Mathematical Sciences: Development of an Advanced Numerical Method for Modeling Thermal Ink Jet Devices

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9626153 Puckett This research project undertakes to develop and implement effective numerical methods for modeling fluid flows in thermal inkjets. Such a flow is multidimensional and is characterized by high thermal gradients, multiple phases, and interfaces and free boundaries. The project, supported under the GOALI initiative, is a collaboration between investigators at the University of California--Davis and Xerox and features joint mentoring of a postdoctoral researcher. A goal of the project is to develop reliable and effective software to model the fluid problems and to validate the numerical methods and software against physical experiments. This project is concerned with developing advanced computational methods for modeling fluid flows in thermal inkjets, and incorporating the methods in software. These flows arise when the ink in an inkjet cartridge is heated to spray characters onto paper. The heated ink (a liquid) forms a vapor bubble (a gas) that shoots the ink onto the paper. In this process, the formation of the bubble, its growth in the surrounding ink, and the way this forces ink out of the cartridge are genuinely three-dimensional phenomena. They involve thermal properties (where the ink is heated to form a bubble), multiphase flow (liquid and gas), and free boundaries (where the bubble grows in the ink, and where a droplet of ink is forced out of the cartridge). These features are difficult by themselves. To verify that their combination is modeled accurately, the investigators compare the computational results against experiments. The project is performed by researchers E. Gerry Puckett at UC--Davis and John Andrews at Xerox's Wilson Research Center, who jointly mentor a postdoctoral researcher. This provides a close integration of research and education in a combination of industrial and academic environments that provides a junior mathematical scientist advanced training in the design, development, and application of sop histicated numerical methods to problems that arise in science and industry. Such integration is a key feature of the GOALI initiative, which supports the project.