UCLA Applied Math
Research Experience for Undergraduates (REU) - Summer 2010
The Summer 2010 UCLA Applied Math REU
program also lasted 10 weeks. I again mentored a project related to
particle-laden flows. Once again I took planned and organized the
project around the Applied Math Lab and selected a group of five
students to work in my fluids team. Two of the students were returning
team-members from REU 2009 - Paul Latterman and Trystan Koch (both seniors); newcomers were Jacob Bouricius (applied math, Harvey Mudd College), Brian Le (physics, UCLA) and Samantha Mesuro
(applied math, Harvey Mudd College). The project was, in a sense, a
continuation of the work from 2009 REU, and it involved experiments,
modeling and simulations. The group dynamics and the nature of my
mentorship were similar to 2009 REU.
The experimental work involved gravity driven
particle-laden thin film flows, but the focus was on the motion of the
fronts rather than categorizing the experimental runs based on the
observed settling regime. For this purpose a special set-up was
constructed by the students, which required some level of ingenuity,
and consisted of a high-precision camera and laser sheet. The set-up
allowed for capturing high resolution images, see Figure 1.
Figure 1: The laser sheet in action.
The images were analyzed using the image processing
tools from MATLAB. As a results, we were able to monitor the evolution
of the cross section of the advancing suspension front, the speed of
the front, and the motion of the particulate bed in the settled regime.
These are novel results for particle-laden flows including free surface
and the presence of the contact lines.
We also developed a dynamic model for particle-laden
thin film flows based on the equilibrium model and formulated as a
system of scalar hyperbolic conservation laws. We carried out numerical
simulations of this model and compared our preliminary numerical
results with the experimental data. The outcome was very promising and
we are currently working on more detailed analysis of the model.
The culmination of the project was again the final
presentation given at the end of the REU program, which was praised by
all other mentors and participants for the quality of results.
Typically, junior level students have just been acquainted with
numerical linear algebra, numerical methods for solving simple ODEs, or
perhaps some theory behind simple linear PDEs. It is then quite
astonishing to see junior level engineering, math and physics students
being able to carry out these experiments, understand complex systems
of PDEs, and handle them numerically. They are set to present
their results at the 63rd Annual Meeting of the Division of Fluid
Dynamics by American Physical Society, to be held in Long Beach in
November 2010. I am currently mentoring Paul Latterman and Brian Le;
they are carrying out experiments on the settled regime in the Applied
Math Lab and studying the dynamic model for particle-laden thin film
flows.