The draining of capillary liquids from containers with interior corners aboard the ISS

The study addresses how to efficiently drain liquids in microgravity where gravity-driven drainage is ineffective and capillary forces dominate. In orbit (g ~ 10^-6 g0), interior corners within containers act as open capillary conduits, enabling liquid removal provided the Bond number Bo = Δρ g H / σ < 1. The work focuses on single-port capillary draining from containers with interior corners, pertinent to spacecraft fluids (fuels, propellants, coolants, water) and terrestrial microfluidics where precious liquids must be drained with minimal hold-up. The Concus–Finn wetting condition predicts whether a corner imbibes liquid depending on contact angle and corner geometry. In microgravity, the characteristic capillary length H can be orders of magnitude larger than on Earth, producing capillary-dominated flows at centimetric scales with unusual viscous and inertial balances. Leveraging NASA’s Capillary Flow Experiments (CFE) aboard ISS (2010–2015), the paper extracts quantitative benchmarks for transient interface profiles and volumetric drain rates from seven container types with interior corners, to assess and improve theoretical and numerical models for capillary draining in low-g.

Prior foundational work includes the Concus–Finn wetting condition for corner imbibition and heuristic/experimental studies on wetting, meniscus stability, and condensation in corners. Lubrication approximations for slender capillary corner flows have been developed and applied to a variety of geometries relevant to spacecraft fluids management, including propellant tank vane networks, curved corners, open rectangular channels, nonplanar corners, and rounded geometrical features. Numerous numerical and experimental investigations have examined capillary rise and flows in single and square corners, stepped and rounded corners/vertices, and real-world corners, typically assuming local parallel flow with negligible streamwise curvature and inertia. Inertial-capillary regimes and cases with significant streamwise curvature are treated elsewhere. These studies provide the theoretical basis (lubrication theory with geometric boundary conditions) that the present work benchmarks against unique low-g data from ISS across multiple container geometries (tapered triangular and rectangular sections, stepped tapers, vane-partitioned squares, and partitioned cone-like sections).

Experiments: NASA’s ISS Capillary Flow Experiments (CFE-ICF) comprised handheld, centimetric-scale containers with interior corners. Each experiment partially filled a container with perfectly wetting PDMS fluids of selected viscosities, established a low-g static equilibrium, and then drained the liquid through a single exit port by manually turning a piston-driven reservoir valve. Astronauts attempted to maximize drain rate while avoiding gas ingestion at the port. Seven ICF geometries (from nine total) included: weakly/strongly tapered triangular sections (ICF-1, ICF-9), tapered rectangular section (ICF-2), stepped tapers (ICF-3, ICF-4), a square section with a tapered diagonal vane (ICF-6), and a partitioned constant section (ICF-8). Many cells were drained from both “small-end” and “big-end,” creating distinct geometries per run. Data acquisition and reduction: HD video (Canon XF305) was backlit and recorded; still frames were extracted at 1 or 0.2 Hz from 60 fps source. Automated interface tracking converted frames to binary images and applied a Canny edge detector (dual thresholds) to reduce noise from bubbles/reflections. Regions of interest were incrementally processed to extract interface pixels and smoothed with moving-average filters to obtain h(z,t) and bulk meniscus position z2(t). Piston positions were tracked to compute volumetric flow rates Q(t); smoothed fits were differentiated to mitigate noise. Optical alignment errors were negligible at ~1 m camera distance; diffraction-induced index mismatch distortions were corrected (2–10%). The processed dataset spans ≈8442 s (>2 h) of low-g draining across runs. Theoretical model (for comparisons): A lubrication approximation for slender corner flows (H^2/L^2 << 1), hydrophilic wetting satisfying Concus–Finn, negligible streamwise curvature and inertia, and constant contact angle is employed. The primary flow is along the corner vertex (z-axis). A dynamical boundary condition sets the corner-film height at the matching point with the bulk meniscus, H(z2), determined from container perimeter Ps, cross-sectional area A, and geometric curvature functions f(α,θ). With appropriate scaling, O(1) self-similar solutions for constant cross-section containers predict: h(z,t) ~ t^1/3, Q(t) ~ t^0 (constant in similarity variables), and z2(t) ~ (2t/3)^{1/2}. For linearly tapered containers, solutions predict h scaling with local H(z), Q(t) ~ t^2/27, and z2(t) ~ t/3 (linear in time). A start-up time offset t0 accounts for initial non-self-similar transient (t0 = 3/2 for constant sections; t0 = 3 for tapered; ICF-8 required different handling). Experimental data for z2(t), Q(t), and h(z,t) were compared against these analytic solutions, recognizing that some geometries (e.g., vane pinning, strong streamwise curvature, partitioned flows) violate model assumptions and are expected to show poorer agreement.

Overall benchmark performance: - Across cells conforming to theory (ICF-1, -2, -3, -4, -9), average agreement: advancing bulk meniscus z2 within ±8% and flow rates Q within ±21%. Deviations arise from manual drain control, finite drain-port meniscus height, inertia, boundary condition violations, and bubbles. Per-geometry highlights: - ICF-1 (weakly tapered triangular, n=3 corners): • Small-end drain: z2 discrepancy up to 11%; Q qualitatively follows theory despite gas-ingestion interruptions and piston resolution limits; self-similar height h overshoots constant-height theory due to H(z) increasing with z. • Big-end drain: z2 max discrepancy ~7%; Q agreement within ≈22%; h undershoots theory as H(z) decreases with z. Model predicts two 75° corners contribute ~3% of total Q. - ICF-2 (tapered rectangular, n=4 corners; effectively constant H): • Small-end: z2 within 5% of theory; Q within 12%; h(z,t) not digitizable due to viewing angle. • Big-end: only one run; qualitative agreement for z2 and Q. - ICF-3 (stepped taper, snow-cone-like, n=1; drained within constant section): • Small-end: z2 error <3.5%; Q error <12%; self-similar h over-predicted, likely due to inertia. • Big-end: z2 over-predicted with max error <8.5%; Q over-predicted on average <14%; near-drain h good, downstream over-predicted, consistent with larger inertia. - ICF-4 (stepped taper, ice-cream-cone-like, n=1; constant section encountered): • Small-end: z2 error <14%; Q lower than theory and nearly constant in time; h under-predicted by theory; finite drain-port height (2–3 mm to avoid gas) reduces Q and slows z2. • Big-end: z2 errors <13%; Q agrees within ≈27% qualitatively; h predicted well with average error <9%. - ICF-6 (square with tapered diagonal vane, n=5 effective edges; dominant 45° vane corners): • Both ends: lubrication theory not appropriate; z2 and Q significantly lower than predicted; nearly linear z2 suggests effective taper but with strong reduction due to contact-line pinning on vane edges, increasing effective contact angle and reducing capillary pressure gradients; improved H(z,t) with pinning needed. - ICF-8 (partitioned constant section with vane gaps, n=1): • Strong streamwise curvature and partitioning violate assumptions; h(z,t) poorly captured; z2 initially slower, then would overtake theory over longer times; surprisingly, Q agrees within ~2%, possibly because constant streamwise curvature across segments and viscous resistance set by vane-gap H rather than actual profile. - ICF-9 (strongly tapered equilateral triangular, n=3): • Small-end: z2 advances linearly in time as predicted; max error <1%; Q increases with time (unique among tests), max error <30%, average <10%; h agrees with average error <20%; inertia exceptionally low relative to other cells. Data quality and processing: - Dataset spans >2 h of flight video; optical diffraction corrections 2–10% applied; automated Canny-based edge detection used with manual intervention when bubbles complicated tracking. Public data and MATLAB files provided (figshare DOI 10.6084/m9.figshare.16632472.v1).

The study demonstrates that, despite incidental and manually controlled ISS experiments, a simple lubrication-based model can reasonably predict capillary draining along interior corners in microgravity for geometries and conditions that satisfy model assumptions (slender films, negligible streamwise curvature/inertia, valid Concus–Finn wetting, constant contact angle). The comparisons validate geometry-dependent dynamic boundary conditions for the interface height at the bulk-corner matching point in several cases and highlight where they fail (e.g., vane edge pinning, partitioned flows, non-negligible streamwise curvature). The results provide rare, quantitative benchmarks for theory and numerics over multiple container families. Discrepancies between data and theory point to the need for refined models incorporating finite drain-port meniscus height, contact-line dynamics and pinning (especially at vane edges), streamwise curvature effects, and complex multi-corner coupling. Given the large capillary length scales and unusual viscous/inertial balances in microgravity, these findings are directly relevant to spacecraft fluids management (e.g., propellant/water systems) and to terrestrial small-scale systems where capillarity dominates.

This work mines and digitizes ISS CFE-ICF video archives to produce a publicly available dataset of transient interface profiles, advancing menisci, and volumetric flow rates for capillary draining from containers with interior corners. Across seven container types and 27 runs, lubrication theory provides adequate predictions for z2(t) and Q(t) in geometries conforming to its assumptions, while identifying clear limitations in vane-partitioned and strongly curved streamwise flows. Contributions include: (i) a curated benchmark dataset corrected for optical distortions; (ii) quantitative validation and falsification of geometry-dependent dynamic boundary conditions for corner flows; and (iii) guidance on model extensions for complex geometries. Future work should incorporate: improved H(z,t) boundary conditions with contact-line pinning and vane effects; models including streamwise curvature and inertia where relevant; and tailored theories for partitioned/vaned networks. The dataset enables further theoretical, numerical, and design advances for efficient capillary draining in space and on Earth.

- Manual operation leads to variable, irregular drain rates; astronauts often paused drainage to avoid gas ingestion, introducing transients. - Finite meniscus height at the drain (typically 2–3 mm to avoid gas) violates the zero-height boundary assumption and reduces flow. - Presence of bubbles and reflections complicates interface detection; some profiles required manual intervention; uncertainties in Q reported (<28% average for ICF-1 cases). - Optical distortions from refractive index mismatch required corrections (2–10%); residual errors possible. - Non-orthogonal viewing prevented interface height extraction for certain cells (e.g., ICF-2 h(z,t)). - Lubrication assumptions (slender films, negligible streamwise curvature/inertia, constant contact angle) are violated in some geometries (ICF-6 vane pinning, ICF-8 partitioning and strong streamwise curvature), limiting quantitative applicability. - Some tests encountered gas ingestion events and step geometries not engaged during the observed drain, constraining the comparison domain. - Start-up transients require time-offset handling; one case (ICF-8) did not follow the standard t0 treatment.