David S. Ross Research Associate Eastman Kodak Company BA Mathematics Columbia University MS Mathematics New York University PhD Mathematics New York University The Computational Science Laboratory at Eastman Kodak's research labs is a group of mathematicians and mathematically-inclined scientists and engineers who work as internal consultants. I have spent my entire career at Kodak-11 years now-as a member of this group. When a new research project is begun, if mathematical modeling will be required, a member of our lab is asked to sign on. Such projects often last for years. We also work on shorter projects in collaboration with other engineers and chemists. For example, if an engineer wants to understand how some fluid waves affect a production process, we might spend a month or two developing a model of the phenomenon. Many of us have standing collaborations with other scientists in the labs, experts in some field, and we work regularly with them on problems in their fields. Also, we are known throughout the labs as experts in mathematics, so people often drop by our offices for help with short mathematical tasks-to solve some ODE's, to help formulate a system of algebraic equations, to perform a regression analysis, to give our opinions on the best software for a particular application, to find the roots of an equation, to compute eigenvalues... My specialty is differential equations. These days, I am working on fluid dynamics problems. One of these is the problem of dynamic surface tension in fluid curtains. The chemically active part of photographic film consists of silver halide crystals and dye-forming chemicals in gelatin. This is coated on a hard backing in liquid form-it's liquid gelatin with stuff suspended in it, just like a strawberry gelatin dessert with cling peaches suspended in it. The thin liquid layer is then dried. One method we use to coat this liquid is curtain coating, in which a thin, controlled waterfall of the gelatin solution coats the hard backing as it runs under the waterfall on a conveyor belt. Surface tension tends to break up such curtains into drops and rivulets in the same way that water from a faucet tends to break up into drops. We put surfactants, chemicals that reduce surface tension, into the fluid to prevent the curtain's breaking up. In collaboration with some surface chemists, I have developed a mathematical model of the transport of surfactant in coating flows, its diffusion to surfaces, and its influence on surface tension. Mathematically, the model takes the form of a system of reaction-diffusion equations. These are equations like the heat equation, but with nonlinear source terms. Another project on which I am working is ink jet printing. Because I knew about fluid surface tension from my work on coating flows, I was asked to model drop formation and ejection from ink jet printers. This problem involves the solution the Navier-Stokes equations with free surfaces with surface tension. In my years at Kodak I've worked on many, many different projects involving many different types of mathematics, from lens design and solid state physics through crystallization and the chemistry of photographic development to statistical analysis of color balance data from photofinishing shops.