**Objectives**

** The objectives of this experiment were: (1) to investigate symmetry breaking for liquid surfaces in microgravity by use of specifically designed containers and (2) to compare observed shapes with mathematical predictions. For the containers in the experiment, the liquid is predicted mathematically to have the striking property that any stable configuration it assumes cannot be rotationally symmetric, even though the containers themselves are rotationally symmetric; furthermore it is predicted that there can be more than one such asymmetric stable configuration for a prescribed liquid volume.
**

**Shuttle-Mir Missions**

NASA-2

**Approach**

Two identical vessels, made of acrylic plastic, were flown. The test portions of the vessels were in the shape of a right circular cylinder with a mathematically determined toroidal-like bulge near the midpoint. The reservoir portions contained the test liquid, an immersion oil indexed matched with the acrylic plastic. At the initiation of each test, the liquid was transferred to the test portion of the vessel. Subsequently, perturbations were applied by the crewmember to induce the liquid to assume different configurations and to test stability. The liquid behavior was recorded on video tape, along with verbal comments of the crewmember.

**Results**

The crewmember skillfully and successfully found two distinct locally stable non-rotationally-symmetric configurations in the same container. Four static surfaces in all were formed: First the (unstable) rotationally symmetric configuration observed during the initial filling, then the apparent global minimizer like the one found numerically, then (following further carefully applied disturbances) another local minimizer that had also been found numerically. Finally, a further disturbance led once more to the minimizing surface, this time in reflected configuration.

It was confirmed that stable equilibrium configurations of liquid in a rotationally symmetric container with symmetric boundary data (contact angles) need not themselves be rotationally symmetric. Thus symmetry breaking in capillary configurations must be expected physically. Additionally, more than one distinct asymmetric stable configuration can occur. These results communicate clearly the need for designers of in-space fluid management systems to take account of possible unusual behavior that may not be easy to anticipate.

**Earth Benefits**

Liquids behave differently in microgravity than they do on the ground. The problem is that the position and shape of liquids in container is not as predictable as on the ground. This makes it difficult to design liquid fuel systems for space vehicles. By understanding how liquids take shape between solid surfaces, scientists and engineers can build better fluid systems. Better knowledge of liquid surface forces can be applied to situations where surface forces predominate over gravitational forces such as in pore spaces of granular materials like rocks.

**Publications**

R. Finn, Non uniqueness and uniqueness of capillary surfaces, Manuscr. Math., 61 (1988), pp. 347-372.

Callahan, M., Concus, P., Finn, R., Energy Minimizing Capillary Surfaces for Exotic Containers, in Computing Optimal Geometries (with accompanying video tape), J.E. Taylor Ed., AMS Selected Lectures in Mathematics, Amer. Math. Soc., Providence, RI, 1991, pp. 13-15.

Concus, P., Finn, R., Exotic Containers for Capillary Surfaces, Journal of Fluid Mechanics, Vol. 224, 1991, pp. 383-394; Corrigenda, Journal of Fluid Mechanics, Vol. 232, 1991, pp. 689-690.

P. Concus, R. Finn, and M. Weislogel, Drop-tower experiments for capillary surfaces in an exotic container, AIAA J., Vol. 3, Jan. 1992, pp.134-137.

P. Concus, R. Finn, M. Weislogel; Interface Configuration Experiment: Preliminary Results, Joint Launch + One Year Science Review for USML-1 and USMP-1 with Microgravity Measurement Group, NASA CP-3272, Vol. 2, 1994, pp. 525-541.

P. Concus, R. Finn, and M. Weislogel, Capillary surfaces in an exotic container: results from space experiments, Report PAM737, Center for Pure and Applied Mathematics, Univ. California, Berkeley, 1998, submitted to J. Fluid Mech.

**Principal Investigators**

Paul Concus

University of California at Berkeley

**Co-Investigators**

Robert Finn

Mark Weislogel

Curator:
Julie Oliveaux
Responsible NASA Official: John Uri |

Page last updated: 07/16/1999