Capillary flows in interior corners have an established place in
fluids-handling operations in reduced gravity environments. A quantitative understanding of corner flows is
essential for the myriad fluid management tasks in space including flows in liquid-fuel tanks,
heat pipes, energy systems, condensers, and life-support systems.
Though low-g fluid system designs are largely successful, current techniques for
predicting system performance are primarily limited to order of magnitude estimates,
delicately guided by the experience of the designer, or direct numerical simulation which can be
prohibitively time consuming. A reliable and quantitative design tool serving between these
extremes would be a welcome contribution to the low-g fluids management community.
Recently, closed form solutions for a variety of corner flows in simple geometries were derived, (see [1], and references contained therein); these results compare favorably with an extensive set of low-g experiments, [1-2]. These results are limited to flows of perfectly wetting fluids (zero contact angle) along a single straight corner for reasonably long times. An example of sudden capillary rise (imbibition) in a partially filled container of equilateral triangular section is shown in Figure 1. An example of a spreading drop in an interior corner is shown in Figure 2. In applications however, the fluids may be partially wetting (aqueous systems) and the non-ideal corners may be rounded, irregular, bent, and may bifurcate or join other corners. Furthermore, one is often interested in “startup” transients. While these inertia-dominated flows are mostly insignificant in 1-g due to the small size of earth-bound capillary flows, inertia often dominates for long periods in the large-scale capillary flows attainable in low-g.
We propose to carry out an applications-oriented experimental and theoretical
study to understand inertia-dominated capillary flows in interior corners as well as
flows in complex corner networks. For the experimental investigation, inertia-dominated flows in
simple geometries will be studied. This work will complement previous research on flows
which occur after the inertial phase is complete. For the complex corner network
experiments, flows in planar and subsequently three-dimensional geometries of increasing complexity
will be quantified in terms of corner geometry, size, fluid volume, and fluid
properties.
An important aspect of this work is the integration of experiment with theory.
In particular, we hope to provide not only the theoretical foundations, but to use comparison with
comprehensive experiments utilizing NASA’s drop tower(s) and aircraft to provide a practical
guide to the utility, error, and limitations of theory. This is expected to be most valuable
for the case of partial wetting, in which hysteresis and other non-ideal effects can be large.
For flows through the complex networks to be studied, numerical solutions would be prohibitively
expensive. We will investigate techniques that combine asymptotics along straight corners with
numerical results at joints between corners.
The overall goal of the proposed research is to provide a firm experimental and
theoretical footing for the design of corner-flow devices so that transient flow rate,
interfacial configuration and stability can be reliably predicted.
Weislogel, M.M., Capillary Flow in Interior Corners, Proceedings of the Fifth Microgravity Fluid Physics and Transport Phenomena Conference, NASA Glenn Research Center, Cleveland, OH, CP-2000-210470, pp. 1398-1400, August 9, 2000.