Non-Spherical Zero-G Liquid Surfaces In actual application of such "capillary" surfaces in "zero-gravity" in space, moreover, a number of new observations arise, together with a new set of measuring instruments (Figures 7 and 8). Figure 4 Pressure balance in an air bubble Thus non-sphericitv of the meniscus surface must be accounted for in cases of distorted (nominally and practically chosen as toroidal) boundaries, as in Figure 9. Here the contact angle is constant, the mean curvature is constant over the surface, but clearly the liquid surface is not spherical. In another significant case of non-sphericity with a zero contact angle in a liquidhydrogen fuel tank in zero-gravity, the liquid surface is described by a mathematical infinite series involving the hyperbolic cosine (Figure 10). Behavior of liquids in zero-g, is further exhibited by Petrash & Otto's illustrations of spherical tanks part-filled with liquids of various contact angles (Figure 11) and of rectangular channels holding liquids of various contact angles (Figure 12), and by E. Benedikt's illustrations of the surface of a single liquid in an infinitely long rectangular trough under various gravitational-equivalent load-factors (Figure 13). Theory and a number of zero-gravity orbital experiments (Figures 11 and 12) and much research (Figure 10, [6, 7]), have established that in space, in zero-gravity (i.e., in orbit or unpowered trajectory), the surface of a free liquid in a container will pull itself into a minimum potential energy configuration. In general, an “epihydrostatic” surface is a liquid surface operated on by zero net acceleration along each of any chosen set of three orthoganal axes. Li [6] and others have shown that the “epihydrostatic” surface of a liquid
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