4:00 PM - 6:00 PM
Room: Salon B - Level 5
For Part I, see MS2
For Part III, see MS38
The mathematics of thin liquid films and fluid interfaces has developed substantially in the last ten years. In particular, the study of the partial differential equations that govern these systems has led to a broad range of new theoretical results. This area of fluid mechanics has applications to several active fields of scientific research, including materials science, nanotechnology, and biology. The interaction of physicists and engineers with applied mathematicians and analysts has played a large role in motivating the mathematics; the mathematics in turn has contributed substantially to the understanding of the wide variety of interesting physical phenomena in this area.
Free-surface flows remain among the most challenging problems in the physical sciences, and are involved in countless industrial and technological processes such as coating flows, film drainage, fluid jetting and droplet formation. Pushing classic engineering models to their physical limits has yielded physical experiments with novel and intricate dynamics. The mathematical modeling and analysis of these problems has produced new generations of more challenging problems in free boundary problems for nonlinear partial differential equations. Direct computation of the full governing equations is intractable in most cases and even when possible, large-scale numerical simulations do not necessarily provide insight into the fundamental physical mechanisms at work. Valuable understanding of the general problems has been gained from the studies of asymptotic models applicable in limiting cases. These models still contain much of the rich dynamics of the original problems, but take more tractable forms, spurring advances in analysis and computations.
The minisymposium will serve as a forum where ideas can be exchanged across disciplines: analysts and modelers will learn about new phenomena and challenges from experimentalists, and experimentalists will learn about new results in analysis and applied mathematics to motivate the next generation of experimental studies.
Organizer:
Andrea L. Bertozzi
University of California, Los Angeles
Michael Shearer
North Carolina State University
4:00-4:25
Reverse Undercompressive Shock Structures in Driven Thin Film Flow
5:30-5:55
Van der Waals Driven Thin Film Rupture, Regularization, and Limitations of the Lubrication Approximation
4:00-4:25
Long-time Results for Thin Film Equations