Imagine water flowing over a wall as in a waterfall. If you stare at the waterfall, you'll notice the flow tapers at the lateral edges where it breaks up into droplets. In fluid mechanics, we call this an instability.

Sitting down to watch television, you might not consider the mechanics involved in creating the plasma screen flashing those crisp images in your living room. On the other hand, Associate Professor of Mathematics Linda Smolka has made it her life's work to understand fluid mechanics.

"A component of the plasma screen starts out as a molten fluid, which is stretched into a smooth, flat screen free of ripples," she says. "Imagine water flowing over a wall as in a waterfall. If you stare at the waterfall, you'll notice the flow tapers at the lateral edges where it breaks up into droplets. In fluid mechanics, we call this an instability." Through mathematical modeling and laboratory experiments to check the validity of her work, Smolka discovers just how far fluid, like the type used in plasma screen manufacturing, can be stretched before it develops an instability, or ripples.

She studies free surface flows, which are flows where the fluid has a boundary with air, or with another fluid. "I use mathematics to help model and predict the behavior of the flows. My goal is to understand how properties of the fluid, surface tension, viscosity, and viscoelasticity compete with gravity to control the stability of such flows," she says.

"Mathematics can solve a range of problems that have applications to industry," she says. Free surface flows appear in nature and are used in manufacturing and industrial processes. "It's very important in industrial processes to control these flows in order to obtain the desired product or effect." Applications range from ink-jet printing to manufacturing fiber optic cable, Kevlar or Lycra.

Smolka mentors student researchers in her fluid mechanics lab -- one of only a handful housed in mathematics departments at colleges and universities across the U.S. Her research program includes both modeling -- often with pencil and paper -- and experiments with actual fluids. She mentors students in both of these areas, and four have become co-authors on her academic papers. "I chose to teach at Bucknell," she says, "because its undergraduate program allows me to involve students in each aspect of my research. I want to help them see how mathematics is important, that it's accessible and that there's a connection to their life."

Posted Sept. 20, 2011

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