Pore-Scale Wetting Process of Capillary-Driven Flow in Unsaturated Porous Media under Micro- and Earth-Gravities

Abstract

Microgravity hinders capillary-driven water flow in unsaturated porous media. Previous studies proposed pore-scale phenomena such as “air entrapment”, “particle separation”, and “interruption on widening void space” to explain gravity-dependent capillary-driven flows. Our objectives were: (1) to measure the water flux densities of the pore-scale capillary-driven flow in micro- and Earth-gravities and (2) to reveal that what makes water flow slower under microgravity than under 1 G. We found that average macroscopic water flux densities had no significant difference under micro- and Earth-gravities (p = 0.30). We did not observe “air entrapment” in the pore spaces of porous media. “Widening on a single particle” and “capillary widening” disturbed capillary-driven flow; however, “widening on a single particle” had no significant gravity dependency. “Capillary widening” may be independent of gravity, since it was observed both under microgravity and under 1 G. Water flux densities in unsaturated porous media may have gravity dependency induced by “particle separation” only when porosity is large enough to allow particles to move.

1. Introduction

A sustainable human settlement on and around the moon will be established in 2028 [1]. Growing plants under extraterrestrial environments are essential for four reasons: producing food, recycling the atmosphere, processing wastewater, and providing a stress-relief environment for astronauts [2]. Massa et al. [3] reported that although red Romain lettuces were grown under microgravity in the International Space Station (ISS) using Veggie, a plant growth platform, lettuces suffered from water stress and died. Therefore, it may be indispensable for sustainable plant growth to understand water movement in cultivation media.

A limited number of research studies have been conducted to understand water movement in porous media under microgravity due to short-time microgravity. Heinse et al. [4] reported that water retention characteristics for the wetting condition under microgravity were similar to those under Earth-gravity (1 G). Saturated hydraulic conductivity, measured under pressurized conditions, had little gravity dependency when the media was densely packed [5]. Heinse et al. (2007) [4] concluded that the Buckingham–Darcy law and Richards’ equation were applicable for describing macroscopic porous-medium fluid behavior under microgravity. However, predicting capillary-driven flow in unsaturated porous media under microgravity was difficult. Under microgravity, the capillary-driven flow in unsaturated porous media became slow [6,7] or did not occur at all [7]. Unsaturated hydraulic conductivity was smaller under microgravity than under 1 G [8].

A few theories have been proposed to explain the gravity dependencies of capillary flows. For example, Jones and Or [8] hypothesized that “air entrapment” and “particle separation” contributed to smaller flux densities under microgravity than under 1 G. When the wetting front moved to the pore body from the pore neck in massive porous media [9] (Figure 1a) or glass tube [10] (Figure 1b), “interruption on widening void space” in the wetting front was observed. Or et al. [11] noted that when fine and coarse beads were packed side by side, water exclusively flowed in the fine beads. Their result suggested that the “interruption on widening void space” was observed on the boundary of the different beads’ diameters (Figure 1b). However, it is not clear whether slow water flow due to the “interruption on widening void space” is gravity-dependent or not. “Air entrapment”, “particle separation”, and “interruption on widening void space” are pore-scale phenomena; most of the previous studies under microgravity, however, focused on Darcy-scale flows. Therefore, studying pore-scale flow is essential for elucidating the gravity dependency of capillary-driven flow in unsaturated porous media.

Pore-scale flow under 1 G is generally not a Darcian flow; it is composed of numerous interfacial jumps called Haines jumps [12]. Since the flux densities of the Haines jumps are more than 50-times larger than the macroscopic mean flux densities [13,14], high-speed cameras are required to observe those flows. Few attempts have been made to develop a quantitative description of those flows even under 1 G. Moebius and Or [13] modeled pore-scale drainage dynamics in a monolayer of regularly arranged glass beads under 1 G by two hydraulically connected sinusoidal capillary tubes. The study revealed that the power balance of capillary pressure, viscous pressure, gravity, and inertia characterized the wetting front movement. Armstrong and Berg [14] observed the drainage process of water replaced by oil in an artificial micro-pattern with spherical pore bodies connected to pore necks under 1 G. The wetting events on pore necks were observed when drainage on pore bodies occurred. The authors noted that part of the drained water from the pore bodies was supplied to the pore necks, and most of the interacting menisci were more than seven pores apart from the location of the drainage event. However, most previous research focused on the drainage process; thus, pore-scale flow in the wetting process is not well understood. Furthermore, the pore-scale capillary-driven flow is not well known, since syringe pumps were used to drive flows in previous studies.

In this study, “particle separation” was reduced by dense packing. Therefore, we focused on the hypotheses of “air entrapment” and “interruption on widening void space.” Our objectives were (1) to measure the water flux densities of the pore-scale capillary-driven flow under microgravity and under 1 G and (2) to reveal what makes capillary flow slower under microgravity than 1 G.

2. Materials and Methods

2.1. Experimental Apparatus

We conducted experiments for the two types of widening: the widening on a single particle and capillary widening as shown in Figure 1. To examine capillary widening, two layers of glass beads, 40 mm in thick for 0.8 mm beads (BZ-08, AS ONE, Osaka, Japan) and 31 mm thick for 1.0 mm diameter beads (BZ-1, AS ONE, Osaka, Japan), were filled in the Hele-Shaw cell made from acrylic plates (inner dimension of 24 mm × 71 mm × 2.4 mm; Figure 2). The boundary of the two layers was the location for widening capillaries (Figure 1b). The beads were packed densely by tapping every 20 mm thick layer using the head of a pestle. The average bulk density and porosity are shown in

Table 1. Average bulk density and porosity of 0.8 mm and 1.0 mm beads layers.

Bead’s Diameter (mm)	Bulk Density (Mg/m3)	Porosity
0.8	1.48	0.41
1.0	1.19	0.52

. Degassed water with a methylene blue dye in a Mariotte bottle was supplied to the cell by means of a solenoid valve. White LEDs lighted the cell from the bottom via a smoked acrylic board. Water was infiltrated in advance about 5 mm ahead of the boundary before observing the flow during capillary widening (Figure 2). Since water moved upon a single particle quickly and microscopically, infiltration was captured about every 0.001 s with a high-speed and closeup camera (DSC-RX100M5A, SONY, Tokyo, Japan). A 2.4 s microgravity condition ($-4.5\times {10}^{-3}\pm 8.8\times {10}^{-3}$ G; Figure 3) was obtained by free fall from the top of a 50 m drop tower (COSMOTORRE, HASTIC, Hokkaido, Japan) from 17 to 19 October 2019. A microcontroller board (Arduino Uno, Arduino) monitored an accelerometer (MMA7361, Freescale Semiconductor, Austin, TX, USA), controlled the solenoid valve, and released the camera’s shutter (Figure 4). The valve was opened 0.2 s after the beginning of the microgravity condition to allow the infiltration of water into the glass beads (Figure 3). While the valve was open, a green LED was lit as the valve’s status indicator. The movie was recorded for about 2.2 s until the end of the microgravity condition. For reference experiments, horizontal infiltration was observed under 1 G. To compensate for the hydraulic head pressure in the cell, the lower end of the Mariotte tube was arranged at the same height as the center of the porous media. The experiments were conducted three times under microgravity and under 1 G, respectively.

2.2. Image Analysis

Infiltration movies were split into pictures and analyzed by Python 3.8 program using OpenCV library (https://opencv.org/: accessed on 9 April 2022). Pixel intensities between the first and subsequent time steps were compared to determine water flux densities at every 0.001 s. The flux densities under microgravity and under 1 G were compared using p values. p values smaller than 0.05 were considered significant. p values were calculated using the t-test analysis tool in Microsoft Excel. Wetted areas detected using the developed program agreed well with more than 90% of the actual wetted areas. Coordinates of target beads were manually provided to the program. Percentages of a wetted area to the entire area for each target bead were calculated over time. The wetting front’s mobilities under microgravity were compared to that under 1 G. Relative volumetric water contents at each distance from the boundary were evaluated.

3. Results and Discussion

The average macroscopic water flux densities were 0.46 mm/s under microgravity and 0.47 mm/s under 1 G, which were not significantly different (p = 0.30). These results support the conclusion that water flux density in unsaturated porous media does not have gravity dependency when porous media are densely packed.

Our results opposed Yendler et al. [6] and Bula et al. [7], who expressed that macroscopic water flux densities were smaller under microgravity than under 1 G. As Jones and Or [8] noted, “particle separation” likely plays an important role in determining the gravity dependency of the capillary-driven water flux density in unsaturated porous media. In other words, water flux density in unsaturated porous media possibly has gravity dependency only when the porosity is large enough to allow particles to move.

Air entrapment in the pore body was not observed in this experiment. In the small void space of porous media, water wetted the entire pore and the particle’s surface. The entrapment was also not observed in the sinusoidal glass tube, which had a larger void space than porous media [10,15]. Therefore, air entrapment probably occurs only in massive void spaces such as a large bottle [16] under microgravity.

3.1. The Wetting Front Mobility of the Widening on a Single Particle

Under microgravity and under 1 G, the wetting front went over the widening of single porous particle. Figure 5 shows water flux densities at every 0.001 s in porous media under microgravity and 1 G. The maximum microscopic flux densities of capillary-driven flows were about 30-times larger than the macroscopic mean flux densities, which is smaller than the pressurized drainage process that is more than 50-times larger [13,14]. Figure 6 shows the relative frequency distribution of the water flux densities in porous media under microgravity and under 1 G. The variances under microgravity and under 1 G were 1.54 and 2.14, respectively, which were slightly larger under 1 G than under microgravity (Figure 6: normal distribution). However, no significant gravity dependency was observed (p = 0.56).

Figure 7 indicates the relative frequency distribution of the wet part on each bead. A higher frequency shows that the wetting front stopped there for a longer period of time. Under microgravity and under 1 G, the wetting front showed bimodal distributions. The wetting front often stopped when 10% to 40% or 80% to 90% of each bead was wetted. Figure 8 shows the diagram of the wetting process observed in this study. When less than 40% of the bead was wetted, the wetting front had difficulties passing over the widening pore; thus, a high relative frequency was observed (Figure 7 and Figure 8: phase 1). On the other hand, the relative frequency was low when 55% to 80% of the bead was wet since the wetting front moved easily upon the narrowing of the pore (Figure 7 and Figure 8: phase 2). When the wetting front reached phase 3 in Figure 8, the wetting front needed to touch the next bead, which allowed it to pass over the widening pore; therefore, a high relative frequency was shown at 80% to 90% of the wetted bead (Figure 7). This wetting process cycle was observed in both gravity conditions. The average wet part of a bead was $0.43\pm 0.26$ mm²/mm² under microgravity and $0.39\pm 0.25$ mm²/mm² under 1 G, which was not a significant difference. Therefore, the widening on a single particle had no significant gravity dependency.

We also found the interesting dynamics of the wetting process both under microgravity and under 1 G. Figure 9a,b indicate the time series of the wet part’s percentage on the five beads shown in Figure 9c,d, respectively. The phenomena shown in Figure 9 were observed under both gravity conditions; 1 G data were shown as representative. Oscillations of the wetting front were observed on the beads and synchronized with each other (Figure 9a). We also found that the wetting front went backward when the front on another bead went forward (Figure 9b). These results suggested that water was supplied not only from the bath but also from the surrounding wetted pores. Armstrong and Berg [14] reported that water replaced oil in the pore neck and drained oil to the pore body. The hydrophilic property of water made it more stable in the pore necks than in the pore bodies. The oscillations and the backward movements of the wetting front observed in this study were probably induced by suction between the pore bodies and the surrounding pore necks, which were in a “tug-and-pull” relationship. In the definition, the backward movement implies negative flux densities. Due to the oscillations and backward movements, 20% of the flux densities took negative values (Figure 6). Armstrong and Berg [14] previously reported that the drainage event was cooperative when more than seven pores apart. However, we found that the wetting event was cooperative as far as 25 pores apart.

It was also observed that the wetting front infiltrated forward more after the front moved backward by “tug-and-pull” movements both under microgravity and 1 G (Figure 9d: bead number 5). Water re-wetted the widening of the pore when suction from the surrounding pore neck was released. Inertia force, induced by this re-wetting momentum, was possibly essential for breaking the balance of the “tug-and-pull” motion and allowed water to infiltrate into the pore body, where larger (less negative) capillary pressure acted at the pore’ neck.

3.2. The Wetting Front Mobility on the Capillary Widening

Relative volumetric water content in each 0.5 s was shown under microgravity (Figure 10a–c) and 1 G (Figure 10d–f). The wetting front crossed the boundary both under microgravity and under 1 G. However, when the most advanced wetting front approached the boundary, water content at 0 to 0.2 did not temporarily increase (0.0 to 1.0 s in Figure 10a,b,d,f; 1.5 to 2.0 s in Figure 10c), with the exception of that shown in Figure 10e for which its boundary was uneven. These results suggest that water was temporarily restricted from flowing at the boundary under microgravity and under 1 G. The wetting front crossed the boundary when the surrounding wetting front caught up. The smaller pore in the 0.8 mm beads than in the 1.0 mm beads resulted in smaller (more negative) matric potentials, and the wetting front preferentially moved into pores in the 0.8 mm beads. This temporary restriction of infiltration on the boundary was observed both under microgravity and under 1 G; therefore, water movement during capillary widening may be independent of gravity.

4. Conclusions

This study observed pore-scale and capillary-driven flows in densely packed porous media under micro- and Earth-gravities. The average macroscopic water flux densities were 0.46 mm/s under microgravity and 0.47 mm/s under 1 G, which showed no significant difference (p = 0.30). “Air entrapment” was not observed in the pore space of porous media. The pore-scale frequency distributions of the water flux densities had no significant gravity dependency (p = 0.56). The widening on a single particle disturbed capillary-driven flow; however, no significant gravity dependency was observed. Capillary widening temporarily restricted the infiltration both under microgravity and under 1 G; therefore, water movement at the widening capillary may be independent of gravity. Water flux density in unsaturated porous media may have gravity dependency by particle rearrangement when porosity is large.

The oscillations and the backward movements of the wetting front were observed by the analysis of wet parts on each porous particle. The suctions between the pore bodies and the surrounding pore necks were in a “tug-and-pull” relationship and probably induced wetting front oscillations and backward movements. The wetting event was cooperative as far as 25 pores apart. This is in contrast to the literature, which deems it as seven pores apart. Inertia force, induced by this re-wetting momentum after backward movements, was possibly important for breaking the balance of the “tug-and-pull” relationship and allowed water to infiltrate into the pore’s body from the pore’s neck.