Printhead Design Research Articles

High-density, high-frequency and large-scale electrohydrodynamic drop-on-demand jetting via a protruding polymer-based printhead design

Electrohydrodynamic (EHD) printing has critical merits in micro/nanoscale additive manufacturing because of its ultrahigh resolution and wide ink compatibility, making it an advantageous choice for electronics manufacturing, high-resolution prototyping, and biological component fabrication. However, EHD printing is currently limited by its rather low throughput due to the lack of high-frequency and high-density multi-nozzle printheads. This paper presents a novel EHD printhead with a protruding polymer-based nozzle design. An insulated, hydrophobic, and protruding polymer nozzle array with an appropriate geometric structure can effectively address key problems in multi-nozzle jetting, such as electrical crosstalk, electrical discharge, liquid flooding, and nonuniform jetting. By investigating the influence of the electrical and geometric characteristics of the nozzle arrays on the electrical crosstalk behavior and fabricating the optimized nozzle array via MEMS technology, we achieve an EHD printhead with a large scale (256), high density (127 dpi), and high jetting frequency (23 kHz), and addressable jetting can be realized by adding independently controllable extractors underneath the nozzle array. Many functional materials, such as quantum dots, perovskite, and nanosilver inks, can be ejected into high-resolution patterns through the optimized nozzle array, demonstrating the great prospects of our designed printhead in electronics manufacturing. This MEMS-compatible printhead design lays the foundation for high-throughput fabrication of micro/nanostructures and promotes practical applications of EHD printing in functional electronics and biomedical/energy devices.

Ultrasonic vibration-assisted high-resolution electrohydrodynamic (EHD) printing

Electrohydrodynamic (EHD) printing has become a promising and cost-effective technique for producing high-resolution and large-scale features. One widely recognized obstacle in EHD printing is nozzle clogging due to solvent evaporation or ink polymerization. Moreover, printing highly viscous materials often requires pressure or other external force to assist the ink flow during the printing, which increases the complexity of process control and the required energy. In this work, we developed a novel ultrasonic vibration-assisted EHD printhead and associated process to effectively eliminate the nozzle clogging for the printing of high-viscosity and high-evaporation-rate inks. A series of experimental tests were conducted to characterize the printhead design and process parameters (i.e., vibration frequency, vibration amplitude, and printing voltage). The results demonstrated that superimposing ultrasonic vibration on the EHD printing nozzle can effectively enhance current EHD printing capabilities, such as reducing required pressure, eliminating nozzle clogging, and providing stable and continuous printing for high viscosity and high solvent evaporation rate material. With the optimal parameters, a filament with a diameter of around 1 µm can be continuously printed. In the paper, we successfully applied this developed ultrasonic-assisted EHD process to print high-resolution 2D patterns.

A versatile 5-axis melt electrowriting platform for unprecedented design freedom of 3D fibrous scaffolds

Melt electrowriting (MEW) is an electrohydrodynamic additive manufacturing technology for the fabrication of precise microfiber scaffold architectures but is so far restricted to printing onto simple collector geometries and, therefore, constrained in design freedom. This is due to current limitations in print head designs, kinematic systems, and software to generate motion commands. We address these aspects by upgrading a low-cost 5-axis kinematic system and complete it with a custom-designed print head and a collector fabrication workflow to enable collision-free MEW onto arbitrarily shaped multicurvature 3D geometries. A universal graphical approach enables generation of Gcodes customized to the 5-axis MEW requirements. The print head is validated by producing polycaprolactone fibers with diameters ranging from 5.6 ± 1.7 µm to 50.7 ± 5.5 µm and by writing both linear and non-linear fiber patterns onto collectors featuring concave and convex surfaces. Stable printing conditions are achieved by continuously reorienting the print head and collector surface perpendicular to each other at a constant working distance. Ultimately, we demonstrate the system’s potential in shaping anatomically relevant scaffold geometries by stacking microfibers onto collectors resembling a trileaflet valve and a bifurcating vessel. This multi-axis MEW platform unlocks exciting avenues towards unprecedented design freedom for MEW scaffolds.

Optimizing Printhead Design for Enhanced Temperature Control in Extrusion-Based Bioprinting.

This study addresses critical challenges in the field of tissue engineering, specifically in the optimization of bioprinting technologies for the construction of complex, multicellular tissues. By utilizing a homemade piston-driven extrusion-based bioprinting (EBB) printhead, we performed detailed thermal and flow analyses to investigate the effects of temperature variations on the extrusion process of temperature-sensitive gelatin-alginate bioink. Through finite element method (FEM) simulations, we explored the temperature distribution within the printhead and its impact on bioink properties, such as viscosity, pressure, and shear stress. Key findings reveal significant temperature gradients from the printhead barrel to the nozzle tip, influencing bioink extrusion and filament morphology. This study further introduces an innovative hardware optimization with thermal insulators, designed to mitigate heat loss at the nozzle tip and ensure uniform temperature distribution. Both simulation and empirical printing experiments confirm the efficacy of thermal insulators in enhancing bioprinting fidelity and efficiency. This research contributes to the advancement of bioprinting technology by optimizing printhead design, with implications for improving the quality of bioprinted tissues and organs.

Multi‐Material Aerosol Jet Printing of Al/Cuo Nanothermites for Versatile Fabrication of Energetic Antennas

AbstractIn the present study, a nanoscale Al/CuO thermite system is patterned using a multi‐material aerosol jet printing technology. Morphological analysis of samples manufactured with different printing configurations reveal a strong effect of the printhead design on microstructure and degree of mixing between the constituent materials, providing insight on fundamental mechanisms of inline aerosol‐phase mixing during printing. The high‐resolution patterning capability of aerosol jet printing is leveraged to fabricate both blended nanoscale Al/CuO thermites and antennas containing the nanothermite, which exhibit rapid and low‐energy ignition upon exposure to a 2.45 GHz free space electromagnetic field, characterized by an ignition delay of ≈130 ms and ignition energy of ≈216 J. Moreover, the versatility of this approach is demonstrated by manufacturing compositionally graded samples, establishing multi‐material aerosol jet printing as a compelling and versatile platform for microscale energetic device fabrication with broader utility for graded materials. This work shows promise for use of the technique for in situ manufacturing of standalone and integrated energetics and electromagnetic devices.

Efficient Creation of Jettability Diagrams Using Active Machine Learning.

The ability to jet a wide variety of materials consistently from print heads remains a key technical challenge for inkjet-based additive manufacturing processes. Drop watching is the most direct method for testing new inks and print head designs but such experiments are also resource consuming. In this work, a data-efficient machine learning technique called active learning is used to construct detailed jettability diagrams that identify complex regions corresponding to "no jetting," "jetting," and "desired jetting," rather than only individually sampled points. Crucially, our active learning method has resolved challenges with model selection that previously limited the accuracy of active learning in practical settings with very small experimental budgets. In addition, the key "desired jetting" zone may be quite small which is a challenge for initializing active learning. We leverage the physical intuition that the "desired jetting" zone tends to exist between the "jetting" and "no jetting" zone, to improve the performance of this highly imbalanced classification problem by performing two binary classifications in sequence. The first binary classification aims to map out the "jetting" zone versus the "no jetting" zone, while the second binary classification targets identifying the "desired jetting" zone with primary drops only. Our experiments use a stroboscopic drop watcher to visualize the jetting behavior of two fluids from a piezoelectric print head with different jetting waveforms. The results obtained from active learning were compared to a grid search method, which involves running more than 200 experiments for each fluid. The active learning method significantly reduces the number of experiments by 80% while achieving a test accuracy of more than 95% in the "jetting" zone prediction for the test fluids. The ability to construct these jettability diagrams will further accelerate new ink and print head developments.

Millimeter-thick 3D tissues constructed by densely cellularized core–shell microfluidic bioprinting

Recently, microfluidic bioprinting methods, which utilize microfluidic devices as printheads to deposit microfilaments, have improved printing resolution. Despite the precise placement of cells, current efforts have not succeeded in forming densely cellularized tissue within the printed constructs, which is highly desired for the biofabrication of solid-organ tissues with firm tissue consistency. In this paper, we presented a microfluidic bioprinting method to fabricate three dimension tissue constructs consisting of core–shell microfibers where extracellular matrices and cells can be encapsulated within the core of the fibers. Using the optimized printhead design and printing parameters, we demonstrated the bioprinting of core–shell microfibers into macroscale constructs and checked the viability of cells after printing. After culturing the printed tissues using the proposed dynamic culture methods, we analyzed the morphology and function of the tissues both in vitro and in vivo. The confluent tissue morphology in the fiber cores indicates the establishment of intensive cell–cell contacts in the fiber cores, which also leads to the upregulation of the albumin-secretion function compared to the cells cultured in a 2D format. Analysis on the cell density of the confluent fiber cores indicate the formation of densely cellularized tissues with a similar level of cell density of in-vivo solid organ tissues. In the future, better culture techniques with improved perfusion design are anticipated to enable further the fabrication of thicker tissues, which can be used as thick tissue models or implantation grafts for cell therapy.

Computational fluid dynamics and experimental validation of aerosol jet printing with multi-stage flow focusing lenses

A 3D computational fluid dynamics (CFD) framework is presented to model and explain critical aerodynamic interactions occurring in the printhead during aerosol jet printing (AJP) with multi-stage flow focusing lenses. AJP has demonstrated great potential to fabricate complex circuits and conductive devices for numerous applications, including flexible electronics, medical diagnostic devices, and fuel cells. However, the devices manufactured by AJP are currently relegated to prototype roles due to poor repeatability of the deposited structures. The lack of process consistency in AJP arises from an incomplete understanding of causal aerodynamic interactions that influence the structure and repeatability of the printed features. Herein, a comprehensive CFD framework is presented to analyze the effects of gas flow rates, nozzle geometry, stand-off distance, printhead design, and aerosol droplet size on the resolution and morphology of printed features. Compressible Navier-Stokes equations with a k-ε turbulence model are solved to simulate flow conditions in the aerosol jet printhead. Additionally, a Lagrangian discrete phase model is used to simulate the transport of aerosolized ink droplets through the turbulent shear flow. The results highlight the crucial role of the design of the mist tube and the first aerodynamic lens, the density of the sheath gas, and the size of the droplets in the aerosol stream in determining print resolution and quality. A favorable comparison was found between numerically calculated results and experimental data obtained using the NanoJet™ system. CFD models presented in this work are expected to aid in identifying optimal process windows a priori, to improve process consistency.

Real-time vision-based control of industrial manipulators for layer-width setting in concrete 3D printing applications

In this paper, to have control over geometry specifications of rectangular bar-shaped layers in a robotic concrete 3D printing process, a real-time vision-based control framework is developed and proposed. The proposed control system is able to set the layer-width by automatically adjusting the velocity of an industrial manipulator during the 3D printing process of concrete based materials relying on a vision system feedback. Initially, details related to the control system, vision and processing units, and robotic platform are discussed. In continue, technical descriptions related to the printhead design, conversion process from a digital 3D drawing model to numerical motion control commands of an industrial manipulator and building material used in this work are reported. The reliability and responsiveness of the developed system is then evaluated through experimental tests by printing several single bar-shaped layers with different wideness by means of an unique printhead geometry and also by printing two layers with the same dimension centrally above another. Overall, the high accuracy and responsiveness of the developed system demonstrate a great potential for real-time vision-based control of industrial manipulators for layer-width setting in concrete 3D printing applications.

Material Extrusion Advanced Manufacturing of Helical Artificial Muscles from Shape Memory Polymer

Rehabilitation and mobility assistance using robotic orthosis or exoskeletons have shown potential in aiding those with musculoskeletal disorders. Artificial muscles are the main component used to drive robotics and bio-assistive devices. However, current fabrication methods to produce artificial muscles are technically challenging and laborious for medical staff at clinics and hospitals. This study aims to investigate a printhead system for material extrusion of helical polymer artificial muscles. In the proposed system, an internal fluted mandrel within the printhead and a temperature control module were used simultaneously to solidify and stereotype polymer filaments prior to extrusion from the printhead with a helical shape. Numerical simulation was applied to determine the optimal printhead design, as well as analyze the coupling effects and sensitivity of the printhead geometries on artificial muscle fabrication. Based on the simulation analysis, the printhead system was designed, fabricated, and operated to extrude helical filaments using polylactic acid. The diameter, thickness, and pitch of the extruded filaments were compared to the corresponding geometries of the mandrel to validate the fabrication accuracy. Finally, a printed filament was programmed and actuated to test its functionality as a helical artificial muscle. The proposed printhead system not only allows for the stationary extrusion of helical artificial muscles but is also compatible with commercial 3D printers to freeform print helical artificial muscle groups in the future.

Phase field simulation of electrohydrodynamic jet droplets and printing microstructures on insulating substrates

The phase field technique is a straightforward and effective mathematical model for resolving interfacial problems in E-Jet printing. The paper presents an exhaustive analysis for the Drop-on-demand electrohydrodynamic jet (DoD E-Jet) printing. The study introduces a phase field method to generate a stable cone jet morphology that can allow the production of micron/nano structures on different insulating substrates. Further, the impact of steel needle and quartz capillary were studied on the cone jet morphology for different insulating substrate. In trials, the optimal settings of flow rate and dc positive pulse voltage were adjusted to print drops for numerical simulation verification. However, a distinctive analysis of droplet formation on PET and glass substrates was demonstrated in order to lower droplet size and polarization of residual charges. The model is based on the Taylor–Melcher leaky dielectric model and employs the 2-phase field method to track the interface. The nozzle is capable of producing a magnificent micro-dripping jet and detaching stable drops from the substrate surface. As a result, the results are primarily concerned with droplet diameter and relative permittivity of ink. According to the simulation findings, microdroplets with a diameter of less than 100 μm are created on PET substrate with quick decay of residual charges, whereas drops with a diameter of less than 50 μm are formed on glass substrate. Furthermore, it is demonstrated in studies employing a nozzle with an internal diameter of 360 μm that is fixed to a quartz capillary with a diameter of 50 μm that it takes a significant amount of time, cost and effort. The approach can significantly guide printhead and parameter design for printing on insulating surfaces. It is a more convenient and efficient method for predicting pattern sizes with a small number of trials for MEMS device applications.

Study on driving waveform design process for multi-nozzle piezoelectric printhead in material-jetting 3D printing

Purpose Material-jetting (MJ) three-dimensional (3D) printing processes are competitive due to their printing resolution and printing speed. Driving waveform design of piezoelectric printhead in MJ would affect droplet formation and performance, but there are very limited studies on it besides patents and know-hows by commercial manufacturers. Therefore, in this research, the waveform design process to efficiently attain suitable parameters for a multi-nozzle piezoelectric printhead was studied. Therefore, this research aims to study the waveform design process to efficiently attain suitable parameters for a multi-nozzle piezoelectric printhead. Design/methodology/approach Ricoh’s Gen4L printhead was adopted. A high-speed camera captured pictures of jetted droplets and droplet velocity was calculated. The waveforms included single-, double- and triple-pulse trapezoidal patterns. The effects of parameters were investigated and the suitable ones were determined based on the avoidance of satellite drops and preference of higher droplet velocity. Findings In a single-pulse waveform, an increase of fill time (Tf) decreased the droplet velocity. The maximum velocity happened at the same pulse width, the sum of fill time and hold time (Tf + Th). In double- and triple-pulse, a voltage difference (Vd) above zero in the holding stage was adopted except the last pulse to avoid satellite drops. Suitable parameters for the selected resin were obtained and the time-saving design process was established. Research limitations/implications Based on the effects of parameters and observed data trends, suggested procedures to determine suitable parameters were proposed with fewer experiments. Practical implications This study has verified the feasibility of suggested design procedures on another resin. The required number of trials was reduced significantly. Originality/value This research investigated the process of driving waveform design for the multi-nozzle piezoelectric printhead. The suggested procedures of finding suitable waveform parameters can reduce experimental trials and will be applicable to other MJ 3D printers when new materials are introduced.

Multi-material stereolithography using curing-on-demand printheads

Purpose This paper aims to present a multi-material additive manufacturing (AM) process with a newly developed curing-on-demand method to fabricate a three-dimensional (3D) object with multiple material compositions. Design/methodology/approach Unlike the deposition-on-demand printing method, the proposed curing-on-demand printheads use a digital light processing (DLP) projector to selectively cure a thin layer of liquid photocurable resin and then clean the residual uncured material effectively using a vacuuming and post-curing device. Each printhead can individually fabricate one type of material using digitally controlled mask image patterns. The proposed AM process can accurately deposit multiple materials in each layer by combining multiple curing-on-demand printheads together. Consequently, a three-dimensional object can be fabricated layer-by-layer using the developed curing-on-demand printing method. Findings Effective cleaning of uncured resin is realized with reduced coated resin whose height is in the sub-millimeter level and improved vacuum cleaning performance with the uncleaned resin less than 10 µm thick. Also, fast material swapping is achieved using the compact design of multiple printheads. Originality/value The proposed multi-material stereolithography (SL) process enables 3D printing components using more viscous materials and can achieve desired manufacturing characteristics, including high feature resolution, fast fabrication speed and low machine cost.

The technology of continuous fibre-reinforced polymers: a review on extrusion additive manufacturing methods

Additive manufacturing technologies have transitioned from the fabrication of prototypes to final product manufacturing with competitive mechanical performance. The use of materials with high strength to weight ratio, and more specifically continuous fibre-reinforced composites, has demonstrated potential when fabricated through fused filament fabrication (FFF). The development and evaluation of such technologies has attracted a lot of attention in recent years, from both academic researchers and from industry, and a plethora of different techniques for its achievement has been proposed. This review presents different methods of FFF for the fabrication of continuous fibre-reinforced composite components as described in both patent and scholarly research literature. Different print head designs and techniques for combining and depositing polymers reinforced with continuous fibre have been developed including pre-impregnation, the use of multiple nozzles for the separate deposition of the fibre and the matrix material, and in situ impregnation of the reinforcing fibre with the matrix material. This review identifies the challenges associated with each of these approaches such as achieving a successful fibre/matrix impregnation, cutting of the continuous fibres during processing, and the introduction of high-performance thermoplastic polymers as the matrix material.

Sustainable additive manufacturing: predicting binder jettability of water‐soluble, biodegradable and recyclable polymers

AbstractAdditive manufacturing potentially generates customized polymeric objects with tailored geometry while reducing waste, employing biodegradable polymers and striving to use recyclable polymer feedstocks for a more sustainable future. Binder jetting additive manufacturing (BJ AM) creates 3D objects upon depositing liquid adhesive onto a powder bed, while a roller spreads powder over a build stage to form subsequent layers. Many factors affect jettability and printability including printhead design, binder material, binder solvent and powder characteristics. Material design for higher strength BJ AM parts using metals, ceramics or polymers exploits binders or particles that transform into thermosets or permanently shaped matrices through thermal or UV curing and sintering. While many BJ AM examples utilize biodegradable, water‐soluble and recyclable polymers for biomedical and industrial applications, a wider array of opportunities exist to degrade, dissolve and reuse printed materials. Systematically shifting to these polymers will facilitate reuse and recycling of both binders and powders, but more studies to improve part strength are required. This review describes an overview of polymer jettability and a perspective into opportunities currently underutilized in transitioning BJ AM into a more sustainable AM platform. © 2020 Society of Industrial Chemistry

High-throughput characterization of fluid properties to predict droplet ejection for three-dimensional inkjet printing formulations

Inkjet printing has been used as an Additive Manufacturing (AM) method to fabricate three-dimensional (3D) structures. However, a lack of materials suitable for inkjet printing poses one of the key challenges that impedes industry from fully adopting this technology. Consequently, many industry sectors are required to spend significant time and resources on formulating new materials for an AM process, instead of focusing on product development. To achieve the spatially controlled deposition of a printed voxel in a predictable and repeatable fashion, a combination of the physical properties of the ‘ink’ material, print head design, and processing parameters is associated. This study demonstrates the expedited formulation of new inks through the adoption of a high-throughput screening (HTS) approach. Use of a liquid handler containing multi-pipette heads, to rapidly prepare inkjet formulations in a micro-array format, and subsequently measure the viscosity and surface tension for each in a high-throughput manner is reported. This automatic approach is estimated to be 15 times more rapid than conventional methods. The throughput is 96 formulations per 13.1 working hours, including sample preparation and subsequent printability determination. The HTS technique was validated by comparison with conventional viscosity and surface tension measurements, as well as the observation of droplet ejection during inkjet printing processes. Using this approach, a library of 96 acrylate/methacrylate materials was screened to identify the printability of each formulation at different processing temperatures. The methodology and the material database established using this HTS technique will allow academic and industrial users to rapidly select the most ideal formulation to deliver printability and a predicted processing window for a chosen application.

Simulation and Validation of Droplet Generation Process for Revealing Three Design Constraints in Electrohydrodynamic Jet Printing.

Droplet generation process can directly affect process regulation and output performance of electrohydrodynamic jet (E-jet) printing in fabricating micro-to-nano scale functional structures. This paper proposes a numerical simulation model for whole process of droplet generation of E-jet printing based on the Taylor-Melcher leaky-dielectric model. The whole process of droplet generation is successfully simulated in one whole cycle, including Taylor cone generation, jet onset, jet break, and jet retraction. The feasibility and accuracy of the numerical simulation model is validated by a 30G stainless nozzle with inner diameter ~160 μm by E-jet printing experiments. Comparing numerical simulations and experimental results, period, velocity magnitude, four steps in an injection cycle, and shape of jet in each step are in good agreement. Further simulations are performed to reveal three design constraints against applied voltage, flow rate, and nozzle diameter, respectively. The established cone-jet numerical simulation model paves the way to investigate influences of process parameters and guide design of printheads for E-jet printing system with high performance in the future.

Design of an Innovative Three-Dimensional Print Head Based on Twin-Screw Extrusion

This paper presents the embodiment design of an interchangeable print head based on twin-screw extrusion, specially developed to allow in-process multimaterial mixing and direct deposition of the product to structure three-dimensional (3D) parts. The print head focus on research applications with middle-end 3D printers. Commercial extrusion-based 3D printers have limited applicability due to the scarce variety of plastic filaments available. In that context, one important trend for the advance of additive manufacturing (AM) is the design of systems capable of using alternative material types in different states. The systematic process is presented as a case study and brings together concepts from mechanical design and polymer processing. The main contribution of this paper is to provide general guidelines to be used on similar projects, in view of the crescent demand for more adequate and flexible additive processes.

Microfluidic Flow Cell Array for Controlled Cell Deposition in Engineered Musculoskeletal Tissues.

Musculoskeletal tissues contain critical gradients in extracellular matrix (ECM) composition and cell types that allow for proper mechanical function of tissues and integration between adjacent tissues. However, properly controlling these patterns in engineered tissues is difficult and tissue engineering (TE) is presently in need of methods to generate integration zones for tissue anchoring, transition zones between tissues, and controlled ECM gradients for proper mechanical function. In this study, we present a novel method of using a microfluidic flow cell array (MFCA) to precisely control cell deposition onto TE constructs to produce tunable cell patterns on engineered constructs. In this study, we characterized MFCA cell deposition to efficiently and reliably deposit cells in controllable patterns and densities. We developed methods for deposition of human adipose-derived stem cells and human osteoblasts using a 12-channel pilot printhead. We mimicked key gradients and transitions by creating two-cell and three-cell-type transitions characteristic of the integration zones of musculoskeletal tissues. Overall, we demonstrate the ability to precisely and reproducibly control cell deposition on engineered constructs using this method and control cell population gradients. We establish the production of multicell transitions and multicell interfaces utilizing MFCA cell deposition, to demonstrate the potential of the method to create an extensive variety of engineered musculoskeletal tissues. Furthermore, customization of the printhead design can accommodate various structures, sizes, shapes, and number of flow cell channels to meet specific requirements for a broad range of musculoskeletal tissues.

Multi Pulse Train Modeling of Piezo-Drop-on-Demand Inkjet Print-Head Response

Resonant oscillations set up internal fluid waves within a piezo-drop-on-demand (DoD) print-head channel as a result of actuation drive pulses. Such waves will persist for some time after droplet ejection from the nozzle, and the residual wave amplitude can interfere (constructively or destructively) with all succeeding actuation drive pulses, potentially altering the speed and volume of successive droplets. As uncontrolled interference would worsen printing quality, residual waves are usually reduced by a combination of print-head design and waveform optimization for better performance at continuous (steady state) printing frequencies. However, the residual waves following any changes of printing frequency can influence “first” drops and short bursts of drops. Exact analytic expressions are provided here for the N-pulse burst DoD print-head response function with fixed printing frequency. This article explains the purpose and application of the model predictions to published piezo-driven DoD data. An examination of the effect of fluid properties, the identification of unexpected jetting behavior and some issues with manufacturing prototype quality, tests of assumptions made in the simple model and extensions to the prediction of print-head performance using realistic complex waveforms are also discussed. An earlier shorter article, mainly introducing the multi pulse train modeling approach and some applications within Xaar, was first presented at NIP31/DF2015 [S. D. Hoath, A simple model for DoD inkjet frequency response, Proc. IS&Ts 31st Int'l. Conf. on Digital Printing Technologies (IS&T, Springfield, VA 2015), 8–12]. © 2016 Society for Imaging Science and Technology.