Up: Research Projects of the Geometry Center

Project Afton

"Flow gently, sweet Afton, among thy green braes,
Flow gently, I'll sing thee a song in thy praise."

-Robert Burns

a picture of a river

Background

The spreading of a liquid on a surface occures in many physical problems, ranging from the protection of microchips to the build-up of ice on an airplane wing. On the theoretical side the dynamics of the thin films raise interesting questions involving the physics of different length scales. There are three significant length scales corresponding to (1) gravity, (2) surface tension, and (3) the relevant physics at the "contact line" or triple juncture of the three interfaces (liquid/air, liquid/solid, and solid/air). In Project Afton we will develop methods for visualizing flows driven by gravity, surface tension, and the interactions between the two.

Two cases of fluid flow:

The first is the rotationally symmetric case. Imagine two open cylinders, the smaller nested inside the larger. Next fill the trough between the two cylinders with a viscious fluid - silicon oil is a good example. The spreading that we are modeling occurs when the smaller cylinder vanishes, causing the fluid to flow into the center. Particularly interesting is what happens at the moment the fluid converges and focuses at the center.

These are movies of two stages of the rotationally symmetric case:

The Beginning (400K)
What you are seeing is a cut-away view showing only half of the ring of liquid. To illustrate the sinking of the liquid as it flows, the central cylinder has been replaced by a more conical dam. When you hit play, this support is removed and the fluid pours inward.
Focusing (300K)
Here the liquid spreads completely over the floor and then rises to fill the container.

The second case is a non-symmetric one. Particularly interesting are any symmetries that might occur as the focusing moment is reached.

Project members

Don Aronson
Andrea Bertozzi
Douglas Clancey
John Lowengrub
Liz Stanhope

References

S.B. Angenent and D.G. Aronson, Intermediate asymptotics for convergent viscous gravity currents, Phys. Fluids, to appear.

A.L. Bertozzi, M.P. Brenner, T.F. Dupont, and L.P. Kadanoff, Singularites and similariteis in interface flow, in "Trends and Perspectives in Applied Mathematics", (L. Sirovich, editor), Springer-Verlag, 1994.