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Mathematical Modeling and Numerical Simulation of Microstructured Materials
Colloquium| Speaker: | John Lowengrub, University of Minnesota |
| Location: | 693 Kerr |
| Start time: | Wed, Apr 17 2002, 4:10PM |
Description
Microstructured materials, such as emulsions and polymer blends,
crystals and metallic alloys, blood and biological tissues,
are fundamental to many industrial and biomedical applications.
These diverse materials share the common feature that the microscale and
macroscale are linked. The phenomena at microscopic scale, such
as the morphological instability of crystalline precipitates and drop
deformation,
break-up and coalescence determine the microstructure and its time
evolution;
thus affecting the rheology and mechanical properties of the materials on
the macroscale.
In this talk, I will focus on mathematical and numerical modeling at the
microscale.
In particular, I will present a class of physically-based models of
complex (multicomponent)
fluid flows which incorporate buoyancy, viscosity, compressibility and
surface tension
at interfaces. The models are capable of describing systems with both
miscible and immiscible components.
In addition, the models allow topological transitions such as pinchoff and
reconnection of interfaces to occur without relying on ad hoc 'cut and
connect' or
smoothing procedures.
Results will be presented for a variety of physically interesting flows.
To validate the
model and numerical algorithms, we examine the pinchoff of liquid/liquid
threads
(Rayleigh instability) and compare the numerical results to
theory and experiments. We then consider the development
of a complex, three dimensional microstructure in which the flow
components fully interpenetrate
one another to yield a sponge-like microstructure. Such co-continuous
microstructures have
many important industrial applications.
Finally, I will demonstrate how these numerical methods can be made
adaptive to more
efficiently and accurately simulate flows with wide-ranges of
length-scales. Time permitting,
I will also demonstrate how the models and numerical techniques can be
modified to
investigate the behavior of other complex materials and biological
systems.
(Coffee & cookies @ 3:45 in 550 Kerr )