Morphology of Rain Water Channeling in Systematically Varied Model Sandy Soils

We visualize the formation of fingered flow in dry model sandy soils under different rain conditions using a quasi-2D experimental setup and systematically determine the impact of the soil grain diameter and surface wetting properties on the water channeling phenomenon. The model sandy soils we use are random closely packed glass beads with varied diameters and surface treatments. For hydrophilic sandy soils, our experiments show that rain water infiltrates a shallow top layer of soil and creates a horizontal water wetting front that grows downward homogeneously until instabilities occur to form fingered flows. For hydrophobic sandy soils, in contrast, we observe that rain water ponds on the top of the soil surface until the hydraulic pressure is strong enough to overcome the capillary repellency of soil and create narrow water channels that penetrate the soil packing. Varying the raindrop impinging speed has little influence on water channel formation. However, varying the rain rate causes significant changes in the water infiltration depth, water channel width, and water channel separation. At a fixed rain condition, we combine the effects of the grain diameter and surface hydrophobicity into a single parameter and determine its influence on the water infiltration depth, water channel width, and water channel separation. We also demonstrate the efficiency of several soil water improvement methods that relate to the rain water channeling phenomenon, including prewetting sandy soils at different levels before rainfall, modifying soil surface flatness, and applying superabsorbent hydrogel particles as soil modifiers.

Figure 1

Schematic of the experimental setup for visualizing rain water channeling in model sandy soils. A sample cell partially filled with model sandy soils is suspended under a 2D rain source built by a linear array of glass capillaries inserted into the bottom of a plastic container with a separation of 1 cm. The sample cell can be shifted up or down to adjust the falling distance $h$ of the rain droplets. Rain rate $Q$ is determined by the water level in the plastic container. A gear pump is used for supplying water during the experiment.

Figure 2

Images (a)–(d) show deionized-water channeling in dry hydrophilic model sandy soils with bead diameters $D$ varying from 0.18 to 1 mm, at a rain rate of $Q=14.5\mathrm{cm}/\mathrm{h}$ and a raindrop impinging speed of $U_T=1\mathrm{m}/\mathrm{s}$. The color images in the first row are the original images taken at steady states; the gray-scale images in the second row are obtained by subtracting the background images taken prior to the rain from the ones taken at steady states, converting to gray scale, and then enhancing the contrast. The sample packing in each image is 26 cm wide, 25 cm high, and 0.8 cm thick. As labeled in the images, $z_{\text{wet}}$ is the infiltration depth of rain water in soils, $d$ is the water channel width, and $d^{\prime }$ is the water channel separation. The saturated hydraulic conductivity ${\kappa }_s$ [Eq. (2)] for these four samples are determined as $73\mathrm{cm}/\mathrm{h}$, $204\mathrm{cm}/\mathrm{h}$, $567\mathrm{cm}/\mathrm{h}$, and $2300\mathrm{cm}/\mathrm{h}$, respectively.

Figure 3

Variation of (a) infiltration depth $z_{\text{wet}}$, (b) channel width $d$, and (c) channel separation $d^{\prime }$, with the raindrop impinging speed ($U_T$) in a dry model sandy soil of $D=1\mathrm{mm}$ hydrophilic glass beads at two fixed rain rates. The parameters are defined in Fig. 2. The raindrop impinging speed is estimated from the falling height of the rain droplets using Eq. (1). When a low rain rate of $Q=14.5\mathrm{cm}/\mathrm{h}$ is applied, deionized water is used as rain water, and the saturated hydraulic conductivity in the model sandy soil is determined to be ${\kappa }_s=2300\mathrm{cm}/\mathrm{h}$ [Eq. (2)]. When a high rain rate of $Q=96.0\mathrm{cm}/\mathrm{h}$ is applied, a glycerol-water mixture is used as rain water, and the corresponding saturated hydraulic conductivity in the same model sandy soil is reduced to ${\kappa }_s=620\mathrm{cm}/\mathrm{h}$ [Eq. (2)].

Figure 4

Variation of (a) infiltration depth $z_{\text{wet}}$, (b) channel width $d$, and (c) channel separation $d^{\prime }$, with the rain rate ($Q$) and rain water viscosity $\mu$ in a dry model sandy soil of $D=1\mathrm{mm}$ hydrophilic glass beads, at a fixed raindrop impinging speed $U_T=1.0\mathrm{m}/\mathrm{s}$. The parameters are defined in Fig. 2. The rain rate $Q$ is scaled by the saturated hydraulic conductivity ${\kappa }_s$ of the model sandy soil. Three different liquids are used as rain water to extend the testing range: deionized water, a 40% glycerol-water mixture, and a 50% glycerol-water mixture. Their corresponding saturated hydraulic conductivities in the same model sandy soil are determined to be ${\kappa }_s=2300\mathrm{cm}/\mathrm{h}$, ${\kappa }_s=620\mathrm{cm}/\mathrm{h}$, and ${\kappa }_s=326\mathrm{cm}/\mathrm{h}$, respectively [Eq. (2)]. Solid lines in (a) and (b) are power-law fits to the data.

Figure 5

Variation of the effective contact angle [$\cos ({\theta }^{*})$] with the percentage of hydrophobic beads. The linear fit goes from complete wetting for untreated beads, to zero for a mixture of 30% treated beads.

Figure 6

Variation of (a) infiltration depth $z_{\text{wet}}$, (b) channel width $d$, and (c) channel separation $d^{\prime }$, with the capillary rise height of the randomly close-packed glass beads $[4\sigma \cos ({\theta }^{*})/\rho gD]$ at a fixed rain condition. The parameters plotted here are defined in Fig. 2. The rain rate is $Q=14.5\mathrm{cm}/\mathrm{h}$, and the raindrop impinging speed is $U_T=1.0\mathrm{m}/\mathrm{s}$. In plots (a)–(c), solid squares represent the data obtained from hydrophilic glass beads with varied diameters (fix ${\theta }^{*}$ and vary $D$), while open stars represent data obtained from 1-mm glass beads with varied surface wetting properties (fix $D$ and vary ${\theta }^{*}$). Solid curve in (a) is a linearly fit to the data. Solid curve in (b) is a power-law fit, and the dashed curves are predictions from Eqs. (4) and (7), respectively.

Figure 7

Gray-scale images (a)–(e) showing the influence of initial water content $S_0$ increasing from 0 to filled capacity, as labeled, on rain water channeling in a model sandy soil, 1-mm hydrophilic glass beads, at a fixed rain condition. The rain rate is $Q=14.5\mathrm{cm}/\mathrm{h}$, and the raindrop impinging speed is $U_T=1\mathrm{m}/\mathrm{s}$. The sample packing is 26 cm wide and 0.8 cm thick. The sample packing height is around 25 cm. In this model sandy soil, the saturated water content is around 36%, and the field capacity is around 7.75%.

Figure 8

Gray-scale images (a)–(d) showing the influence of four different surface flatnesses, as labeled, on rain water channeling in a dry model sandy soil, 1-mm hydrophilic glass beads at a fixed rain condition. The rain rate is $Q=14.5\mathrm{cm}/\mathrm{h}$, and the raindrop impinging speed is $U_T=1\mathrm{m}/\mathrm{s}$. The sample packing is 26 cm wide and 0.8 cm thick. The sample packing height varies due to the wavelike surface. More water channels may form when the wavelike surface creates an extra hydraulic pressure gradient on the wetting front.

Figure 9

Sequence of gray-scale images (a)–(e) at different times, as labeled, showing the influence of uniformly mixed hydrogel particle additives on the rain water channeling in a sandy soil composed of 1-mm hydrophilic glass beads; 0.1 wt% of dry hydrogel particles (0.3–0.5 mm in axis) are uniformly mixed into the top 10 cm of the dry model sandy soil before the rain. The rain rate is $Q=14.5\mathrm{cm}/\mathrm{h}$, and the raindrop impinging speed is $U_T=1\mathrm{m}/\mathrm{s}$. The sample packing is 26 cm wide and 0.8 cm thick. The sample packing height is 25 cm (dry). The red line in each image indicates the boundary of the mixture and the pure model soil. The swelling of hydrogel particles extends the water channels.

Figure 10

Sequence of gray-scale images (a)–(e) at different times, as labeled, showing the influence of a layer of hydrogel particle additives on the rain water channeling in a sandy soil composed of 1-mm hydrophilic glass beads; 0.1 g of dry hydrogel particles (0.3–0.5 mm in axis) are placed in a layer under the top 10 cm of the dry model sandy soil before the rain. The rain rate is $Q=14.5\mathrm{cm}/\mathrm{h}$, and the raindrop impinging speed is $U_T=1\mathrm{m}/\mathrm{s}$. The sample packing is 26 cm wide and 0.8 cm thick. The sample packing height is 25 cm (dry). The red line in each image indicates the location of the hydrogel particles. The swollen hydrogel particles partially clog the water channels, form a wet hydrogel layer across the sample packing, and create a fully saturated region in the soil above them.