Modeling Fluid Dynamics

Originally, Christel Hohenegger, assistant professor of mathematics, had wanted to study chemistry because she thought that reaction equations were beautiful. But she didn’t like doing the lab work and decided instead to study mathematics, without a clear idea of what a mathematician does—she just knew that she liked structure and order. Later, as an undergraduate at the renowned Eidgenössische Technische Hochschule Zürich (ETH Zurich), she took a course in the history of math and learned about all of the famous mathematicians who taught at the ETH. “I found it fascinating to learn that they were trying to answer both math and physics questions,” said Hohenegger. After graduating from the ETH, she earned a Ph.D. from the Georgia Institute of Technology.

Practical Applications

Hohenegger’s research focuses on questions concerning fluid dynamics that can be solved using different mathematical tools from modeling and analysis to simulations and predictions. “I study how solid objects and liquids interact in a fashion that is counterintuitive,” said Hohenegger. “For example, I look at models of swimming organisms in water, where reciprocal swimming results in zero net displacement. Or I’m interested in how the stickiness and gooeyness of a liquid can affect how far an object moves.”

Brownian motion is used to describe the random motion of particles suspended in a fluid resulting from their collision with other fast-moving molecules in the fluid. In a complex fluid with memory, such as ketchup or mucus, the particle motion is different. Hohenegger, along with colleague Scott McKinley, associate professor of mathematics at Tulane University, developed a framework to model these kinds of interactions.

Her research has practical applications in many industries, such as pharmaceuticals and aerospace. “Understanding how particles diffuse in a complex fluid or knowing how much time it takes a sphere to traverse a layer has potential application in drug delivery,” she explained. “In aerospace, understanding how and at which frequency a liquid will slosh around the wall of a container is a problem associated with aerospace engineering, particularly in designing rocket boosters.”

Helping Women in Math

Hohenegger serves as the faculty advisor for the U’s student chapter of the Association for Women in Mathematics. “I only realized some of the challenges faced by women in mathematics as my career progressed,” she said. “The biggest one I experienced, which is common to women, is the ‘imposter syndrome’—the idea that I wasn’t good enough.” She learned to overcome this by focusing on her work, forging her own path, and not comparing herself to others. “If it takes you an extra year to graduate or find a job, so what? It’s fine,” she said. “I would also encourage anyone to take full advantage of the help and benefits offered by a department—things such as mentoring or the opportunity to chair a committee—as well as basic benefits like maternity leave.”

She believes that both her Ph.D. advisors and postdoctoral advisors were critical in shaping her research and helping her achieve career milestones. She chose her Ph.D. advisor Peter Mucha, now professor of mathematics and applied physical sciences at the University of North Carolina at Chapel Hill (UNC), because of his energy and excitement for the material. In turn, he introduced Hohenegger to her postdoctoral advisor, Gregory Forest, a Grant Dahlstrom Distinguished Professor in the Department of Mathematics, also at UNC. She credits Michael Shelley, a Lilian and George Lyttle Professor of Applied Mathematics and professor of mathematics, neural science, and mechanical engineering at New York University, with helping her become her own person in the field.

“My research is evolving to new and exciting areas where math, physics, engineering, and biology intersect,” she said. “Finding the balance between teaching and research is difficult. My biggest challenge is still managing my time efficiently, but I’m getting there.”