Surface Evolver
Created by K. Brakke, Surface
Evolver is one of my favorite computer programs. It can compute surfaces of minimum
energy, which includes surface energy, gravitational energy of the body
included by the surface, and other forms of potential energies.
Recently, the application of SE in studying capillary
surface interfaces has been growing substantially. Below you will see some
projects that I have done either by myself or with a group of people. All the
time, I have been fascinated by the beauty of those interfaces under different
settings.
Ullage Bubble in Gravity Probe-B Helium Tank
Yongkang Chen and Steven H. Collicott, Effects
of wicking and spin on bubble position in gravity probe-B helium tank geometry,
AIAA-2002-1004, 40th AIAA Aerospace Sciences Meeting & Exhibit,
14-17, January 2002, Reno, Nevada
The helium tank of Gravity Probe-B, a sketch is shown below, rotates at a constant rate during its mission. A ullage bubble presents within the liquid. It is of interest to know the topology and the location of the bubble, which determines the center of mass of the spacecraft. In this project, it is assumed that the bubble possesses a toroidal shape and we were interested in the location of the bubble near one end where the central post forms a cusp with the end cap. Basically, the position of the bubble is a result of the competition between the kinetic energy, caused by the rotation of the tank, and surface energies. Because the geometry is rotational symmetric, the problem is simplified to a 2-D configuration using the String mode of the Evolver.
Bathtub
Imagine a bathtub with one end narrower than the other. What will happen if the tub filled with enough water is put, say, onboard space station?
In micro-gravity, the free surface between the liquid and the air is fundamentally different than that on the earth. In addition, there is another important question concerning existence of equilibrium capillary surface in micro- or zero gravity. Such existence is determined by the appropriate boundary condition, such as the contact angle formed between the liquid and the solid surface, as studied extensively by P. Concus and R. Finn.
Concus and Finn show that for free surfaces in cylindrical containers, there is a critical contact angle. Whenever the contact angle is greater than the critical value, there is always equilibrium surface. Otherwise, equilibrium surfaces fail to exist. The equilibrium surface for the bathtub for certain contain contact angle is shown above.
What if equilibrium surfaces fail to exist? For the bathtub, the liquid would move along the narrow end of the tub all the way up. And the consequence is either the liquid reaches the top of the container and wrap around to from another type of equilibrium surface, or part of the tub bottom is exposed. Actually, if there is a tub of infinite height and there is enough liquid, the liquid would keep moving to infinity. The moving of the liquid is called capillary driven flow, which is another fascinating subject that I have been investigating.
Single Vane in a Cylindrical Tank
Wall-Edge-Bound-Drop
Particles on Interface