Capillary channel flow experiments aboard the International Space Station

In the near-weightless environment of orbiting spacecraft capillary forces dominate interfacial flow phenomena over unearthly large length scales. In current experiments aboard the International Space Station, partially open channels are being investigated to determine critical flow rate-limiting conditions above which the free surface collapses ingesting bubbles. Without the natural passive phase separating qualities of buoyancy, such ingested bubbles can in turn wreak havoc on the fluid transport systems of spacecraft. The flow channels under investigation represent geometric families of conduits with applications to liquid propellant acquisition, thermal fluids circulation, and water processing for life support. Present and near future experiments focus on transient phenomena and conduit asymmetries allowing capillary forces to replace the role of gravity to perform passive phase separations. Terrestrial applications are noted where enhanced transport via direct liquid-gas contact is desired.

Figure 1

Capillary channel configurations that have been studied over the past decades. (a) Parallel plates, (b) groove, and (c) wedge. The channels have a width $a$, a height $b$, and a length of the free surface $l$. A pressure gradient between channel inlet and outlet is applied to generate a liquid flow with a flow rate $Q$.

Figure 2

Parallel plate channel geometry: (a) $yz$ plane with the cross-sectional area of the flow $A\left(x\right)$ and the radius $R\left(x\right)$ at the surface. (b) $xz$ plane with the channel inlet at $x=0$ and the channel outlet at $x=l$ with free surface contour $k\left(x\right)$ (flow in the $x$ direction). The liquid pressure in the channel is lower than the outside pressure due to the curvature of the free surface.

Figure 3

Schematic of the flow configuration and boundary conditions of the CCF ISS experiment. A reference pressure is provided by the meniscus in the compensation tube, the nozzle delivers the flow conditions at $x=0$, and the flow rate $Q$ sets the mean velocity at the outlet.

Figure 4

Choking phenomenon with periodical gas ingestion in a supercritical capillary channel flow (flow is upward). The free surfaces are depicted by bold curved lines in the lower half of each image. In this example $l=25$ mm and the flow rate $Q=5.72$ ml/s is 1% above the critical value. The time step between two frames is $0.41$ s and about one bubbles in 4 s is ingested into the channel.

Figure 5

Three representative free surface contours for parallel plate channels of different lengths for the maximum flow rate with stable deformations. The combined systematic and statistic error of the contour position $k\left(x\right)$ due to flow rate adjustment and image processing is below 0.2 mm. The critical flow rates in experiment, model with plug inflow, and model with Poiseuille inflow were (i) for $l=20$ mm: $Q_c=5.87,5.84,6.29\mathrm{ml}/\mathrm{s}$, (ii) for $l=35$ mm: $Q_c=5.55,5.31,5.82$ ml/s, and (iii) for $l=48$ mm: $Q_c=5.27,5.06,5.58\mathrm{ml}/\mathrm{s}$. Further increases of the flow rate would lead to choking as shown in Fig. 4.

Figure 6

Dependence of critical flow rate on open channel length for both experimental results and numerical predictions for the parallel plate channel. The experimental error is less than $\pm 0.2$ ml/s.

Figure 7

Pressure loss factor $K_{\mathrm{Sf}}$ and its gradient ${\widehat{K}}_{\mathrm{Sf}}$ in dependence of the transformed entrance length $\widehat{x}$ for the entrance flow between two parallel plates.