M AT H E M AT IC S
QUESTION
through the motion of small passive particles,”
Can mathematicians build accurate models to
says Hohenegger.
analyze complex, seemingly random, systems such as fluid dynamics?
The concept to use small, neutrally buoyant particles to characterize a viscous fluid dates back to
“Applied mathematicians contribute to the
Brown and was formalized by Einstein, Langevin, and
advancement of our understanding of complex fluids
other mathematicians in the first half of the twentieth
by modeling, analysis and simulations. To model
century. However, there are significant gaps in the
a complex fluid and its interaction with a particle,
generalization of this theory to complex fluids.
I use a set of partial differential equations derived
“Together with Scott McKinley at Tulane
from principles that are similar to the Navier-Stokes
University, we are developing a first-of-its-kind
equations,” says Christel Hohenegger, an Associate
model of passive fluctuations in complex fluids,”
Professor of Mathematics at the U.
says Hohenegger. “This requires deriving the equations from first principles, developing new
WHO Hohenegger joined the Mathematics
The Dynamics of Fluids CHRISTEL HOHENEGGER
simulation techniques and validating the results against experimental data.”
Department in 2010 and was promoted to an Associate Professor in 2018. Her research focuses on analytical and
FUNDING Hohenegger’s current research is funded by the
computational modeling of problems arising in the
National Science Foundation, with a grant of $166,000
dynamics of complex fluids, such as biological fluids,
for five years. The purpose of the grant is to study the
polymer solutions, and particle suspensions.
diffusion of foreign particles in complex fluids.
Purely viscous fluids like water, sucrose, or oil
She plans to apply for new funding through the
are characterized by their viscosity, or resistance to
National Science Foundation to use statistical and
deformation. However, complex fluids are not easily
optimization tools to study the inverse problems of
described since their response to an applied force
data measurement in complex fluids.
can be like a solid or a liquid. A good example of a complex fluid is ketchup.
12
IMPACT
“I’m mainly interested in how we can infer the
The study of fluid dynamics is important in
mechanical properties of a family of complex fluids
a wide range of industries, including aerospace,
