Equilibrium fluid interface behavior under low- and zero-gravity conditions

We describe here some of our recent mathematical work, which forms a basis for the Interface Configuration Experiment scheduled for USML-2. The work relates to the design of apparatus that exploits microgravity conditions for accurate determination of contact angle. The underlying motivation for the procedures rests on a discontinuous dependence of the capillary free surface interface S on the contact angle gamma, in a cylindrical capillary tube whose section (base) omega contains a protruding corner with opening angle 2 alpha. Specifically, in a gravity-free environment, omega can be chosen so that, for all sufficiently large fluid volume, the height of S is uniquely determined as a (single-valued) function mu(x,y) entirely covering the base; the height mu is bounded over omega uniformly in gamma throughout the range absolute value of (gamma -(pion/2)) less than or equal to alpha, while for absolute value of (gamma - (pion/2)) greater than alpha fluid will necessarily move to the corner and uncover the base, rising to infinity (or falling to negative infinity) at the vertex, regardless of volume. We mention here only that procedures based on the phenomenon promise excellent accuracy when gamma is close pion/2 but may be subject to experimental error when gamma is close to zero (orpion), as the 'singular' part of the domain over which the fluid accumulates (or disappears) when a critical angle gamma theta is crossed then becomes very small and may be difficult to observe. We ignore the trivial case gamma is equal to pion/2 (planar free surface), to simplify the discussion.