A Model of Direct Thermal Printing
William T. Vetterling, Alexei Azarov, Brian Busch, and Chien Liu, ZINK Imaging , Massachusetts, USA
ZINK — Zero Ink — technology prints full-color digital images without cartridges or ribbons. ZINK renders images using a single thermal print head that passes over a coated medium infused with layers of dye crystals. Using timed heat pulses and temperatures, ZINK melts these crystals to release colors that then combine to produce photographicquality images.
The ZINK system consists of a thermal print head, the medium moving beneath the print head, and a rotating platen. The interplay between the mechanics, the thermal effects, and the chemical layers of the media structure is inherently a multiphysics problem. We used COMSOL Multiphysics to develop a model framework for direct thermal printing and applied the model to the ZINK media, demonstrating its ability to produce full-color photographic-quality images in a direct thermal printing process.
ZINK System Components
Figure 1: Model geometry showing the features of the ZINK print head.
The ZINK print head is a linear array of heating elements, usually 300-600 per inch, sitting on an insulating glass bump that rides on a ceramic substrate attached to an aluminum heatsink (see Figure 1). The print medium is a layered structure made of three dye layers, two dye-separating layers, and a number of protective layers.
In our simulation, the medium was a single, uniform sheet with mechanical and thermal properties characteristic of the plastics used. We drew common material properties from the COMSOL Material Library and the rest from manufacturers, in-house measurements, or resources like MatWeb.
The platen is a rubber-coated roller that presses the print medium against the heating elements. Since the heaters are on a curved glass surface and the medium is flat, it is a function of the rubber to promote “wrapping” of the medium around the heaters, thus ensuring good thermal contact. The moving medium and platen carry heat away from the printing region, providing some additional cooling to the print head.
Models to Dye For
We used multiphysics modeling to model the mechanical and thermal behavior of our direct thermal printing process and to postprocess the data. The mechanical simulation investigated the compressive contact between the platen and the print medium as well as between the medium and print head. To avoid interpenetration of these components, we used the “contact pairs” feature of the Structural Mechanics Module.
Since we simulated a single heater of the print head, the mechanical constraint at the sides would be zero displacement normal to the boundaries. COMSOL enabled us to conserve memory by setting the material properties to be orthotropic with a Poisson ratio of zero in the normal direction, which had the effect of maintaining fixed walls.
Our thermal simulation subjected the structure to periodic thermal pulsing of the heater elements. One problem was the thin layer of air in the vicinity of the contact between the heating element and the medium, which can develop poor mesh quality under compression. Model set-up tools let us omit this air layer and use extrusion coupling to communicate the surrounding material surface temperatures and positions across the gap. This allowed independent evaluation of heat flow through the layer.
Another concern was that both the media and platen move and transport heat. COMSOL helped us with this by letting us apply a linear convective term with the velocity of the medium and a cylindrical convective term with the velocity of the platen. To represent the medium entering the printer at ambient temperature and leaving warmer, we set a fixed-temperature boundary condition at the entrance and a convective boundary condition at exit.
With these features in place, we ran a time-dependent thermal simulation with a pulsing heat source on the compressed geometry.
Colorful Postprocessing
Our main interest was the temperatures in a crystal dye layer a fixed distance below the heated medium’s surface, so we traced a time history of the temperature at points in the layer fixed to the medium. Since we used a convective term to simulate the media motion, our results referenced points fixed in the global coordinates.
Figure 2: Temperature profile following a heat pulse. The color indicates temperature, with a scale going from 273 K to 315 K.
Armed with the temperature and time history of every point in the layer, we used a “media model” to determine the opacity of the dye at each point in the medium. Here, we considered a so-called “amorphochromic” dye developed for ZINK that consists of colorless crystals that become colored upon melting. Since a point in the medium heated above a crystal’s melting point gets colored, applying the media model meant comparing the temperature history of each point to a threshold melting temperature.
The surface plot in Figure 2 shows the temperatures in the components following a thermal pulse and as the system cools to the heat-sink temperature as the heated media exits the printing region. It’s apparent that the print medium carries away heat, cooling the center of the heater, and that the platen also carries away heat.
Post-processed data shows the maximum temperatures reached by points in a plane below the medium’s heated surface (see Figure 3). If you place a layer of dye crystals at these points and heat it, you get a regular array of colored dots. If you apply pulses of higher energy, temperature peaks rise and exceed threshold temperatures over a wide area, producing larger dots, increased color density, and even a layer of solid color.
Figure 3: A surface plot showing the maximum temperatures reached at points in a 2D plane lying 3 microns below the heated surface medium after the medium was heated with 3 ms pulses, spaced by 33 ms. The temperature at the peaks is 436 K (163° C).
Our simulations showed us how the temperature peaks diffuse away from the heat source. A comparison of the peak temperatures at various planes of the media indicated that we could produce bichrome images by intermixing short, high-power pulses and long, low-power pulses to melt crystals at different layers and with dissimilar melting points. With this knowledge, we knew we could position three dye layers to make a full-color medium and obtain photographic quality images with one pass of the medium under the thermal print head.
Future Considerations
As a component of our ZINK thermal printing development, we make frequent use of COMSOL Multiphysics tools. Moving from product invention to product development, and then to manufacturing, we have touched on many engineering fields — mechanical, thermal, chemical, and fluid dynamics. The combination of all these fields in a single approachable tool with a single user interface has significantly lowered the barriers to the use of modeling as a daily tool rather than a special enterprise.
In the future, we will, of course, refine our models and use optimization to find the most favorable material properties for extending our color palette. As we enter the manufacturing phase of our project, in which we work with high-speed commercial coaters and driers, the additional capabilities of the Chemical Engineering Module in fluid dynamics and process design become very attractive as possible additions to our toolset. Beyond that, our modeling will be guided by the imagination of our customers!
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William Vetterling (second from right) Research Fellow and Director of the Image Science Lab at ZINK Imaging with, from left to right team members Alexei Azarov, Chien Liu, and Brian Busch. Vetterling, Busch, and Liu are among the co-inventors of the ZINK technology. |
CONTACTS
ZINK Imaging
www.zink.com
MatWeb
www.matweb.com