Mathematics - Featured Research

The Dynamics of Fluids

QUESTION Can mathematicians build accurate models to analyze complex, seemingly random, systems such as fluid dynamics?

“Applied mathematicians contribute to the advancement of our understanding of complex fluids by modeling, analysis and simulations. To model a complex fluid and its interaction with a particle, I use a set of partial differential equations derived from principles that are similar to the Navier-Stokes equations,” says Christel Hohenegger, an Associate Professor of Mathematics at the U.

WHO Hohenegger joined the Mathematics Department in 2010 and was promoted to an Associate Professor in 2018.

Her research focuses on analytical and computational modeling of problems arising in the dynamics of complex fluids, such as biological fluids, polymer solutions, and particle suspensions.

Purely viscous fluids like water, sucrose, or oil are characterized by their viscosity, or resistance to deformation. However, complex fluids are not easily described since their response to an applied force can be like a solid or a liquid. A good example of a complex fluid is ketchup.

“I’m mainly interested in how we can infer the mechanical properties of a family of complex fluids

through the motion of small passive particles,” says Hohenegger.

The concept to use small, neutrally buoyant particles to characterize a viscous fluid dates back to Brown and was formalized by Einstein, Langevin, and other mathematicians in the first half of the twentieth century. However, there are significant gaps in the generalization of this theory to complex fluids.

“Together with Scott McKinley at Tulane University, we are developing a first-of-its-kind model of passive fluctuations in complex fluids,” says Hohenegger. “This requires deriving the equations from first principles, developing new simulation techniques and validating the results against experimental data.”

FUNDING

Hohenegger’s current research is funded by the National Science Foundation, with a grant of $166,000 for five years. The purpose of the grant is to study the diffusion of foreign particles in complex fluids.

She plans to apply for new funding through the National Science Foundation to use statistical and optimization tools to study the inverse problems of data measurement in complex fluids.