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Capillary flow in containers or conduits with interior corners are common place in nature and industry. The majority of investigations addressing such flows solve the problem numerically in terms of a friction factor for flows along corners with contact angles below the Concus-Finn critical wetting condition for the particular conduit geometry of interest. This research effort provides missing numerical data for the flow resistance function F(sub i) for partially and nonwetting systems above the Concus-Finn condition. In such cases the fluid spontaneously de-wets the interior corner and often retracts into corner-bound drops. A banded numerical coefficient is desirable for further analysis and is achieved by careful selection of length scales x(sub s) and y(sub s) to nondimensionalize the problem. The optimal scaling is found to be identical to the wetting scaling, namely x(sub s) = H and y(sub s) = Htan (alpha), where H is the height from the corner to the free surface and a is the corner half-angle. Employing this scaling produces a relatively weakly varying flow resistance F(sub i) and for subsequent analyses is treated as a constant. Example solutions to steady and transient flow problems are provided that illustrate applications of this result.

Closed-form analytic solutions useful for the design of capillary flows in a variety of containers possessing interior corners were recently collected and reviewed. Low-g drop tower and aircraft experiments performed at NASA to date show excellent agreement between theory and experiment for perfectly wetting fluids. The analytical expressions are general in terms of contact angle, but do not account for variations in contact angle between the various surfaces within the system. Such conditions may be desirable for capillary containment or to compute the behavior of capillary corner flows in containers consisting of different materials with widely varying wetting characteristics. A simple coordinate rotation is employed to recast the governing system of equations for flows in containers with interior corners with differing contact angles on the faces of the corner. The result is that a large number of capillary driven corner flows may be predicted with only slightly modified geometric functions dependent on corner angle and the two (or more) contact angles of the system. A numerical solution is employed to verify the new problem formulation. The benchmarked computations support the use of the existing theoretical approach to geometries with variable wettability. Simple experiments to confirm the theoretical findings are recommended. Favorable agreement between such experiments and the present theory may argue well for the extension of the analytic results to predict fluid performance in future large length scale capillary fluid systems for spacecraft as well as for small scale capillary systems on Earth.

Recent investigations have successfully demonstrated closed-form analytical solutions of spontaneous capillary flows in idealized cylindrical containers with interior corners. In this report, the theory is extended and applied to complex containers modeling spacecraft fuel tanks employing propellant management devices (PMDs). The specific problem investigated is one of spontaneous rewetting of a typical partially filled liquid fuel/cryogen tank with PMD after thrust resettling. The transients of this flow impact the logistics of orbital maneuvers and potentially tank thermal control. The general procedure to compute the initial condition (mean radius of curvature for the interface) for the closed-form transient flows is first outlined then solved for several 'complex' cylindrical tanks exhibiting symmetry. The utility and limitations of the technique as a design tool are discussed in a summary, which also highlights comparisons with NASA flight data of a model propellant tank with PMD.

Spectroscopic measurements of liquid-vapor interfaces are made in +/- 1-g environments to note the effect of gravity on surface tension. A slight increase is detected at -1-g0, but is arguably within the uncertainty of the measurement technique. An increased dependence of surface tension on the orientation and magnitude of the gravitational vector is anticipated as the critical point is approached.

The linearized governing equations for an ideal fluid are presented for numerical analysis for the stability of free capillary surfaces in rectangular containers against unfavorable disturbances (accelerations,i.e. Rayleigh-Taylor instability). The equations are solved for the case of the right square cylinder. The results are expressed graphically in term of a critical Bond number as a function of system contact angle. A critical wetting phenomena in the corners is shown to significantly alter the region of stability for such containers in contrast to simpler geometries such as the right circular cylinder or the infinite rectangular slot. Such computational results provide additional constraints for the design of fluids systems for space-based applications.