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Hernandez Engineering, Mail Code C77, Johnson Space Center, National Aeronautics and Space Administration, 2101 NASA Parkway, Houston, TX 77058
* Corresponding author (susan.l.steinberg1{at}jsc.nasa.gov)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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10–4 cm s–1 for both particle-size distributions. Significant differences in log10K due to method and porous medium were less than one order of magnitude and were attributed to variability in air entrapment. The van Genuchten/Mualem parametric models provided an adequate prediction of K of the interaggregate pore space, using residual water content for that pore space. The instantaneous profile method covers the range of water contents relevant to plant growth using fewer resources than Method A, all advantages for space flight where mass, volume, and astronaut time are limited.
Abbreviations: 
, volumetric water content • 
, matric potential • Method A, steady state • Method B, instantaneous profile • K, hydraulic conductivity
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The study of flow through porous media on earth has commonly involved the use of models, such as the Richards equation, to estimate hydraulic parameters (Hillel, 1998). For example, measurement of K has presented many challenges on earth, thus parametric models have been developed to estimate this property from parametric models alone (Mualem, 1976) or in combination with inverse methods (Hopmans et al., 2002). However, the use of these methods to simulate hydraulic properties of porous medium in microgravity has been questioned due to the lack of understanding of fundamental mechanisms controlling water and air distribution and transport in microgravity (Jones and Or, 1999; Bingham et al., 2000a; Steinberg et al., 2002).
While microgravity conditions can be simulated by simply eliminating the gravity term in conventional unsaturated flow models, it is not clear whether experimental measurements of K, water retention, or hydraulic gradient made in earth gravity implicitly reflect the influence of earth gravity on transport. In one example from microgravity, saturated K had to be reduced from measured values by several orders of magnitude to fit fluxes calculated from data using existing parametric models (Jones and Or, 1999). There is evidence of accentuated hysteresis, reduced K, and changes in water retention properties of particulate plant growth media in microgravity as compared with earth (Jones and Or, 1999). These differences have been attributed to enhanced interfacial flow, particle rearrangement, and air entrapment.
Unsaturated K of porous media commonly used for space flight has not been well characterized in earth gravity. To date, there has not been a space flight experiment dedicated to understanding flow through porous plant growth media. The few microgravity data sets available come from engineering tests or plant growth experiments (Morrow et al., 1994; Bingham et al., 1996). To improve the understanding of fluid flow through porous media in microgravity it is necessary to directly measure water retention and K in the particulate medium and shallow root zones common to space flight, both on earth and in microgravity.
Measurement of K in microgravity will preclude the use of many standard methods (Klute and Dirksen, 1986) that rely on gravity to move water. Furthermore, experimental designs for space flight will be constrained by mass, volume, power, and flight time. The objective of this research was to characterize the K of plant growth media commonly used for space flight using earth-based analogs to microgravity conditions. The efficacy of Methods A and B to directly measure saturated and unsaturated hydraulic K were compared within a single test apparatus using horizontal flow through shallow sections of porous medium to minimize gravitational head. The methodology and experimental design are compatible with future comparisons in microgravity or between microgravity and earth gravity. Additionally, direct measurements of K were compared with that predicted from numerical analysis of the water retention curve as a first step toward understanding the use of parametric models to represent hydraulic properties of porous medium in microgravity.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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) within the range of 0.7 to 0.4, representing the interaggregate pore space that supports viable plant growth.
Hanging Water Column System
Water retention and flow experiments were conducted in 15.24 by 15.24 cm trays similar in size to those used in Orbital Technology's (Orbitec, Madison, WI) Biomass Production System that supported PESTO (Photosynthesis Experiment System Testing Operation), a plant experiment conducted on the International Space Station during Spring 2002. Media depth was 3 cm, similar to that used in recent science and commercial space flight experiments.
A 15.24 cm long, 0.95 cm OD, stainless steel microporous tube (Mott Metallurgical, Farmington, CT) was located at opposite ends of each tray (Fig. 1). The center of the tube was located 1.5 cm above the bottom of the tray. Tubular rather than rectangular membranes were used in this study for compatibility with flight units due to the inability to remove air bubbles from square or rectangular configurations in microgravity, and to minimize gravitational head on the waterside of the membrane. Membrane pore size of 20 and 40 µm for 0.25- to 1- and 1- to 2-mm porous medium, respectively, was selected to for maximum K while still allowing control of matric potential () over the range of interest. Saturated K of 20 and 40 µm stainless steel tubes were 0.08 cm s–1 and 0.10 cm s–1.
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0.4 cm. Although a hanging water column control system cannot be used in microgravity, it is analogous to the porous tube water delivery systems used for space flight in which pumps are used to create a water tension with the microporous tubes, and pump rotation counts are used to quantify water inflow or outflow from a tray. A predetermined mass of dry porous medium was added to the tray and packed to a bulk density of 0.69 and 0.65 for 0.25- to 1-mm and 1- to 2-mm particles, respectively. Variation in bulk density that occurred by holding the 3-cm depth constant was ±2% or less and was attributed to the shallow square container, presence of objects within the porous medium, and random variation. The medium was covered with a porous PVC lid such as would be used to contain the particulates in microgravity, and then polypropylene plastic to prevent evaporation.
The medium was slowly wetted to satiation (Hillel, 1998, p. 130) (saturation achievable under natural conditions) to minimize air entrapment. Complete saturation of 0.25- to 1- and 1- to 2-mm porous medium results in 0.74. These water contents can only be achieved by having a headspace above the medium, physical removal of entrapped air after wet up, or evacuation of the pore space with CO2. These scenarios are unlikely in microgravity, and thus satiated water contents, obtained by the procedure outlined above, represent the scenario commonly achievable either under space flight conditions or for plant growth.
Matric Potential Measurement
Two mini-tensiometers were installed in the satiated porous medium, one each on opposite sides of the tray, 3 cm from each porous tube, 7 cm apart, at a depth of 1.5 cm. The tensiometers were constructed of the following components—for 0.25- to 1-mm medium: a 0.432-cm-o.d. by 1.63-cm-long stainless steel porous cup (Mott Metalurgical, Farmington, CT), pore size of 20 µm, attached to a 6-cm length of 0.32-cm-i.d. tygon tube; for 1- to 2-mm medium, a 0.635-cm-o.d. by 2.54-cm-long stainless steel cup, pore size of 10 µm, and 0.3-mm stem attached to 0.16-cm-i.d. tygon tube. A larger cup was used with 1- to 2-mm aggregate out of concern for reduced contact points with larger particles. An Omega PX40 pressure transducer (Omega, Stamford, CT) (accuracy: pressure, ±0.8 cm H2O; pressure change, ±0.008 cm H2O) was used to read the vacuum. The tensiometers were used to measure s and pressure gradients within the medium.
Hydraulic head (h) measured during horizontal flow consisted only of since both tensiometers were inserted at the same vertical depth, thus eliminating the gravitational potential. For analysis purposes, the arithmetic mean of the two tensiometer measurements was used as the of the bulk volume of porous medium in the tray during K measurements.
Water Content Measurement
Water content was calculated from the water level change in the supply reservoir and represented the bulk volume of porous medium within the tray. Use of pressure transducers to measure water level changes in the supply container resulted in a water content measurement accuracy of ±1 to 2%.
Water Retention Measurements
Static water retention of the interaggregate pore space was measured under drying and wetting conditions in 2- to 5-cm H2O increments. The porous medium was assumed equilibrated with a given set point when no further change in either tensiometer or supply reservoir output was recorded. Dynamic water retention under drying conditions was measured during transient drainage.
Hydraulic Conductivity Measurements
Steady State Measurements
Measurements were conducted at five progressively dryer s between satiation and –20 cm H2O (for 0.25- to 1-mm porous medium) or –10 cm H2O (for 1- to 2-mm porous medium). To minimize water content variation across the porous medium during steady flow, a 1-cm pressure difference was maintained between the two porous tube fluid loops using the hanging water columns. For 0.25- to 1-mm medium, steady state flow measurements were made in intervals between 0 to –1, –5 to –6, –10 to –11, –15 to –16, and –19 to –20 cm H2O; and for 1- to 2-mm medium, the intervals were 0 to –1, –2 to –3, –4 to –5, –6 to –7, and –7 to –8 cm H2O. Before initiation of steady state flow, the porous medium was brought to equilibrium at the wetter for each interval. Steady state flow was attained when the inflow (wet side) was equivalent to the outflow (dry side). Darcy's equation was used to calculate K() for horizontal flow (Hillel, 1998).
Transient Internal Drainage
A –25 (for 0.25- to 1-mm medium) or –15 (for 1- to 2-mm medium) cm H2O suction was applied to one side of the porous medium that had previously been equilibrated to satiation (0-cm H2O). Outflow and were recorded every 10 s for 8 to 10 h, at which time the change in and outflow was very small, but the had not equilibrated with the applied suction. The instantaneous profile approach was used to compute K from outflow and hydraulic head (Daniel, 1982; Klute and Dirksen, 1986; Hillel et al., 1972):
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The instantaneous profile method was modified for horizontal flow on the root module scale using the following conditions: (i) There was a single horizontal length (x = 0 to x = L = 15.24 cm). (ii) Because of the small volume of porous medium within the tray, the change in water content of the entire profile (between x = 0 and x = L) was obtained from the outflow by:
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Saturated Hydraulic Conductivity
For comparative purposes, saturated K was also measured in a 20-cm-long by 5-cm-i.d. vertical flow cell using the constant head method of Klute and Dirksen (1986). Two measurements were made on each sample: (i) after the porous medium had slowly been wet up to satiation, and (ii) after air had been physically removed from the satiated sample.
Prediction of the Hydraulic Conductivity Function
Mualem's (Mualem, 1976) model was used to predict the unsaturated K function from the saturated K and the draining portion of the static water retention curve. The water retention curve was fitted to van Genuchten's closed form equation for relating water content to matric suction (van Genuchten, 1980) with the commonly used assumption that fitting parameters m and n are related by: m = 1 – 1/n. Model parameters are listed in Table 1. The residual water content equaled the water content when the interaggregate pore space was drained.
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The instantaneous profile method provided a nearly continuous record of K over the porous medium wetness range of interest. For statistical analysis purposes, measurement points from the instantaneous profile method were selected that matched those from steady state measurements. Matric potential, rather than water content, was used as the independent variable since only it possessed the variability necessary to estimate K as a function of an independent variable. The median (Table 2) of actual values within each interval was determined for use in the computation of statistical orthogonal polynomials. Sign tests and Wilcoxon signed rank tests showed that the actual values within each interval do not differ significantly at the 5% level from the medians.
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s within the experimental periods are the split plots. The whole-plot effects and the split-plot effects have different error variances used in testing for significance in the ANOVA (Milliken and Johnson, 1992, p. 46–91). Those whole-plot and split-plot factors with significant effects are displayed in Table 3. The response variable used in the analysis is the base 10 logarithm of the hydraulic conductivity (log10K). An ANOVA was performed using the mixed linear models procedure Proc Mixed (SAS Institute, 2001). The experimental factors which can affect the response variable are (i) measurement Method—A and B; (ii) porous medium—0.25- to 1- and 1- to 2-mm; (iii) experimental period—1, 2, and 3; (iv) prior period measurement method—none, A, and B; and (v) . Prior period measurement method can produce an effect on the response in the current period, called a carryover effect. Higher order carryover effects are due to treatments in periods before the immediately previous period, are usually negligible, and are not considered. Because the experimental design is balanced, the effects for factors or interactions in Table 3 are independent of each other.
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s permit the response to be fit to uncorrelated polynomials in (SAS Institute, 2004, Language Reference. Statements, Functions, and Subroutines. ORPOL Function). These statistical polynomials depend on the spacing of the medians. Since each particle-size distribution has its own set of targeted values, a separate set of orthogonal polynomials was computed for each. Orthogonal polynomials permit independent inferences about the shape of the response of log10K to .
The correlations among the responses within a period at the median levels were modeled by a covariance of the form that decreases exponentially with the distance in steps between measurements [SAS Institute, 2004, The Mixed Procedure. Syntax. REPEATED Statement. Table 46.5: Covariance Structures. Description: Autoregressive(1)].
Two out of 120 repeated measurement data values of K were missing, and their values were imputed as the medians of the extant hydraulic conductivities arising from like conditions. There were no differences in conclusions when the ANOVA was computed with or without the missing values. Using the imputed values restores balance to the data, thereby providing independent inferences for the factor effects.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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0.37, but measurements were conducted for a larger range of suction for the smaller particle-size medium. Differences between the static water retention curves from sample to sample are likely due to differences in packing and air entrapment. In general, dynamic measurement of water retention was in reasonable agreement with static results, although variability between repeated measurements was greater for 1- to 2-mm than for 0.25- to 1-mm porous media. The higher variability in the 1- to 2-mm medium is likely due to processes such as air entrapment and discontinuous water phase formation documented to occur to a greater extent in coarse—as compared with fine-textured porous medium during transient flow (Wildenschild et al., 2001).
Steady state flow measurements were made within five intervals, each described by a median for statistical analysis. Data in Table 2 show that the greatest difference between actual and median s occurs near satiation, where changes in matric suction produce little or no change in (Fig. 2). At the dryer end of the water retention curve where large changes in occur for small changes in , the percentage difference between actual and median s was smaller than the measured variation observed between sequences. Thus, median s were used with the confidence that water content did not vary significantly within the range of actual measurements for each steady flow interval.
Without the contribution of a gravitational component, hydraulic gradients due to horizontal flow through the porous medium were very small for both steady and transient flow. An example of output from the two tensiometers during the approach to steady state is illustrated in Fig. 3. The tensiometer on the dry side shows a greater change in output than the tensiometers on the wet side, indicating that the gradient can adequately be determined from the before- and after-signals from both tensiometers. Horizontal gradients within the porous medium during steady state flow range from 0.003 to 0.06 for both particle-size distributions (Fig. 3). This is lower than the 0.08 gradient imposed between the microporous tubes at either end of the medium sample. The pressure drop of 0.2 to 0.9 cm H2O across the porous membrane indicates that use of pressure readings obtained within porous tubes or on the waterside of membranes to calculate hydraulic head should be used with caution for microgravity applications. In a vertical position in earth gravity, the pressure drop across the porous membrane may seem insignificant due to the much larger hydrostatic pressure gradient.
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gradient across the porous medium profile during transient flow is shown in Fig. 4B. There is an initial increase to about 0.23 or 0.04 cm H2O cm–1 immediately after inducing a –25 or –15 cm H2O pressure on one side of the satiated 0.25- to 1- or 1- to 2-mm porous medium profile. The gradient gradually tapers off to about 0.07 or 0.015 cm H2O for 0.25 to 1 or 1 to 2 mm, respectively. Figure 4C shows the s as a function of position for the two tensiometers at different times during internal drainage. At any given point in time, hydraulic gradients were very small, which indicates that changes in water content across the profile are also of a very small magnitude and that the profile drains nearly uniformly.
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at satiation (0 cm H2O) is 0.04 to 0.08 cm3 cm–3 less than complete saturation due to air entrapment. In addition, the direction of airflow into the 3-cm-deep porous media was perpendicular to the horizontal water flow, unlike many vertical flow studies. These results support the use of outflow from the tray as a measure of the change in water content of the medium within the tray in the modified instantaneous profile approach. Table 3 shows that when averaged across the two media, there is no effect due to measurement method, justifying modifications to the instantaneous profile approach for small volumes of porous medium. However, the significance of the method by medium interaction indicates that within each porous medium, there is a statistically significant difference in response due to measurement method. The prior period measurement method has a significant effect on the current period response. Since the design is balanced, the factor effects are independent, and hence, the effect of the prior period measurement method is not included in the effects of the other factors in the table.
Interpolated log10K values and 95% confidence limits predicted from factors in Table 3 are displayed on the graphs in Fig. 5 along with direct measurements of K. For 0.25- to 1-mm porous medium, K values ranged from 0.09 to 0.12 cm s–1 for satiated flow to 10–3 cm s–1 at the water content transition between interaggregate and intraaggregate pores. Conductivity for 1- to 2-mm porous medium ranged from 0.5 to 2 cm s–1 for satiated flow to 10–4 cm s–1 at the interaggregate/intraaggregate transition. These results agree well with K measured by constant head method in the vertical flow cell: 0.08 and 0.17 cm s–1 (0.25–1 mm) and 0.62 and 1.26 cm s–1 (1–2 mm) for satiated and saturated medium, respectively. This confirms that both Methods A and B are capable of measuring satiated as well as unsaturated K in a single test, and that variation in satiated K is likely due to air entrapment.
The estimates of differences in log10K for interactions of measurement method with porous medium are displayed in Table 4. On the basis of the logarithm-transformed data for the range of s measured, Method B yields a statistically significantly higher response of K than Method A for 0.25- to 1-mm medium. On the other hand, Method A yields a statistically higher response of K than Method B for 1- to 2-mm medium (Table 4). For both media, differences in log10K are less than one order of magnitude. The question is whether the estimated differences in log10K of less than one order of magnitude are of practical significance.
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Additionally, in small containers it may be harder to describe water flow through the porous medium alone due to interaction with the wall. Hopmans (Hopmans et al., 1992) observed preferential flow pathways along cell walls. Packing of media in the vicinity of the wall will be looser than in the bulk medium, thus increasing porosity, while at the same time the surface area of the wall may increase resistance to flow (Franzini, 1956). However, increased porosity at the wall is less significant with high permeability materials such as used in the experiments presented in this manuscript (Tokunaga, 1988). The 3-cm medium depth for 1- to 2-mm medium is less than optimal for particles of that size, making the wall effect more sensitive to the fluid velocity profile (Franzini, 1956). Fluid velocities were likely higher in the instantaneous profile approach given the larger pressure gradient imposed at the start of each run. Thus, it is possible that the wall effect was different for the 0.25- to 1- and 1- to 2-mm particle-size distributions. On earth there is concern that laboratory measurements may not be representative of field-scale transport conditions. For space flight, however, the need to minimize root zones and contain particulates, combined with the dominance of surface tension forces, increase the likelihood that wall effects will be an ever-present reality.
Close agreement was found between hydraulic K measured by instantaneous profile and predictions based on numerical analysis of the water retention curve for sands and sandy loams (Ragab et al., 1981; Paige and Hillel, 1993). In the present study, there was also reasonable agreement between the K function directly measured by Methods A and B and that predicted by van Genuchten/Mualem models (Mualem, 1976; van Genuchten, 1980) (Fig. 6). Even though baked ceramic aggregates have a bimodal pore size distribution, water contents relevant to plant growth essentially constitute the single pore system of interaggregate pores. Van Genuchten (1980) found that a reliable measure of the residual water content was important for prediction of the K function. Use of equilibrium water contents at –20 cm H2O proved to be a suitable residual for the interaggregate space.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The direct measurement methods must be examined in the context of space flight where pumps and pressure transducers instead of hanging water columns will be used to control and monitor flow. The modified instantaneous profile approach is appealing for several reasons. It may be easier to impose a –15 to –25 cm H2O rather than a 1 to 2 cm H2O pressure difference across a porous medium profile using pumps and pressure transducers to control the pressure/vacuum in fluid loops. Hydraulic gradients within the porous medium are slightly larger during transient outflow. It also only requires a single fluid loop, which minimizes hardware mass and complexity. Lastly, transient internal drainage covering the range of water contents relevant to plant growth can be performed in hours, whereas a series of steady state measurements with properly equilibrated porous medium takes days. All of these factors are advantageous for space flight where mass, volume, power, and astronaut time are limited.
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ACKNOWLEDGMENTS |
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Received for publication March 26, 2004.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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nek, N. Romano, and W. Durner. 2002. Inverse Methods. p. 963–1008. In J.H. Dane and G.C. Topp (ed.) Methods of soil analysis: Part 4. SSSA Book Ser. No. 5. SSSA, Madison, WI.This article has been cited by other articles:
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  M. B. Kirkham Horizontal Root Growth: Water Uptake and Stomatal Resistance under Microgravity Vadose Zone J., August 13, 2008; 7(3): 1125 - 1131. [Abstract] [Full Text] [PDF]
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R. Heinse, S. B. Jones, S. L. Steinberg, M. Tuller, and D. Or Measurements and Modeling of Variable Gravity Effects on Water Distribution and Flow in Unsaturated Porous Media Vadose Zone J., October 8, 2007; 6(4): 713 - 724. [Abstract] [Full Text] [PDF]
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h1 and 
used in the van Genuchten/Mualem prediction models for water retention and hydraulic conductivity.
= wetting curve. Data are means ± SD. Predicted by the Van Genutchen (
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