] Gómez-Pastora et al., Separation and Purification Technology2017, 172, 16–31.

[2] Gómez-Pastora et al., Journal of Physical Chemistry C2017, 121, 7466−7477.

## Computational Analysis of Drop Formation and Detachment

This article was contributed by Jelena Dinic and Vivek Sharma, Department of Chemical Engineering, University of Illinois at Chicago, Chicago, IL

## Introduction and Problem Statement

The rapid, repeated, precise creation and deposition of droplets, printing or patterning of small features (say l = 10-3-1 mm), and the formation of thin films with controlled, uniform thickness by spraying, are of great importance to a variety of old and new industrial applications (1-5). The liquid transfer and drop formation/deposition processes involve complex free-surface flows and formation of columnar necks that undergo spontaneous capillary-driven instability, thinning and pinch-off (1-5). Despite the progress made using experimental, theoretical and one-dimensional simulation studies for analyzing drop formation and liquid transfer for simple Newtonian and inelastic fluids, mechanistic understanding of printing and spraying remains a challenge. The primary motivation for the present computation effort is to examine the possibility of using the volume-of-fluid (VOF) approach embedded in the FLOW-3D to obtain mechanistic understanding of pinch-off dynamics of Newtonian fluids. We show that our computational analysis captures the complex interplay of capillary, inertial and viscous stresses that determines the self-similar capillary thinning and pinch-off dynamics. For the drop formation and detachment of Newtonian fluids, we show that the self-similar neck evolution obtained from the computational analysis can be described using the universal scaling laws expected from theory and 1D simulations (1-7) as well as experiments (1, 2, 8-12). Our success in simulating such prototypical flows is a necessary step towards using FLOW-3D for careful computational analysis of the nonlinear dynamics underlying finite-time singularity, satellite drop formation as well as printability in more complex geometries, that are significantly harder to describe or study using 1D models and experiments.

## Modeling Approach and Parameter Space

Simulations of drop formation and detachment from a nozzle were performed using uniform mesh size in FLOW-3D by using the Surface Tension and Gravity models. Drop formation and detachment of a finite volume of fluid involves the interplay of capillarity, inertia, viscosity and gravitational-induced drainage within a neck that connects a pendant growing drop to a nozzle. In the simulation, a finite volume of a Newtonian fluid is issued from a stainless steel nozzle (${{D}_{0}}=2{{R}_{0}}=1.7\,\text{mm}$). Detachment of a newly formed drop occurs once the gravitational force overcomes surface tension force ($mg>2\pi \sigma {{R}_{0}}$). Simulations are divided into two groups to elucidate the dramatic influence of fluid viscosity: low viscosity fluids (e.g., water and glycerol/water mixtures with glycerol content <40% by weight) and high viscosity fluids (e.g. glycerol and glycerol/water mixtures with shear viscosity > 100x Water Viscosity). Properties of the fluids of both groups are listed in Table 1 and 2, respectively.

Simulation of low viscosity fluid (Fluid 2 in Table 1) dripping from a nozzle. Color variable is the velocity magnitude (units: cm/s) and velocity vectors are shown.

Simulation of high viscosity fluid (Fluid 8 in Table 2) dripping from a nozzle. Color variable is the velocity magnitude (units: cm/s) and velocity vectors are shown.

## Discussion of the Simulation Results

Drop formation and detachment was simulated using FLOW-3D for fluids listed in Table 1 and 2, and the neck shape and neck radius evolution over time were analyzed. The shape of the neck and the neck thinning dynamics of low viscosity fluids (see Figure 1) exhibits the characteristic self-similar, inertio-capillary thinning behavior, anticipated by experiments, potential flow theory and 1D simulations (1, 2, 6, 7, 13):

(1) $\displaystyle \frac{{R(t)}}{{{{R}_{0}}}}\approx 0.8{{\left( {\frac{\sigma }{{\rho R_{0}^{3}}}} \right)}^{{\frac{1}{3}}}}{{\left( {{{t}_{c}}-t} \right)}^{{\frac{2}{3}}}}$

Here R(t) is the instantaneous radius of the neck, R0 is outer radius of the nozzle, $\displaystyle \sigma$ is the surface tension, $\displaystyle \rho$ is the density of the fluid and tc is the pinch-off time. Likewise, the radius evolution datasets for these higher viscosity Newtonian fluids appear to show a linear decrease in neck radius with time, and the thinning dynamics follow Papageorgiou’s visco-capillary scaling (8, 9) described by the following expression:

(2) $\displaystyle \frac{R}{{{{R}_{0}}}}=0.0709\frac{\sigma }{{{{\eta }_{s}}{{R}_{0}}}}({{t}_{p}}-t)$

We find that the measured values of capillary velocity (ratio of surface tension and viscosity) are comparable to the values obtained using commercially-available instrument called Capillary Break-up Extensional Rheometer (CaBER) by McKinley and Tripathi (8), and to the capillary velocity computed using their nominal surface tension and viscosity.

FLOW-3D allows for visualization of velocity vectors in the neck during thinning which gives insight into a nature of the flow. In addition, it gives the possibility of determining the moment during thinning after which the flow field within the thinning neck after initially experiencing a combination of shear and extension becomes purely extensional as shown in Figure 1. Additionally, thinning dynamics of low viscosity fluids show a qualitatively different behavior compared to high viscosity Newtonian fluids (see Figure 2). The neck profile for a low viscosity Newtonian fluid, becomes self-similar in agreement with theory (6, 13), in frames leading to the pinch-off.

## Conclusions, Outlook and Ongoing Work

Our preliminary results show that FLOW-3D based computational analysis can be used for simulating prototypical free-surface flows underlying drop formation and detachment. We find that the simulated radius evolution profiles match the scaling laws and pinch-off dynamics that are experimentally-observed and theoretically-predicted for inviscid fluids as well as high viscosity Newtonian fluids.

In contrast with often-used 1D or 2D models, FLOW-3D allows a robust evaluation of the magnitude of the underlying stresses and extensional flow field (both uniformity and magnitude) and the visualization of the flow filed within the thinning liquid filament (see Figure 1 and 2, for example). Stream-wise velocity gradients associated with extensional flow field arise within the columnar necks undergoing capillary-driven thinning. In rheologically-complex fluids, extra elastic stresses as well as non-Newtonian shear and extensional viscosity dramatically alter the nonlinear pinch-off dynamics (2, 10-12). We are currently implementing constitutive models with viscoelasticity and non-Newtonian rheology into FLOW-3D to develop robust computational protocols for assessing processability of complex fluids.

### References

1. J. Eggers, Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865-929 (1997).
2. G. H. McKinley, Visco-elasto-capillary thinning and break-up of complex fluids. Rheology Reviews, 1-48 (2005).
3. B. Derby, Inkjet Printing of Functional and Structural Materials: Fluid Property Requirements, Feature Stability, and Resolution. Annual Review of Materials Research 40, 395-414 (2010).
4. O. A. Basaran, H. Gao, P. P. Bhat, Nonstandard Inkjets. Annual Review of Fluid Mechanics 45, 85-113 (2013).
5. S. Kumar, Liquid Transfer in Printing Processes: Liquid Bridges with Moving Contact Lines. Annual Review of Fluid Mechanics 47, 67-94 (2014).
6. R. F. Day, E. J. Hinch, J. R. Lister, Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80, 704-707 (1998).
7. J. Eggers, M. A. Fontelos, Singularities: Formation, Structure, and Propagation. (Cambridge University Press, Cambridge, UK, 2015), vol. 53.
8. G. H. McKinley, A. Tripathi, How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J. Rheol. 44, 653-670 (2000).
9. D. T. Papageorgiou, On the breakup of viscous liquid threads. Phys. Fluids 7, 1529-1544 (1995).
10. J. Dinic, L. N. Jimenez, V. Sharma, Pinch-off dynamics and dripping-onto-substrate (DoS) rheometry of complex fluids. Lab on a Chip 17, 460-473 (2017).
11. J. Dinic, Y. Zhang, L. N. Jimenez, V. Sharma, Extensional Relaxation Times of Dilute, Aqueous Polymer Solutions. ACS Macro Letters 4, 804-808 (2015).
12. V. Sharma et al., The rheology of aqueous solutions of Ethyl Hydroxy-Ethyl Cellulose (EHEC) and its hydrophobically modified Analogue (hmEHEC): Extensional flow response in capillary break-up, jetting (ROJER) and in a cross-slot extensional rheometer. Soft Matter 11, 3251-3270 (2015).
13. J. R. Castrejón-Pita et al., Plethora of transitions during breakup of liquid filaments. Proc. Natl. Acad. Sci. U.S.A. 112, 4582-4587 (2015).

This article was contributed by Prof. Edward Furlani and his students from the University at Buffalo, SUNY.

Microfluidics and nanofluidics are interdisciplinary fields that involve the science and technology of fluid flow through materials and systems with micro to nanoscale features. Research and applications in these fields have proliferated in recent years due to unique advantages of small-scale fluidic processes combined with rapid advances in materials development and system integration. Microfluidic and nanofluidic systems enable highly efficient, repeatable and rapid processing of small fluid samples for applications that can involve integrated sequential or multiplexed processes such as chemical reactions, fluid heating, mixing, and sensing. Research in Professor Furlani’s group involves modeling and simulation towards the development of novel processes and devices. Much of this work emphasizes the use of state-of-the-art computational fluid dynamics (CFD) analysis for studying fluidic phenomena involving Newtonian and non-Newtonian fluids, conjugate heat transfer, phase change analysis, free-surface and multiphase analysis, fluid media interactions, flow through porous media, fully coupled fluid-structure and particle-fluid interactions and colloids. Three papers will be presented at the International Nanotech Conf. 2014 that will take place June 15-18, at the Gaylord National Hotel and Convention Center in Washington, D.C. They showcase some of the breakthrough work being done at the University at Buffalo. Here we present a preview of these works and some of the simulation results that were generated with FLOW-3D.

## Analysis of Stem Cell Culture Performance in a Microcarrier Bioreactor System

Koushik Ponnuru1, Jincheng Wu1, Preeti Ashok1, Emmanuel S. Tzanakakis1,3,4,5,6 and Edward P. Furlani1,2

1Dept. of Chemical and Biological Engineering, 2 Dept. of Electrical Engineering, 3Dept. of Biomedical Engineering, 4New York State Center of Excellence in Bioinformatics and Life Sciences, 5Western New York Stem Cell Culture and Analysis Center, 6Genetics, Genomics and Bioinformatics, University at Buffalo, SUNY

An analysis of the effects of the turbulent shear stress on cell culture in a stirred tank microcarrier bioreactor system using a synergistic combination of CFD-based simulations and experiments is presented. A 3D computational model of Corning’s bench-scale spinner flask was built using a state-of-the-art CFD software, FLOW-3D. The effects of parameters such as the impeller speed, culture medium fluid properties, and particle size on the steady-state shear stress acting on the cell-laden microcarrier particles in the bioreactor are studied using CFD analysis. This is used to predict the precise shear conditions experienced by cells and identify optimum operating conditions that prevent turbulent shear damage of the cells. In addition, the effect of the shear of the pluripotency of hPSCs is studied by determing the percentage of cells carrying the pluripotency markers Oct4, Sox2, and Nanog using flow cytometry and quantitative PCR.

## Numerical Analysis of Fully-Coupled Particle-Fluid Transport and Free-Flow Magnetophoretic Sorting in Microfluidic Systems

Chenxu Liu1, Xiaozheng Xue1 and Edward P. Furlani 1,2

1Dept. of Chemical and Biological Engineering, 2Dept. of Electrical Engineering, University at Buffalo, SUNY

Magnetic particles are increasingly used in microfluidic systems to selectively separate and sort biomaterial for biomedical and clinical diagnostic applications. A computational model is introduced that can be used for the rational design of such systems. The model takes into account dominant mechanisms that govern particle transport including magnetic and hydrodynamic forces, fully-coupled particle-fluid interactions, and magnetic dipole-dipole interactions that induce self-assembly of the particles. It is demonstrated via application to a continuous flow separation system and a microfluidic mixing process based on rotating self-assembled particle chains.

## Numerical Analysis of Laser Induced Photothermal Effects using Colloidal Plasmonic Nanostructures

Ioannis H. Karampelas1, Young Hwa Kim2 and Edward P. Furlani 1,2

1Dept. of Chemical and Biological Engineering, 2 Dept. of Electrical Engineering, University at Buffalo, SUNY

Colloidal noble metal (plasmonic) nanostructures are finding increasing use in a variety of photothermal applications that range from nanoparticle synthesis to bioimaging to medical therapy. In many applications, a pulsed laser is used to excite the nanostructures at their plasmon resonance frequency, which results in a peak absorption of incident photons and highly localized (sub-wavelength) field enhancement. In addition to enabling efficient nanoscale heating from a remote source, the resonant heating wavelength can be tuned within the ultraviolet through near-infrared spectrum by adjusting the geometry of the nanoparticle during synthesis. Our group has developed computational models that predict fundamental photonic and thermo-fluidic behavior of nanosecond-pulsed, laser-heated colloidal metallic nanoparticles. These models have been used to simulate energy conversion within nanoparticles at plasmon resonance, heat transfer from a particle to the surrounding fluid and phase change of the fluid leading to homogenous bubble nucleation. Various nanoparticle geometries have been studied including nanorods, nanotori, nanorings and nanocages. The analysis shows that process parameters such as the laser intensity, incident wavelength, polarization, pulse duration and the orientation and shape of the nanoparticles can be tuned to optimize the photothermal process. Plasmonic nanoparticles are currently used in photothermal applications involving bioimaging, drug delivery and the therapy of malignant tissues.

## Microscopic Bubbles Switch Fiber-Optic Circuits

Computer simulation played a critical role in understanding and solving a problem with microscopic bubbles in a revolutionary switch used to switch optical signals in fiber-optic circuits. The Agilent Photonic Switching Platform operates by blowing bubbles in just the right spots in a tiny trench cut in a planar lightwave circuit. The bubbles redirect light beams into different paths in order to reconfigure fiber-optic networks. Early prototypes showed performance problems that indicated the something was unstable with the bubble reflection. But the small size of the bubbles made it impossible to make the comprehensive physical measurements that would be needed to diagnose and solve the problem.

Agilent senior scientist John Uebbing used computational fluid dynamics (CFD) software to simulate the bubble. The bubble is sustained by evaporation induced by electrical heaters located in the silicon substrate. The Agilent team discovered that the corresponding condensation on the walls of the trench causes a fluid buildup. It is this buildup that determines much of the behavior of the switch. Further simulations helped the researchers validate two different methods of altering the device to give stable signals. “At first, some members of our team refused to believe these results, but continued physical testing proved they were true,” Uebbing said. “Without CFD, we would never have gotten to the bottom of this problem.”

## Developing a New Technology

Fiber-optic cable has provided dramatic increases in data communications throughput, and there has been a big desire to be able to switch large volumes of fiber optic data without turning the optical signals into electrical signals for switching and then back to optical signals. In the mid-1990’s, Agilent Laboratories (when it was part of Hewlett-Packard Labs) realized the importance of an all-optical circuit switch and started a research program to develop such a technology. A team of engineers and scientists was formed within what is now Agilent Labs’ Communications and Optical Research Laboratory (CORL) to develop this unique switch fabric, which is compact, scalable, and has minimal impact on the optical signal. The team capitalized on two very established technologies – inkjets and planar lightwave circuits — to build a switch that routes an optical beam from one path to another without having to convert the switching signal from optical to electronic and back.

Simulation helped us determine exactly what was causing the dimple and helped us to identify and evaluate several alternative solutions. This progress in bubble switch engineering would not have been possible without the advanced modeling features available in the FLOW-3D software. Just as important for us was the knowledge and integrity demonstrated by the Flow Science team from the start of the project. While the other software companies that we talked to had sales reps with only a surface understanding of the issues involved, Flow Science engaged technical staff with the expertise to understand exactly what we wanted to accomplish. At several stages of the process, they provided critical help that allowed us overcome significant obstacles. – John Uebbing, Agilent senior scientist

In order to work, the Agilent Photonic Switching Platform is placed at the intersection of two fiber-optic networks (Figure 1). When a light signal comes in through a fiber, it can cross the planar lightwave circuit unimpeded via the straight through wave-guide. However, if the signal must be redirected to a different optical fiber, inkjet technology inserts a bubble into the cross point of the two wave-guide paths, altering its optical properties and reflecting the signal down the path to the output fiber. The bubbles can be formed and removed in less than five milliseconds, all without the use of mirrors or mechanical moving parts. This switch operates by blowing bubbles in a fluid that is index-matched to the array of crossed optical wave-guides. The bubbles are formed by evaporation induced by electrical heaters on the device substrate. The fluid fills an array of micro-trenches located at the cross points of the waveguides. Total internal reflection from the bubble wall causes light to be switched from one waveguide to another. The problem is that the acceptance angle, or numerical aperture, of the optical waveguides is fairly low. If the vertical reflecting wall of the bubble is not perpendicular to the axis of the waveguide, the light will not be properly reflected into the output wave-guide and there will be signal loss.

## Dimples Impact Performance of Prototypes

Extensive experimental testing was performed on early prototypes, showing the effects of heater power and ambient pressure on the optical reflection characteristics and on the bubble shape and size. These tests showed that the reflected optical signal vs. heater power curve not did not meet the tight requirements needed for effective optical switching and that there were instabilities in the reflected light signals.

When the computer simulations showed that there were dimples forming on each side of the bubble as shown in Figure 2, it dawned on the Agilent research team that the dimples might be what caused the humps on the power curve and why the reflected signal was so unstable. The team’s ability to take physical measurements with sensors did not extend to the scale of the MEMS device. The most they could do was use special optics to take photomicrographs. These pictures could not show the dimple directly, because the dimple is very thin on a wavelength scale.

## Simulating the Bubble

Initially, a number of alternatives for simulating the operation of the bubble were considered. The team had been using various analytical models to investigate the bubble formation, but these models predicted that the current prototypes should produce good bubbles, so they were clearly too simple to capture the problem. A college professor was hired to write custom software but this project was going to take a considerable amount of time to complete. In the meantime, Uebbing began searching for a commercial software package that could handle the complicated physics of the problem. “I talked to several CFD software developers but from what I could determine none of them had a bubble model that would solve the problem without extensive modification,” Uebbing said. “Flow Science, on the other hand, said they were working on a model that they thought could handle the problem and that it would be ready soon.”

Flow Science’s new homogeneous bubble model assumes a uniform bubble pressure and temperature. This is a good approximation to reality. One of the key issues is the modeling of the contact line, where the liquid, vapor and solid all come together. The homogenous bubble model balances the forces and fluxes in the computational cell at this point. Uebbing started out using the older version of the software, but as soon as the new model was released, Uebbing tried it on the problem at hand. “The simulation results showed the dimples that were eventually to prove so important in explaining the experiments,” Uebbing said. “Just as interestingly, the simulation showed that the bubble oscillated at 35 kHz. We had taken experimental data that showed it really did oscillate at that frequency, but we had no idea why. The simulation showed that it was just a simple spring mass or a trenched version of the classic bubble radial oscillation.

This rather unexpected correlation with reality gave the team confidence in the results of the simulation. The simulation results went far beyond what we were able to measure in the tests by showing us the flow velocity, pressure and temperature at every point in the problem domain. With these results we were able to figure out what was happening. The dimple is caused by capillarity. What happens is the condensing fluid piles up on the wall of the bubble. It tries to escape through the thin film of the liquid on the wall of the trench. To push liquid through such a thin layer requires a significant pressure difference. The high pressure in the center of the bubble wall causes the bubble to form a dimple.”

## Solving the Problem

Understanding how the dimples were formed suggested two methods of correcting the shape of the bubbles in order to provide stable signals. The first is to extend the bubble heater under the glass sidewall of the trench. Heat then flows up the wall of the micro-trench and dries out its surface. Simulations with FLOW-3D show that dry wall bubbles give very stable switched signals. Basic physics suggests that if the bubble temperature is less than the wall temperature the wall will be dry. This expectation was confirmed with FLOW-3D simulations.

The second method, also verified with FLOW-3D, is to make a so-called static bubble in the micro-trench. Static bubbles exist if the device temperature is somewhat hotter than the pressure setting reservoir temperature. This device temperature creates enough pressure to push the bubble into the corners of the trench, but not enough for the bubble to blow out through the gap between the waveguide array and the heater substrate. These static bubbles can be turned off with a nearby “crusher” bubble. This bubble temporarily generates enough overpressure to cause the static bubble to collapse. The crusher bubble itself is in a smaller trench so that surface tension forces are enough to make it collapse after it has done its work. FLOW-3D simulations were also used to show the switch operation in this mode.

Developing a new inkjet printhead technology is challenging because the extremely high speed and tiny size of these microelectromechanical systems (MEMS) make them very difficult to measure or observe. Océ Technologies has met this challenge by using a combination of several different computer simulation technologies to understand how inkjet design parameters affect printhead performance.

For the computational fluid dynamics work, Océ used FLOW-3D to predict the free-surface flow with surface tension and wall flexibility. Simulations enable Océ engineers to quickly evaluate the performance of a wide range of possible designs and zero in on the most promising alternatives into which substantial time and expense required for MEMS prototyping is invested. Using CFD simulation to confirm and improve their inkjet printhead performance, Océ was recently able to develop new wide-format printers delivering a printing speed much faster than the current generation of printers.

An electric voltage on a piezo element enlarges the channel and a negative pressure is generated. After reflection at the reservoir this pressure is amplified by the second slope of the driving waveform to get a large positive pressure peak at the nozzle, which fires a drop.An inkjet printhead contains many long channels with a nozzle at one end and an ink reservoir at the other end. A piezo actuator element provides the driving force by enlarging and contracting the channel which produces pressure waves. To initiate the firing cycle, the actuator first enlarges the channel cross-section, producing a negative pressure wave that is reflected at the reservoir. In the second step, the driving voltage is turned off, thus reducing the channel cross-section to its original size and amplifying the reflected positive pressure wave, which fires a drop. The head of the drop drags a long tail along. Long tails are formed when the head of the drop has a higher speed than the tail and the tail breaks up into satellite droplets. After the drop is fired, the channel is refilled with ink.

## The Challenge of Doubling Printhead Speed

Océ’s goal in designing the new printhead was to increase speed by at least a factor of two while maintaining print quality and reliability at levels equal to or better than the high standards of the previous generation of printheads. They also wanted to keep driving voltages low to reduce power consumption and the cost of the electronics. Doubling the speed of the printhead meant increasing the frequency of the driving electronics to several tens of kHz. In order to maintain print quality at this speed, it was necessary to maintain a high drop speed. Drop speed is usually limited by the tail because if the tail gets too long it will break up into satellite drops which will adversely affect quality. So, one of the key factors in increasing the speed of the printhead is increasing the tail speed.

Another critical factor in increasing the speed of the printhead is refilling the printer at a faster rate without wetting the nozzle to a degree that would affect print quality. In order to fire drops at a very high speed, free-surface flow in the nozzle and acoustics in the channel must be designed to refill the nozzle very quickly. However, this creates a tendency for the nozzle to overfill which can cause wetting of the nozzle plate. A wet nozzle can affect drop formation depending on the thickness of the wet layer and the size of the drop. For example, 5 micron wetting will not be a problem with a 50 micron droplet but will have a major effect on a 10 micron droplet.

## Build and Test vs. Simulation

Earlier generations of inkjet printers were designed by building and testing prototypes. The problem with this approach is that it takes several months to physically build and test a printhead. In addition, it’s very difficult to obtain diagnostic information when testing because of the small size and the high speed at which it operates. Droplets can be observed by optical methods such as stroboscopic illumination but the critical phenomena inside channels are very difficult to measure.

For these reasons, Océ engineers rely heavily on computer simulation to evaluate printhead performance prior to building prototypes. The simulation of printhead operation is complicated by multiple physical mechanisms. FEA modeling is used to understand the deformation of the printhead walls when voltage is applied to the piezo elements, and also to identify complex interactions of the printhead structure dynamics with channel acoustics.

A 2D axi-symmetric FLOW-3D model is used to obtain the details of the drop formation process. This is the most challenging part of the simulation because of the difficulty of modeling free surfaces. Océ engineers previously evaluated all of the leading CFD software programs for their ability to handle this challenging simulation problem. They simulated the printhead using each of the codes and compared the results to physical experiments. For example, they evaluated the ability of each software program to correctly predict the formation of a drop and its secondary tail. FLOW-3D‘s simulation results were very close to Océ’s experimental measurements and were substantially more accurate than the other CFD programs. Océ has been using FLOW-3D for many years and has found that the software continually provides highly accurate results.

The secondary tail has a width of about 1 micron, which is close to the optical resolution of the measurement setup. The recordings are made using a strobe, so only the reproducible part of the drop formation is shown.Océ engineers also used FLOW-3D to simulate the effects of their design parameters, such as evaluating tail breakup based on such factors as ink viscosity and channel geometry. Simulation allowed them to examine the formation of a secondary tail as a consequence of going through three flow regimes with different dominating forces.

First the tail width decreases slowly with only viscous and surface tension forces present. Then, when the tail starts to break off, inertia, becomes important and the tail width decreases rapidly. Viscous forces play no role when the tail width becomes smaller than the viscous length scale. With two remaining factors, surface tension and inertia, the tail width again decreases slowly. The small secondary tail breaks up into very small droplets, which are dragged along with the airflow induced by the firing sequence of drops.

## Simulation Matches Physical Measurements

FLOW-3D provides very accurate predictions of even the finest details of the tail breakup as can be seen by comparing Figures 2 and 3. The accuracy of these predictions makes it possible to determine the effect of varying design parameters on tail breakup with a high degree of precision. FLOW-3D simulations can take several days, but this is much faster than the several months required to build and test a prototype. However, Océ engineers have developed a method that enables them to evaluate the performance of a combination of design variables even more quickly.

They perform multiple simulations with FLOW-3D to determine the sensitivity of various design objectives such as tail speed to design variables such as channel length and nozzle diameter. They use these results to write a MATLAB routine that can provide predictions of the performance of thousands of different combinations of design variables in a single day. When Océ engineers identify a promising new design through the MATLAB routine, they run a more detailed FLOW-3D simulation to verify its performance. Using this approach, they narrowed tens of thousands of possible design combinations down to just a few that provided the combination of high-speed print performance, optimal print quality, high reliability and low manufacturing costs need for the new printhead design.

When Océ engineers built and tested the prototypes they discovered that performance closely matched FLOW-3D’s simulation results. The new printheads will be used in a family of wide-format printers, ranging in width from 42 to 62 inches, that significantly increase the performance in terms of productivity, quality, reliability and running costs. Without using CFD simulations, Océ’s engineers believe this project would have required at least twice as much time using traditional design methods, if it could have been accomplished at all.