The heat exchangers maintained constant temperatures throughout the duration of the study (28 days) as indicated by the mean temperatures and standard deviations of the upper and lower boundaries (Table 3).
Figure 2 shows the transient and steady-state temperature distributions for all of the soils for 1, 4, 7, 13, and 28 days after the temperature gradient was imposed. Quasi steady- state temperature distributions were generally obtained within five days for the wettable and hydrophobic soils. The temperature distributions for all soils displayed a non-linear decrease
in soil temperature from the warm to the cold end of the soil cells. This is clear from the deviation of the soil temperature distributions from a linear temperature distribution (Fig. 2). Non-linearity indicates non-uniform λ distributions within the soil cells, which is associated with changing θ as water redistributes within the soil cells in response to temperature gradients. Concavity in the temperature distributions is expected when the dependence of λ on soil moisture is dominant. Furthermore, the concave temperature distributions for the soils indicate that ambient temperature interference was negligible and one-dimensional temperature gradients were maintained.
For the wettable sand and hydrophobic sand, concavity extended from 1.5 to 8.5 cm from the warm end of the soil cells (Fig. 2b and 2d). Concavity in the temperature
distributions of the wettable silt loam and hydrophobic silt loam was most noticeable from 2.5 to 7.5 cm and 1.5 to 7.5 cm from the warm end of the soil cells, respectively (Fig. 2a and 2c). The concavity in the temperature distributions of the wettable and hydrophobic soils indicate that soil water content distributions were non-uniform and considerable soil water redistribution occurred within the cells in response to the temperature gradients.
Thermal Conductivity
Figure 3 shows the transient and steady-state Δλ (change in soil thermal
conductivity) distributions. Δλ distributions are shown for 1, 4, 7, 13, and 28 days after the temperature gradient was imposed for all of the soil cells. Both the wettable and
hydrophobic soils showed a decrease and an increase in soil λ at the warm and cold ends of the soil cells, respectively. The degree to which λ decreased and increased at the warm and cold end of the soil cells differed between the wettable silt loam and hydrophobic silt loam soils. For the wettable silt loam, the steady-state Δλ distribution was constant from the warm
end to 5 cm and increased significantly in the cold region of the soil cell (Fig. 3a). The steady-state Δλ at 8.5 cm from the warm end of the wettable silt loam and hydrophobic silt loam soil cells was 0.32 and 0.06 W m-1oC-1, respectively (Fig. 3a and 3c). Δλ distributions
obtained for the wettable sand and hydrophobic sand were similar (Fig. 3b and 3d). In the wettable sand, λ decreased by 0.37 W m-1oC-1 and increased by 0.17 W m-1oC-1 at 1.5 and
8.5 cm from the warm end of the soil cells, respectively (Fig. 3b). The Δλ was 0.46 W m-1
oC-1 at 1.5 cm from the warm end of the hydrophobic sand soil cell (Fig. 3d). The variations
in the Δλ distributions of the wettable and hydrophobic soils are associated with changes in soil volumetric water content within the wettable and hydrophobic soil cells.
Soil Moisture Redistribution and Net Water Transfer
Observations of transient and steady-state Δθ (change in soil volumetric water content) distributions for all four soil conditions are shown in Fig. 4. Δθ distributions are shown for 1, 4, 7, 13, and 28 (steady-state) days after the temperature gradient was imposed. During the first week, significant amounts of water moved from the warm end towards the cold end of the wetttable and hydrophobic soil cells. Soil moisture redistribution began to approach a quasi steady-state at the end of one week. From day 7 to day 28, θ decreased and increased by approximately 1% at the warm and cold end of soil cells, respectively. In Fig. 4, it is apparent that more net movement of water occurred in the wettable silt loam than in the hydrophobic silt loam. The net movement of water in the wettable sand was similar to that observed in the hydrophobic sand.
Net water transfer was determined using the Δθ distributions obtained for the different soils. After one week, net water transfer was reduced by 48% in the hydrophobic silt loam when compared to the wettable silt loam. No difference in net water transfer was
observed after one week in the wettable sand and hydrophobic sand. At the conclusion of the study on day 28 after the temperature gradient was imposed, net water transfer was reduced by 56% in the hydrophobic silt loam when compared to the wettable silt loam.
We hypothesized that in the hydrophobic soil cells there would be a significant build- up of water in the cold region of the soil cells. In both the wettable and hydrophobic soil cells, water vapor transfer occurred from the warm to the cold region of the soil cells. However, due to soil water repellency, liquid water would not readily move from the cold region to the warm region of the hydrophobic soil cells. In the wettable soils, liquid water transfer would occur unimpeded from the cold to the warm region of the wettable soil cells. The inability of water to return readily as liquid water from the cold to the warm region of the hydrophobic soil cells would cause soil moisture to accumulate in the cold region of the hydrophobic soil cells. The observations in Fig. 4 fail to support our hypothesis regarding the effect of soil wettability on soil water redistribution under nonisothermal conditions. Although net water transfer was similar in the wettable sand and hydrophobic sand, there was not a significant build-up of soil water in the cold region of the hydrophobic sand soil cell when compared to the wettabe sand soil cell. The observations of soil moisture redistribution within the hydrophobic silt loam soil indicate that water vapor transfer from the warm to the cold region of the soil cell was reduced when compared to the wettable silt loam soil. These results suggest that in hydrophobic soils, soil moisture redistribution under nonisothermal conditions may be affected by soil texture.
The reduction in water vapor transfer in hydrophobic soils has been reported in other studies (Globus, 1960; Bachmann et al., 2001 a). Globus (1960) found that a layer of hydrophobized material placed in the middle of a column of the same non-hydrophobized
material reduced the water vapor flux when a temperature gradient was applied. The reduction of the water vapor flux was attributed to the disruption of series-parallel thermal moisture transfer by the hydrophobic layer. Series-parallel thermal moisture transfer refers to the condensation of water vapor on one side of a liquid island and an equal amount of evaporation from the other side of the liquid island combined with liquid water movement by capillary action or in thin films. In wettable soils, series-parallel thermal moisture transfer has been associated with the enhancement of thermal water vapor diffusion (Philip and de Vries, 1957; Cass et al., 1984; Lu et al., 2011). The enhancement of thermal water vapor diffusion has been found to decrease significantly with a decrease in the length of the liquid island (Webb and Ho, 1998). Bachmann et al. (2001 b) noted that the average diffusive pathway for water vapor may be affected due to increases in hydrophobicity and decreases in the amount of water located between the points of contact of the solid phase. Furthermore, in a separate study, Bachmann et al. (2001 a) noted that wettability affected thermal water vapor diffusion based on the effect of wettability on nonisothermal evaporation. They found that thermal water vapor diffusion was reduced in hydrophobic soils and enhanced in wettable soils. The thermal water vapor enhancement factor of the wettable soil was 10 times greater than the thermal water vapor enhancement factor for the most hydrophobic soil. The
reduction of water vapor transfer observed in the hydrophobic silt loam agrees with the observed reduction of thermal water vapor diffusion in hydrophobic soils when compared to wettable soils as noted by Bachmann et al (2001 a).
CONCLUSIONS
We studied the effect of soil wettability on coupled heat and water transfer. Two wettable soils, a silt loam and a sand, and their hydrophobic counterparts were investigated. Closed soil cells instrumented with T-TDR sensors were used. The soil cells consisted of an inner soil column surrounded by an outer soil column of the same soil material. The outer soil column served as a buffer to ensure 1-D temperature gradients. Spiral circulation heat exchangers connected to temperature controlled water baths were placed at the upper and lower boundaries of the soil cells to provide a 150 oC m-1 temperature gradient. The heat pulse function of T-TDR sensors positioned at various depths within the soil cells were used to obtain measurements of soil temperature, λ, and θ. All soils displayed a non-linear
decrease in soil temperature from the warm to the cold ends of the soil cells. Non-linearity in the temperature distributions of the wettable and hydrophobic soils indicated the existence of non-uniform λ distributions. In both the wettable and hydrophobic soils, λ decreased and increased in the warm and cold regions of the soil cells, respectively. The change in soil thermal conductivity in the warm and cold regions of the wettable and hydrophobic soils was attributed to distributions of soil moisture within the soil cells. Δθ distributions indicated that considerable amounts of water moved from the warm end towards the cold end of the
wettable and hydrophobic soil cells. Soil moisture redistribution was similar in the wettable sand and hydrophobic sand soils. More net water movement occurred in the wettable silt loam than in the hydrophobic silt loam. Net water transfer was reduced by 56% in the hydrophobic silt loam when compared to the wettable silt loam. The results of this study indicated that soil moisture redistribution in hydrophobic soils may be affected by soil
silt loam indicated that water vapor transfer from the warm to the cold regions of the soil cells was reduced when compared to the wettable silt loam because liquid water flow was expected to be greater in the wettable soils. Additional research, such as using a salt tracer to help separate liquid and water vapor transport, is needed to fully identify and understand the mechanisms involved in the redistribution of soil moisture in hydrophobic soils under non- isothermal conditions.
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Table 1. Particle size analysis and organic matter content of the sand and silt loam soils. Soil Sand > 50 µm Coarse silt 50-20 µm Fine silt 20-2 µm Clay <2 µm Organic matter ---%--- --- Silt loam 2.2 42.9 30.0 24.9 4.4 Sand 91.7 5.0 2.2 1.1 0.6
Table 2. Electrical conductivity of the saturation extracts of the hydrophobic and hydrophilic treatments for the sand and silt loam soils.
Electrical conductivity
Soil Wettable Washed hydrophobic Unwashed hydrophobic ---mS cm-1---
---
Silt loam 0.631 0.633 17.3 Sand 0.137 0.135 5.05
Table 3. Mean temperatures of the upper and lower boundaries for each soil column for the duration of the experiment. Standard deviations of the mean temperatures are listed in parenthesis. Soil Boundary Wettable Silt loam Hydrophobic Silt loam Wettable Sand Hydrophobic Sand ---oC--- Upper boundary 37.37 (0.03) 37.24 (0.04) 37.50 (0.00) 37.31 (0.04) Lower boundary 22.82 (0.03) 22.84 (0.05) 22.89 (0.02) 22.77 (0.02)
Fig. 1. Diagram of closed soil cell. Inside diameter of the inner column and outer column is 8.9 and 20.2 cm, respectively. The height of the inner and outer column is 10 cm.
Fig. 2. Transient and steady-state temperature distributions for the four soil columns obtained 1, 4, 7, 13, and 28 days after the temperature gradient was applied. The straight lines represent linear temperature distributions.
b. wettable sand a. wettable silt loam
Tem pe ratur e o C 20 22 24 26 28 30 32 34 36 38 40 1 day 4 day 7 day 13 day 28 day Linear
c. hydrophobic silt loam
Distance from warm end (cm)
0 2 4 6 8 10 20 22 24 26 28 30 32 34 36 38 40 d. hydrophobic sand 0 2 4 6 8 10
Fig. 3. Transient and steady-state Δλ distributions for the four soil columns obtained 1, 4, 7, 13, and 28 days after the temperature gradient was applied.
b. wettable sand a. wettable silt loam
Δ λ (W m -1 O C -1 ) -1.0 -0.5 0.0 0.5 1.0 1 day 4 day 7 day 13 day 28 day
c. hydrophobic silt loam
Distance from warm end (cm)
0 2 4 6 8 10 -1.0 -0.5 0.0 0.5 1.0 d. hydrophobic sand 0 2 4 6 8 10
Fig. 4. Transient and steady-state Δθ distributions for the four soil columns obtained 1, 4, 7, 13, and 28 days after the temperature gradient was applied.
b. wettable sand a. wettable silt loam
Δθ (cm 3 cm -3 ) -0.10 -0.05 0.00 0.05 0.10 1 day 4 day 7 day 13 day 28 day
c. hydrophobic silt loam
Distance from warm end (cm)
0 2 4 6 8 10 -0.10 -0.05 0.00 0.05 0.10 d. hydrophobic sand 0 2 4 6 8 10
CHAPTER 4. COUPLED HEAT AND MASS TRANSFER IN WETTABLE AND