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

Efficient draining of liquids is crucial in various applications, from biofluidics processing on Earth to cryogenic fuel management in spacecraft. In microgravity, capillary forces dominate liquid behavior, making the geometry of the container a key factor in drainage efficiency. This study focuses on the draining of liquids from containers with interior corners, using NASA's Capillary Flow Experiments (CFE) conducted aboard the ISS. These experiments, though not initially designed for quantitative analysis, provide valuable data on large-scale capillary phenomena. The Bond number (Bo = ΔρgH/σ < 1, where Δρ is the density difference, g is gravity, H is the characteristic height, and σ is surface tension) determines if capillary forces dominate. In the ISS's low-gravity environment (g ~10⁻⁶g₀), Bo < 1 is readily achieved, making capillary forces the primary driver of liquid movement. The Concus-Finn wetting condition determines when a corner imbibes a liquid, influencing the drain rate and amount of residual liquid. Previous research has explored capillary corner flows in various geometries, but low-g environments present unique challenges and opportunities to study these phenomena at larger length scales. The rarity of access to microgravity environments necessitates thorough data extraction from existing experiments. This paper uses existing NASA video records to quantitatively analyze these low-gravity drainage events.

The literature review discusses existing theoretical and experimental work on capillary corner flows, including the Concus-Finn wetting condition, lubrication models for slender flows, and studies of capillary flows in various geometries (propellant tank vane networks, curved corners, open rectangular channels, etc.). The review highlights previous numerical investigations of capillary flows in different low-g conditions (single interior corners, square channels, stepped corners, etc.). These investigations often simplify the governing equations using the lubrication approximation, assuming local parallel flow with negligible streamwise curvature and inertia. The review mentions limitations of existing models, particularly those neglecting streamwise curvature and inertia. The authors note that the capillary length scale, typically sub-millimetric on Earth, can reach sub-metric levels in microgravity, leading to unique viscous-capillary time scales and inertial-capillary balances.

The study utilizes data from NASA's CFE conducted on the ISS. The CFE experiments involved partially filling containers with liquid, observing their behavior in low-g, and then draining the liquid. The focus is on single-port draining from containers with interior corners. The researchers digitized hours of archived video data using in-house automated interface tracking algorithms. This involved converting videos to still images, applying a Canny filter to reduce noise, and tabulating interface pixel data to determine transient fluid interface profiles. The process yielded time-dependent interface profiles, bulk meniscus receding velocities, and volumetric drain rates. Corrections were applied to account for optical distortions due to misalignment and refraction index mismatches. The methodology details how the researchers extracted the advancing bulk meniscus position (z₂(t)) and interior corner height profiles (h(z, t)), while tracking piston position to calculate volumetric flow rates (Q(t)). The analysis used in-house developed automated interface tracking algorithms that convert videos to still images, apply a Canny filter to reduce image noise, and tabulate interface pixels to determine the meniscus profiles. Optical distortion corrections were also applied to improve data accuracy.

The key findings are presented through a detailed analysis of seven different container types (ICF-1 through ICF-9, except for ICF-5 and ICF-7). For each container, the authors compare experimental data (advancing bulk meniscus location z₂(t), volumetric flow rate Q(t), and corner flow profile h(z,t)) to predictions from a lubrication model. The lubrication model considers slender flows along interior corners, with different assumptions depending on the container geometry (constant cross-section or tapered). The model is relatively accurate in some cases and inaccurate in others, providing valuable insights into the limitations of the model and highlighting the importance of parameters such as container taper, presence of vanes, and the impact of streamwise curvature and inertia. The findings show varying degrees of agreement between the experimental data and the lubrication model. Some containers (ICF-1, -2, -3, -4, and -9) show good agreement for flow rates within ±21% and advancing meniscus positions within ±8%, while others (ICF-6 and -8) exhibit significant deviations due to the complexities of their geometries (vanes and partitions). Discrepancies are attributed to manual drain rate control, gas ingestion, non-negligible inertia, boundary condition violations, and the presence of bubbles. Specific analyses are performed for each of the ICF containers, demonstrating varying degrees of agreement and disagreement with the theoretical lubrication model. The analysis provides a detailed breakdown of the factors influencing the drain rate and interface profiles.

The study demonstrates the value of utilizing archived data from space experiments to validate theoretical models. The comparison of experimental data with the lubrication model highlights the model's strengths and weaknesses, suggesting areas for improvement. The deviations between experimental results and model predictions can be attributed to factors like manual control of drain rates, gas ingestion, inertial effects, and deviations from the assumed slender flow conditions. The results emphasize the importance of considering these factors in future model development. The study also emphasizes the need for more sophisticated models that account for complex geometries and flow dynamics. The findings are valuable for improving liquid management systems in both large-scale spacecraft applications and small-scale terrestrial applications. The significant differences observed between experiment and model predictions for certain container types, particularly those with vanes or partitions, highlight the need for further theoretical and numerical work to account for geometric complexities and boundary conditions.

This study provides a valuable dataset for benchmarking theoretical and numerical models of capillary draining in low-g environments. The analysis of NASA's CFE-ICF data shows that a simple lubrication model provides a reasonable estimate of the drainage behavior for certain geometries, but more sophisticated models are needed to account for the complexities observed in more irregular shapes. Future research should focus on extending the lubrication model to account for factors like streamwise curvature, vane geometry, and contact line pinning. The authors make all data publicly available to encourage further investigation.

The study's limitations include the manual control of the drain rate by astronauts, leading to variations in the drainage process and possible gas ingestion. The lubrication model's assumptions (slender flow, negligible streamwise curvature, and inertia) may not hold for all geometries and flow conditions, explaining the deviations between model predictions and experimental results for some containers. The presence of bubbles and image noise could also impact data accuracy. The analysis focuses primarily on single-drain scenarios; thus, the data may not fully capture the complexities of more realistic multi-drain configurations.