Rain water transport and storage in a model sandy soil with hydrogel particleadditives

Y. Wei1,2, D. J. Durian11Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6396, USA and

2Complex Assemblies of Soft Matter, CNRS-Rhodia-UPenn UMI 3254, Bristol, PA 19007-3624, USA(Dated: September 24, 2018)

We study rain water infiltration and drainage in a dry model sandy soil with superabsorbenthydrogel particle additives by measuring the mass of retained water for non-ponding rainfall using aself-built 3D laboratory set-up. In the pure model sandy soil, the retained water curve measurementsindicate that instead of a stable horizontal wetting front that grows downward uniformly, a narrowfingered flow forms under the top layer of water-saturated soil. This rain water channelizationphenomenon not only further reduces the available rain water in the plant root zone, but alsoaffects the efficiency of soil additives, such as superabsorbent hydrogel particles. Our studies showthat the shape of the retained water curve for a soil packing with hydrogel particle additives stronglydepends on the location and the concentration of the hydrogel particles in the model sandy soil.By carefully choosing the particle size and distribution methods, we may use the swollen hydrogelparticles to modify the soil pore structure, to clog or extend the water channels in sandy soils, orto build water reservoirs in the plant root zone.

PACS numbers: to be determined

Sandy soils are widely distributed in the world and areknown as the hungry soil due to their poor water-holdingcapacity and low nutrients. To grow plants in sandy soils,additives such as superabsorbent hydrogel particles [1–3]have been developed to improve the soil water retentionand to prevent nutrient runoff. The study of hydrogelparticle additives started in the early 1980’s [4–7]. Todate, such additives have been proven to significantly in-crease the soil moisture content [6–11] and affect the wa-ter transport in sandy soils [9, 10, 12–15]. However, mostof these studies were conducted using a complex plant-soil system with varied irrigation conditions. A few stud-ies that used simplified model sandy soils either focus onthe effect of swollen hydrogel particles in fully-saturatedenvironment such as hydraulic conductivity [14] and soilwater retention curve measurements [15], or emphasizevisualizing the swelling of hydrogel particles under suffi-cient water supply such as 2-dimensional water infiltra-tion studies [8].

The situation in the field may significantly differ fromthe assumptions made in those experiments, since rainand irrigation water creates preferential paths when infil-trating into sandy soils. Both field evidence [16–20] andlaboratory researches [21–25] have shown that fingeredflows form in dry sandy soils under non-ponding rainfall.This water channelization phenomenon may be causedby the structure heterogeneity of soils or the space inho-mogeneity of water supply, but also may be induced inuniform sandy soils by instability of a downward-movingwetting front. On one hand, the efficiency of the soiladditives may not be correctly determined without ac-counting for this phenomenon. On the other hand, un-derstanding the effects of hydrogel particle additives onrain water channelization may help us to further improvethe soil additives, optimizing both their physical proper-ties and their distribution methods.

In this paper, we build a 3-dimensional laboratory set-up that measures the mass of the retained water in amodel sandy soil under controlled rainfall. The modelsandy soil has a well-known pore structure and surfacewetting properties. The water flow profile inside the soilpacking is determined based on the curve of excess re-tained water. Then a commercial product of hydrogelparticles with a carefully chosen size are added into themodel sandy soil with different distribution methods, forexample uniformly mixed or placed in a layer. The re-tained water curves during and after rainfall are mea-sured so that the effects of hydrogel particle additives onwater flow profile in the model sandy soil can be deter-mined and discussed.

I. EXPERIMENT

Fig. 1 shows a schematic of the laboratory set-up. Apolypropylene dispensing needle (Intramedic, BD Inc.) isconnected to a syringe pump (Harvard Apparatus Inc.)by Tygon tube and then fixed on the front grill of a6 inches clip-on fan (Air King Inc.). The fan is facedown and clipped on a stage about 1.5 m higher thanthe bench. The syringe pump infuses deionized (DI) wa-ter to the needle at a fixed volumetric flow rate Q tocreate rain droplets. The size and the frequency of thedroplets can be controlled by modifying the needle innerdiameter and the pump infusing rate. The fan createsturbulence to perturb the horizontal impinging locationof the rain droplets, and slightly accelerates the dropletsvertically. By adjusting the speed of the fan, we ensure arandom impingement of the rain droplets on the surfaceof a soil sample packing placed under it.

The sample column is made by fitting a 30 cm heightcylindrical Plexiglass tube into a standard copper sieve

arX

iv:1

310.

6258

v2 [

cond

-mat

.sof

t] 1

0 Fe

b 20

14

2

Balance

Capillary rise level

ΔH, Δm

Fan

Syringe pump:Q = 2.54cm/hr

Needle

A=38.5cm2

h = 130cm

Sieve

FIG. 1: (Color online) Schematic of the laboratory set-up forthe retained water measurements. A needle is connected to asyringe pump and suspended under a small fan. The syringepump provides a fixed flow rate of Q. Fan makes rain dropletscreated on the needle tip randomly impinging on the surfaceof a soil packing. The soil packing has a cross-sectional areaof A = 38.5 cm2 and is placed in a drainage container withwater in it. Due to the capillary rise effect, a water table isthen formed on the bottom of the soil packing. The capillaryrise level maintains the same during and after rainfall. ∆Hhere represents the height of a soil packing above the watertable and ∆m represents the mass of the retained water inthat region. Before rain starts, the mass of the retained waterequals zero. During and after rainfall, the mass of the retainedwater is recorded as a function of time.

(Dual Manufacturing Co.). The tube has hydrophobicsurfaces and a inner cross-sectional area of A = 38.5 cm2.The mesh size of the copper sieve is 0.106 mm; our testsshow that it doesn’t have a detectable influence on thewater flows. The sample column is placed in a home-made drainage container with water in it, kept at a fixedheight by a drainage outlet. An electrical balance (Citi-zen Inc.) with a resolution of 0.1 gram is used to measuretheir mass change (∆m) during and after rainfall. Due tocapillarity, the water level in a soil packing will be higherthan that in the drainage container and this wetted sat-uration zone mimics the water table in the real field. Akey advantage of our set-up is that it allows for the pos-sibility of a steady-state situation, where the rate of rainonto the sample equals the flow rate of water from thedrainage outlet – in which case the configuration of theliquid channels within the model soil would be constant.

A. Materials

The model sandy soil we used is a random close packingof glass beads (Potters Industries Inc.) with a diameterof 1 mm (±20%). For cleaning, they were first burnt ina furnace at 500◦C for 72 hours and then soaked in a1M HCl bath for one hour. After that the glass beads

were rinsed with plenty of DI water, baked in a vacuumoven at about 110◦C for 12 hours, and cooled to roomtemperature. The clean beads have hydrophilic surfaces.By weighting several hundreds of beads together, andcounting the actual number carefully, we determine thatthe average mass of a single glass bead is mbead = 1.17±0.01 mg.

The hydrogel particle additives are a commercial prod-uct provided by Degussa Inc.(Stockosorb SW). They are50/50 potassium acrylate and acrylamide cross-linkedtogether through industrial polymerization. Since theparticles are obtained by grinding hydrogel bulks, theirshapes are faceted and random. The hydrogel particleswe used are further sieved to be between 0.3 mm and0.5 mm sized meshes. The average mass of a single hy-drogel particle is mgel = 0.067 ± 0.002 mg, obtained bycounting over 500 dry particles and weighting them to-gether. To determine the global water holding capac-ity of these particles, we place 0.01 gram dry particlesin plenty of DI water. After three hours, the swollenparticles are collected and wiped. Their swollen mass isaround 300 times higher than that in dry. We also checkthe swelling ratio δ in the long axis of hydrogel parti-cles using a microscope and find they swell to 6 timestheir dry length when placed in contact with DI water forthree hours. These values are used in the determinationof the gel layer number. When exposed in atmosphereat room temperature, the swollen hydrogel particles de-swell slowly so as to lose 85% of their stored water withina day. The cycle of swelling and de-swelling repeats againand again without degradation when their surroundingenvironment changes, and the ability of storing and re-leasing water makes them a good candidate in sandy soilmoisture modification.

B. Procedures

We first set the raining condition. According to litera-ture [26–29], the diameter d of rain droplets in a real rainvaries from 0.5 mm to 4 mm depending on the rain rate,and the corresponding terminal falling speed Ut variesfrom 2.1 m/s to 8.8 m/s. Therefore, we choose a rainrate of Q = 2.54 cm/hr for a heavy rain. A high speedcamera (Phantom 630, Vision Research Inc.) is used torecord the motion of the droplets right before they im-pact the soil surface. We determine that the diameterof the rain droplets is d = 3.0 ± 0.1 mm and the impactspeed of the rain droplets is Ut = 6.1 ± 0.1 m/s for afalling height of h = 130 cm. Due to the influence of thefan, this value of Ut is about 1.0 m/s higher than thatestimated from a free fall.

To prepared a soil packing, we carefully pour dry glassbeads into the sample column, 1 to 2 cm each time, to thedesigned packing height. The sample column is gentlytapped from time to time to get a random close packing.The tetrahedral holes in such a packing have a radius of2Rtet = 0.225 mm, which is a bit smaller than the axis

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of the dry hydrogel particles. Therefore, when hydrogelparticles are mixed in, either uniformly or placed in alayer at certain depth, they will not be moved or carriedaway by the infiltrating flow of rain water.

The partially-filled sample column is then placed inthe dry drainage container, right under the rain source.Water is slowly added into the container until the de-signed drainage level is reached and excess water beginsto drain out. The designed drainage level is about 1.5 cmhigher than the mesh position inside the sample column.Since water can freely flow in or out of the sample col-umn through the mesh, a horizontal wetting front appearinside the soil packing and moves upward due to capil-larity [30]. We keep adding water until it rises to a stableheight. The final capillary rise height in the model soilpacking is 1.0 ± 0.1 cm. A cover is then added on thedrainage container to minimize the evaporation in thesystem. During and after rainfall, the position of thewetting front is monitored to make sure that it is stableall times.

We start a rain at t = 0 and record the balance readingonce per minute. The mass of the retained rain water ina soil packing is then determined as

∆m = mt −m0, (1)

where m0 is the reading at t = 0 and mt is the reading attime t. We stop the rain when the reading is quasi-stableor when the soil packing is fully saturated to top, andcall that time as tstop. The mass of the drainage waterafter rain stops is then given as

∆m− ∆mstop = mt −mstop, (2)

where mstop is the reading at t = tstop and ∆mstop isthe mass of the retained water at t = tstop. The mass ofthe retained water is then scaled by water density ρ andthe sample cross-sectional area A so that it has units oflength, to better correspond with rain rate in the usualunits of length per time.

II. PURE MODEL SANDY SOIL

We begin by first determining retained water curves inthe pure model sand soil of glass beads, with no hydro-gel additives. Fig. 2 shows an example of the mass ofretained water as a function of time. ∆H = 12.5 cm la-beled in the figure refers to the height of the soil packingabove the fully-saturated water table, which exits beforethe rain starts. We see that at first the retained waterincreases the same as the rain rate, Q. But after a fewminutes, at a time we denote tc, it abruptly deviates andthereafter increases only very slowly. The quasi-stablemass retained water, around ∆m/(ρA) ≈ 0.12, is lessthan one tenth of the water required to fully saturatethe whole dry region of the soil packing. With this sameprocedure, we then vary the packing height ∆H from0 to 22 cm and repeat the same measurement over ten

0 2 0 4 0 6 0 8 0 1 0 0 1 2 00 . 0

0 . 1

0 . 2

0 . 3

0 . 4

N o g e l

∆H = 1 2 . 5 c m

∆m / (

ρA) (

cm)

t ( m i n )

Q = 2 . 5 4 c m / h r

t c

FIG. 2: (Color online) Variation of the retained water withtime for a model sandy soil, 1 mm hydrophilic glass beads,at a rain rate of Q = 2.54 cm/hr. The mass of the retainedwater ∆m is scaled by water density ρ and the cross-sectionalarea A of the soil packing. Rain starts at time t = 0. Thedry glass beads above the water table have a packing heightof ∆H = 12.5 cm. During the rain, the water table in the soilpacking is stable. In the first few minutes of rain, the retainedwater increases the same as the rain rate. After that it slowlyapproaches a stable value. tc marks the time at which thewater channel reaches the water table and fully penetratesthe whole dry packing.

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 20 . 0

0 . 1

0 . 2

0 . 3

0 . 4Q = 2 . 5 4 c m / h r

N o g e l

@ t = 6 0 m i n

∆m / (

ρA) (

cm)

∆H ( c m )

FIG. 3: (Color online) Variation of the retained water afteran hour of rain (t = 60 min) at a rain rate of Q = 2.54 cm/hrwith the packing height ∆H above the water table for a modelsandy soil, 1 mm hydrophilic glass beads. The mass of theretained water ∆m is scaled by water density ρ and the cross-sectional area A of the soil packing. Solid line is a linear fitfor ∆H ≥ 0.6 cm data. The slope of the fit confirms twothings: the water channel is very narrow compared to thepacking size, and the channel is in partially saturated stateduring the rain.

times. Similar water retention curves are obtained forthese packings, but sometimes an overshoot may occurin the transition point of those curves. Fig. 3 summarizesthe quasi-stable values of the retained water in those soilpackings at different heights, which we estimate based onthe behavior at t = 60 min. The results are close to eachothers except those with packing height less than 0.6 cm.

Based on Fig. 3 and visual observations, we come to

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the conclusion that rain water only uniformly infiltratesinto a shallow top layer of the model sandy soil and af-ter that it creates a narrow channel penetrating downthrough the whole dry region of the soil packing. Oncethe water channel connects to the water table in the soilpacking, any additional rain water flows down and outthe channel and the system reaches a quasi-stable state.We speculate that the subsequent observed slow increasein retained water mass is not due to a gradual thickeningof the channel or the top layer, but rather due to adsorp-tion of water vapor as a wetting layer on the glass beads(and in the hydrogel particles, in the next sections).

The two lines fit to the data in Fig. 3 support this pic-ture. For ∆H smaller than the thickness of the wettedshallow top layer, the mass of retained water should beproportional to ∆H consistent with the first line. Theslope has a value of 0.22 ± 0.01, which gives the volumefraction of water in the top layer. If it were fully satu-rated, the value would be 0.36 since the packing fractionof random-packed spheres is 0.64. Thus, the wetted toplayer is a little more than half saturated. This behaviorpersists until about ∆H = 1 cm, which corresponds wellwith visual observation of the thickness of the wetted toplayer. For taller packings, a water channel forms and themass of retained water increases with ∆H due only tothe increase of water volume in the channel. In particu-lar, the slope should be set by d∆m/d∆H = ρAw whereAw is the cross-sectional area of the water in the channel.The slope of the second line in Fig. 3 is (3.8± 3)× 10−4,which gives Aw = (3.8×10−4)A = 0.015 cm2. This com-pares to the size of the tetrahedral hole between glassbeads as Aw/(πR

2tet) = 30. Thus the radius of the ac-

tual water channel is about√

30/π = 3 beads. This isconsistent with observation made by turning off the rainand quickly excavating the sample. We note that actualchannels do not have a perfectly constant cross section,nor are they perfectly vertical.

With these results as a baseline, we are now readyto modify the pure model soil by addition of hydrogelparticles and measure their effects on the retained watercurve.

III. HYDROGEL PARTICLES MIXED INUNIFORMLY

One controlled way to apply hydrogel particle additivesis to uniformly mix them with the glass beads. We firstuse this distribution method to study the effects of hy-drogel particle concentration and mixing depth. A modelsandy soil packing with packing height ∆H = 12.5 cmabove the water table is used as the base packing (‘Nogel’ packing). Different amount of hydrogel particles areuniformly mixed into a shallow or a deep layer at the topof the dry soil packing. We determined the gel numberratio α in a mixture region as

α = Ngel : Nbead (3)

0 6 0 1 2 0 1 8 00 . 00 . 20 . 40 . 60 . 81 . 01 . 21 . 40 . 00 . 20 . 40 . 60 . 81 . 01 . 21 . 4

Qα = 0 . 1

α = 0 . 0 4

N o g e l

α = 0 . 0 4

α = 0 . 0 2

α = 0 . 0 2α = 0 . 0 1

α = 0 . 0 1

∆m / (

ρA) (

cm)

t ( m i n )

( b ) g e l i n t o p 1 0 c m

N o g e l

∆m / (

ρA) (

cm) ( a ) g e l i n t o p 1 c mQ

FIG. 4: (Color online) Variation of the retained water withtime for 1 mm hydrophilic glass bead packing under a heavyrain, with dry hydrogel particles (0.3 − 0.5 mm in axis) uni-formly mixed into (a) top 1 cm region and (b) top 10 cmregion of the soil packing. The initial packing height abovethe water table is ∆H = 12.5 cm for all packing. α is thenumber ratio of hydrogel particles to glass beads in the mix-ture region and is determined in Eq. (4). The mass of theretained water ∆m is scaled by the water density ρ and thecross-sectional area A of the packing. Rain starts at timet = 0 with a rain rate of Q = 2.54 cm/hr. During the rain,the water table remains stable. Dashed line marks rain water;the solid lines are linear fits to determine the cumulate rate ofrain water in each packing. As α increases, more rain water isretained in the packing. For a sufficient high α, the retainedwater curve overlaps with the dashed line of the rain rate.

=Mgel/mgelMbead/mbead

. (4)

Here Ngel and Nbead are the total number of the addedhydrogel particles and the total number of the glass beadsin the mixed region; Mgel and Mbead are the total massof the added hydrogel particles and the glass beads in themixture region respectively; mgel is the average mass ofa single gel particle while mbead is the average mass of aglass bead.

Fig. 4 (a) shows the retained water curves for pack-ings with dry hydrogel particles uniformly mixed intotop 1 cm region under a heavy rain, and compares themto the dashed line of the rain rate and the retained watercurve for the ‘No gel’ packing. Three gel number ratiosare tested: α = 0.01, α = 0.02, and α = 0.04. Similarto the ‘No gel’ curve, these curves follow the dashed lineof the rain rate right after rain starts but deviate fromit at later times. As defined in Fig. 2, these time pointsrefer to tc and illustrate how long rain water may taketo penetrate through a dry packing and reach the watertable. As the α value in a packing increases, the packing

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shows a larger tc. This is reasonable since the hydro-gel particles may lock part of the rain water inside byswelling and slow down the infiltration speed of the restrain water. When looking closely, we also notice anotherdifference between the ‘No gel’ curve and the other curveswith hydrogel particle presenting (α > 0): the ‘No gel’curve approaches a quasi-stable value almost right aftert = tc; while the other curves show a long transition re-gion starting at t = tc and ending when the incrementon the curve becomes ignorable and a quasi-stable stateapproaches. The appearance of the transition region isdue to the continuously swelling of the hydrogel particlesthat distribute in the uniformly wetted top layer and inthe fully-built water channel below it. Thus the lengthand the shape of the transition region depend on multi-ple factors, including the mixing depth, the gel numberratio, and the gel swelling properties. In these shallowmixing cases, since the mixing depth is comparable to thesize of the uniform wetted region, the added dry hydro-gel particles are all able to contact rain water in a shorttime after rain starts. They absorb water, swell in size,perturb the soil pore structure around them, and expandthe uniformly wetted top region of a packing vertically.This process is time-consuming and the expansion of thewetted region can be clearly observed by eye. For thethree packings shown in Fig. 4 (a), both our observa-tion and the obtained retained water curves indicate thatthey have approached a quasi-stable state after 3 hours ofraining (t = 180 minutes) and a shorter time is requiredto reach quasi-stable as the the gel number ratio α de-creases. We compare the amount of the retained waterat t = 180 minutes and find that its increment is almostproportional to the gel number ratio α. We also estimatethe expanding volume of a packing at the quasi-stablestate and find that it is consistent with the total swellingsize of the applied hydrogel particles in a packing.

When we extend the mixing depth to a larger value, forexample to 10 cm, the situation is a bit different. Manyadded dry hydrogel particles are located in the waterchannel region and can not contact rain water at the earlytime of the rainfall. If the hydrogel particles that luckilylocated in or near the water channel can significantlymodify the water channel and lead water to them, theymay get a chance to swell at a later time of the rainfall;if not, they will stay in dry for ever. For this situation,it takes too much time to reach a quasi-stable state butthe extended transition region usually shows a linear partwhose slope closely relates to the gel number ratio α in apacking. Fig. 4 (b) summarizes the retained water curvesfor packings with dry hydrogel particles uniformly mixedinto top 10 cm depth under a heavy rain. Here four gelnumber ratios are tested: α = 0.01, α = 0.02, α = 0.04,and α = 0.1. The first three values are the same asthe shallow mixing cases shown in Fig. 4 (a) while thelast value is applied to test if we can prevent the channelformation by rising the gel number ratio in a soil packing.In the figure, we see that the retained water curves ofthe first three α values again show different delays on tc

1 E - 3 0 . 0 1 0 . 10 . 00 . 51 . 01 . 52 . 02 . 53 . 0

1 1 0 1 0 0

G e l m i x e d i n

Q � 1 - e - � n / 4 . 7 � 4 �

Q � 1 - e - � � / 0 . 0 4 �3�

Water

cumu

late r

ate (c

m/hr)

G e l n u m b e r r a t i o i n m i x t u r e ( α)

Q = 2 . 5 4 c m / h rG e l i n l a y e r

W e t g e l l a y e r n u m b e r ( n )

FIG. 5: (Color online) Variation of the rain water accumu-lation rate with the mass of hydrogel particle additives in1 mm hydrophilic glass bead packing, with dry hydrogel par-ticles (0.3 − 0.5 mm in axis) uniformly mixed in top 10 cmregion and placed in a layer under top 10 cm soil, at a rainrate of Q = 2.54 cm/hr. The gel number ratio α is definedin Eq. (4); while the wet gel layer number n is determined inEq. (7). The data points are obtained from the slopes of thelinear fits in Fig. 4 (b) and in Fig. 8 respectively. Dashed linemarks the rain rate and the solid lines are sigmoidal fits ofthe data. When the same amount of hydrogel particles areapplied, the accumulation rate of rain water is far larger inpacking with hydrogel particles placed in a layer under theground than uniformly mixed into a top region of soils.

compared to the ‘No gel’ curve.When compared with the shallow mixing cases shown

in Fig. 4 (a), the transition regions are longer and have amore obvious linear part. We fit the major parts of thesetransition regions to a line, determine the slopes, and plotthe values against its gel number ratio α in Fig. 5. Theseslopes have a unit of centimeters per hour, the same asthe rain rate, and they tell us the accumulation rate ofrain water in a packing. Here we may consider them as ameasure of the changes on the water channel and use theplot in Fig. 5 to determine how gel number ratio affectsthe efficiency of hydrogel particles on modifying the waterchannel. We also fit the quasi-stable region of the ‘No gel’curve to a line and confirm that its slope value is veryclose to zero and far smaller than those obtained from themixture packing. For packing with α = 0.1, the retainedwater curve follows the dashed line of the rain rate all thetime and no deviation occurs even after 3 hours of rain(t = 180 minutes). No rain water flows out the packingor ponds on soil surface – the added hydrogel particlesare sufficient to absorb all of the supplied water in time.We again extract the slope of this curve and add its valueto the plot in Fig. 5.

In Fig. 5, we fit the obtained slope values to a sigmoidalfunction given below:

Water accumulation rate = Q[1 − e−(α/0.04)3

] . (5)

Here, rain rate Q is the maximum water accumulation

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0 . 00 . 20 . 40 . 60 . 81 . 0

0 6 0 1 2 0 1 8 00 . 00 . 20 . 40 . 60 . 81 . 0

2 X 1 0 3 g e l i n t o p 1 c m

2 X 1 0 3 g e l i n t o p 2 c m

1 0 3 g e l i n t o p 1 c m

1 0 3 g e l i n t o p 2 c mN o g e l

N o g e l

( b )

( a )

∆m / (

ρA) (

cm) Q

Q

t ( m i n )

∆m / (

ρA) (

cm)

FIG. 6: (Color online) Variation of the retained water withtime for 1 mm hydrophilic glass bead packing under a heavyrain, with (a) 103 and (b) 2×103 dry hydrogel particles (0.3−0.5 mm in axis) uniformly mixed into top 1 cm and top 2 cmregion of the soil packing respectively. The initial packingheight above the water table is ∆H = 12.5 cm for all packing.The mass of the retained water ∆m is scaled by the waterdensity ρ and the cross-sectional area A of the packing. Rainstarts at time t = 0 with a rain rate of Q = 2.54 cm/hr.During the rain, the water table remains stable. More rainwater is retained when hydrogel particles are concentrated ina shallower top soil layer in the packing.

rate of the system and the fit gives us a critical gel num-ber ratio of αcri = 0.04. More discussions on this figurewill be given in the next section.

To further demonstrate the effect of mixing depth, wecompare the retained water curves obtained from pack-ings with the same number of hydrogel particles uni-formly mixed into different deep top region under a heavyrain. A thousand dry hydrogel particles are applied inFig. 6 (a); while two thousand particles are applied inFig. 6 (b). The mixing depth is chosen to be 1 cm and2 cm for each case. In both Fig. 6 (a) and (b), we seethat more rain water is retained in soil packing with hy-drogel particle additives concentrated to a shallower toplayer. The reason is that extending the mixture regiondecreases the gel number ratio in the mixture region thusreduces the number of the dry hydrogel particles that areable to contact water during the rain. Without couplingrain water channelization phenomenon into the measure-ments, this influence will never be noticed.

A. Drainage after rainfall

Another way to determine if the swollen hydrogel par-ticles significantly change the soil pore structure and it

- 0 . 3- 0 . 2- 0 . 10 . 0

0 2 0 4 0 6 0- 0 . 3- 0 . 2- 0 . 10 . 0

α = 0 . 0 1 i n t o p 1 c mα = 0 . 0 2 i n t o p 1 c mα = 0 . 0 4 i n t o p 1 c m

�∆m

- ∆m s

top) /

(ρA) (

cm)

( a )

( b )

N o g e l

1 0 3 g e l i n t o p 1 c m 1 0 3 g e l i n t o p 2 c m

t - t s t o p ( m i n )

N o g e l

FIG. 7: (Color online) Variation of the draining water withtime for 1 mm hydrophilic glass bead packing after rain stops,with dry hydrogel particles (0.3 − 0.5 mm in axis) uniformlymixed in top 1 cm and top 2 cm of the soil packing. Resultsin (a) are obtained from packings shown in Fig. 4 (a); whileresults in (b) are obtained from packings shown in Fig. 6 (a).Rain stops at time t = tstop, when the retained water ina packing is quasi-stable. The mass of the retained waterat that time is labeled as ∆mstop. The water table in thesoil packings is stable during the drainage. The mass of thedraining water (∆m−∆mstop) is scaled by the water density ρand the cross-sectional area A of the packing. α is the numberratio of hydrogel particles to glass beads and is determined inEq. (4). Packings with hydrogel particles uniformly mixed intop region show similar drainage curves as the ‘No gel’ one.

hydraulic conductively is to monitor the drainage behav-ior of packings after stopping the rain. As a continuationof the experiments shown in Fig. 4 (a), we stop the rain att = 180 minutes for all the packings, record their drainagecurves, and compare with the ‘No gel’ case. In Fig. 7 (a),we see that the drainage curves of the mixture packingsbehave the same as that obtained from the ‘No gel’ pack-ing. Within the gel number ratio range we tested, theswollen hydrogel particles cannot efficiently slow downor reduce the gravitational drainage of the rain water.We also stop the rain at t = 180 minutes for packingsshown in Fig. 6 (a) and compare their drainage curvesin Fig. 7 (b). Again, we see all the drainage curves col-lapse together. No matter appearing in the top uniforminfiltration layer or in the water channel, the swollen hy-drogel particles do not affect the drainage of the retainedrain water in sandy soil pores. After free drainage, the fi-nal remaining water in a packing is mostly locked in theswollen hydrogel particles. Comparing its value to theswelling ratio of hydrogel particles, we may estimate thepercentage of the swollen hydrogel particles in a packing.For examples, when a thousand dry hydrogel particlesare applied in a model sandy soil packing, about 80% ofthem swells under rain when they are uniformly mixedin top 1 cm region, but only 40% of them swells underrain when they are uniformly mixed in top 2 cm region.

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IV. HYDROGEL PARTICLES PLACED IN ALAYER UNDER THE GROUND

Previous studies [8, 12, 13] have reported that whentoo many hydrogel particles are mixed into a shallowtop layer of sandy soils they may swell to form a ‘gelshell’ which prevents the infiltration of water into soiland thereby increases the surface water runoff. We maybuild a similar structure under the ground to slow downrain water drainage and create extra water reservoirs nearthe plant roots, without runoff, as follows. Instead ofmixing, we place dry hydrogel particles in a layer underthe surface of a model sandy soil packing with a heightof H = 12.5 cm. We define a wet gel layer number nto replace the gel number ratio α used in the mixingcases. The wet gel layer number n represents the max-imum number of the pure wet gel layers that the addedhydrogel particles can form in a packing with sufficientwater supply. It is estimated as

n = Ngel/N′onelayer (6)

=Mgel/mgelA/(δd)2

. (7)

Here, Ngel is the total number of hydrogel particles thatare placed under the ground; N ′onelayer is the number ofthe hydrogel particles that are required to form a singewet gel layer; Mgel is the total mass of the added hydrogelparticles and mgel is the average mass of a single hydrogelparticle; A is the cross-sectional area of the soil samplepacking; d = 0.4 ± 0.1 mm is the average axis size of dryhydrogel particles; and δ = 6 is the free swelling ratioof hydrogel particles in sufficient DI water obtained bymicroscope measurements.

Fig. 8 summarizes the retained water curves obtainedfrom packings with different mass of dry hydrogel par-ticles placed in a layer at H ′ = 10 cm depth under thesoil surface. The wet gel layer number in these packingsvaries from n = 2 to n = 6. Rain starts at t = 0 andthe rain rate Q = 2.54 cm/hr is marked by the dashedline. From the figure, the first thing we notice is thatwithin the n range we tested the dry gel layer under theground cannot efficiently prevent the full formation of thewater channel: all the retained water curves show a devi-ation from the dashed line of rain rate at an early time ofthe rainfall, the same as the ‘No gel’ case shown by theblue square symbol. Their tc values are slightly largerthan that of the ‘No gel’ case and close to those obtainedfrom the uniformly mixing cases shown in Fig. 4. Thisis reasonable since the hydrogel particles we applied hereare not sufficient to from a dense layer in dry and theirswelling is time-consuming. Another obvious thing wefind is that the transition region in these curves signifi-cantly differs from that of the mixing cases, which showsa single linear increase until reaching the quasi-steadystate. The transition regions shown in Fig. 8 are morecomplex and most of them can be clearly separated intotwo parts: a slowly increasing region corresponds to the

0 6 0 1 2 0 1 8 0 2 4 0 3 0 00

1

2

3

4

5

n = 3

n = 2

n = 4n = 5

N o g e l

n = 6

∆m / (

ρA) (

cm)

t ( m i n )

QH ’ = 1 0 c m

FIG. 8: (Color online) Variation of the retained water withtime for 1 mm hydrophilic glass bead packing under a heavyrain, with different amount of hydrogel particles (0.3−0.5 mmin axis) placed in a layer in dry at a depth of H ′ = 10 cmunder the soil surface. n is defined in Eq. (7) and representsthe maximum number of the wet gel layers the added hydrogelparticles can build in a packing with sufficient water supply.The initial packing height above water table is ∆H = 12.5 cmfor all packing. The mass of the retained water ∆m is scaledby the water density ρ and the cross-sectional area A of thepacking. Rain starts at time t = 0 with a rain rate of Q =2.54 cm/hr. During the rain, the water table remains stable.Dashed line marks the rain rate; the solid lines are linear fitsto determine the rain water cumulate rate in each packing.The well-built wet gel layers partially clog the water channeland force part of the rain water to cumulate in pores of themodel sand soil.

formation of the wet gel layers; while a sharp linear in-creasing region corresponds to the accumulation of therain water in the sandy soil due to the clogging effects ofwell-built wet ‘gel shell’ under the ground. As the wet gellayer number n increases, less time is consumed to fullbuild the wet gel layers and more rain water is retainedinside the packing. The reason is that when the densityof the dry hydrogel particles increases in a packing morehydrogel particles locate in the cross-section of the waterchannel and their swelling horizontally directs more rainwater to their dry neighbors. During the experiments,through the transparent sample column we can clearlysee an optically-clear swollen hydrogel region built acrossthe soil packing and the model sandy soil above is liftedup. The size of the swollen gel region is consistent withthat estimated from the wet gel layer number n in thepacking.

The fully-built wet gel layers can be very efficient inclogging the rain water. In Fig. 8, we see that the sec-ond part of the transition region in the different retainedwater curves all have very different slopes. Experimen-tally, we observed a fully saturated region in the modelsandy soil forming and growing upward right above theoptical-clear swollen hydrogel region. The clogging effi-ciency depends on the wet gel layer number n: the satu-rated region in packings with high n values keeps growingup to the top of the packing and then ponding on the soil

8

surface; the saturated region in packings with low n val-ues usually stops growing up at certain level and reachesa quasi-steady state. We stop the rain right before wa-ter begins to pond on soil surface for the first case andwhen system reaches the quasi-steady state for the sec-ond case. Since the major rain water storage mechanismfor packings shown in Fig. 8 is to create water reservoirin sandy soil itself rather than to lock water inside hy-drogel particle additives, we fit the second part of thetransition regions to a solid line, as shown in the figure,use the slope values to represent the rain water accumu-lation rates in these soil packings, and compare to theuniformly mixing cases discussed in the last section. Thevariation of the slopes with the corresponding wet gellayer number n are also shown in Fig. 5 and it behavesvery similar to that obtained from the mixing cases butshifts to left in x-axis. We again fit the data using thesame sigmoidal function and have

Water accumulation rate = Q[1 − e−(n/4.7)4

] . (8)

Here, rain rate Q is the maximum water accumulationrate of the system and the fit gives us a critical wet gellayer number of ncri ≈ 5. If we convert both ncri andαcri back to the mass of the added hydrogel particles, wewill see that the former one is far smaller than the laterone. So we come to the conclusion that placing hydro-gel particle additives in a layer under the ground is moreefficiency in improving sandy soil water storage than uni-formly mixing them into soils. The reason is because byplacing hydrogel particles in a layer under the groundwe successfully add a new water storage mechanism intothe system. Beside storing rain water inside the hydrogelparticles, the clogging effects of swollen hydrogel parti-cles is also carefully applied to create a temporary waterreservoir inside sandy soils, which largely accumulatesrain water and extends the soil region where rain watercan reach.

A. Drainage after rainfall

The drainage behavior for packings with hydrogel par-ticles placed in a layer is far more complex and interestingthan that of the uniformly mixing cases. Fig. 9 collectsthe drainage curves obtained from exactly the same soilpackings shown in Fig. 8. Differing from the uniformlymixing cases, the rain stop time tstop for these drainagecurves varies from each other. As we mentioned before,the strong clogging effects due to the well-built wet gellayer may prevent a soil packing to reach a steady stateunder the rainfall. So, for n = 6 and n = 5 packing,we have to stop the rain when its fully saturated regiongrows to the soil surface to prevent water ponding. Forn = 4, n = 3, n = 2 packings, we again stop rain whenthey reach the quasi-steady state. The values of tstopfor these packings can be determined from the last datapoint in each curve shown in Fig. 8 and the maximumtstop value is 300 minutes. In Fig. 9, we see that most

0 2 0 4 0 6 0- 1 . 0

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0 . 0N o g e l n = 2n = 3

n = 6

n = 5

n = 4

(∆m - ∆

m stop

) / (ρA

) (cm

)

t - t s t o p ( m i n )

H ’ = 1 0 c m

FIG. 9: (Color online) Variation of the draining water withtime for 1 mm hydrophilic glass bead packing after rain stops,with different amount of hydrogel particles (0.3 − 0.5 mm inaxis) placed in a layer in dry at a depth of H ′ = 10 cmunder packing surface. These results are obtained from thesame packings shown in Fig. 8. n is defined in Eq. (7) andrepresents the maximum number of the wet gel layers theadded hydrogel particles can build in a packing with sufficientwater supply. Rain stops at t = tstop when a packing is inquasi-steady state (n ≤ 4) or when a packing is fully saturatedto its surface by rain water (n > 4). The mass of the retainedwater at tstop is labeled as ∆mstop. During the drainage,the water table remains stable. The mass of the drainingwater (∆m−∆mstop) is scaled by the water density ρ and thecross-sectional area A of the packing. The maximum drainagehappens at the n = 4 packing and the drainage decreases forpackings with smaller n values and with larger n values.

of the drainage curves obtained from packings with hy-drogel particles place in a layer under the ground showlarge deviation from the ‘No gel’ curve. An interestingthing we notice is that these curves even not changesmonotonously. The maximum drainage occurs in then = 4 packing. For n < 4 packings and n > 4 packings,the drainage reduces as n value decreases or increases,respectively. Considering the difference of the drainablewater at t = tstop in each packing, we should not be sur-prised by the results. The drainable water refers to theamount of water that only temporarily stays in a packingafter rain stops and does not lock by the hydrogel parti-cles or by the capillary forces in soil pores. Due to thewell-built wet gel layers, there is a dramatic increase inthe drainable water from the n = 2 packing to the n = 4packing. Therefore, for the n ≤ 4 packings the drainagebehavior is dominated by the amount of drainable waterin a packing at t = tstop; while for the n ≥ 4 packingsthe drainage behavior is mainly determined by the clog-ging efficiency of the well-built wet gel layers on reducingwater draining speed.

B. Depth of gel particle layer

Another important parameter that may affect the clog-ging efficiency is the location of the wet gel layers. Since

9

the soil confinement on the wet gel layers comes fromthe weight of the model sandy soil above them, placinghydrogel particles in a shallower location under groundreduces the soil confinement thus may modify the effi-ciency of the wet gel layers in slowing down rain waterdrainage. Fig. 10 shows the retained water curves ob-tained from packings with the same amount of hydro-gel particles placed in a layer in dry at different depthsH ′ under the soil surface. The base packing (‘No gel’one) has a packing height of ∆H = 12.5 cm. Two thou-sand hydrogel particles, giving a wet gel layer numberof n = 4, are added in each packing but the locationsvaries from H ′ = 5 cm to H ′ = 10 cm. Rain starts att = 0 with a rain rate of Q = 2.54 cm/hr, as marked bythe dashed line in the figure. In Fig. 10, we notice sev-eral things: first, changing the location of the gel layerdoes not affect the formation time of the water channeland the tc values for all the packings are roughly thesame; second, packings with hydrogel particles placedin a shallower location (smaller H ′) require less time toreach the quasi-steady state and retain less rain water atthat state; third, the slopes of the transition regions forall these curves are very close to each other. In detail,when hydrogel particles are placed in a shallow locationin the packing, the corresponding retained water curveno longer shows a clear sharp change in the slope of thetransition region, such as H ′ = 5 cm and H ′ = 6 cmcurves. The reason is that hydrogel particles feel lessvertical confinement in a shallow location of the packing.They can swell more freely and pack more loosely un-der the rain, which strongly reduces their water cloggingefficiency. During the experiments, we indeed observedthe following facts: the thickness of the wet optical-clearhydrogel region formed in H ′ = 10 cm packing is onlyabout 70 % of that formed in H ′ = 5 cm packing; thesize of the fully-saturated region created above the wetgel layers is less than 0.5 cm in H ′ = 5 cm packing butincrease to about 3 cm in H ′ = 7 cm packing and 8 cmin H ′ = 10 cm. Fig. 10 clearly demonstrates that thevertical soil confinement plays a critical role in buildingthe wet gel layers with efficient clogging effects.

We also compare the drainage behavior for packingswith the same gel layers formed at different depth underthe ground after rain stops. Fig. 11 collects the drainagecurves for exactly the same packings shown in Fig. 10.Again, we stop the rain when a packing reaches quasi-steady state. The tstop values vary for these packingsand can be obtained form the last data point of thecurves shown in Fig. 10. In Fig. 11, we see that mostof the drainage curves significantly deviate from the ‘Nogel’ case. And this time a monotonously change in thedrainage curves is seen in the figure as the H ′ value de-creases: the draining water decreases as the wet gel lay-ers locates closer and closer to the soil surface. The mainreason is that the amount of drainable water stored inpackings with large H ′ values at t = tstop is far largerthan that stored in packings with small H ′ values. Com-paring the amount of water that retains in a packing at

0 6 0 1 2 0 1 8 0 2 4 0 3 0 00

1

2

3

4

5H ’ = 1 0 c m

H ’ = 8 c m

H ’ = 7 c m

H ’ = 5 c mH ’ = 6 c m

∆m / (

ρA) (

cm)

t ( m i n )

Q

N o g e l

n = 4

FIG. 10: (Color online) Variation of the retained water withtime for 1 mm hydrophilic glass bead packing under a heavyrain, with two thousand hydrogel particles placed in a layer indry at different depths H ′ under the soil surface. The initialpacking height is ∆H = 12.5 cm for all packing. The massof the retained water ∆m is scaled by the water density ρand the cross-sectional area A of the packing. Rain starts att = 0 with a rain rate of Q = 2.54 cm/hr. During the rain,the water table remains stable. Roughly the same amount oftime is taken to build the wet gel layers but their efficiency inshowing down the rain water drainage is very different. Onlythe wet gel layers formed under sufficient depth under groundare able to significantly reduce the rain water penetrationspeed and force part of the rain water to cumulate in thepores of the model sandy soil about them.

0 2 0 4 0 6 0- 1 . 0

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0 . 0N o g e l H ’ = 5 c m

H ’ = 6 c mH ’ = 7 c m

H ’ = 8 c m

(∆m - ∆

m stop

) / (ρA

) (cm

)

t - t s t o p ( m i n )

n = 4 H ’ = 1 0 c m

FIG. 11: (Color online) Variation of the draining water withtime for 1 mm hydrophilic glass bead packing after rain stops,with two thousand hydrogel particles placed in a layer in dryat different depths (H ′) under the soil surface. These resultsare obtained from the same packings shown in Fig. 10. Rainstops at t = tstop when a packing reaches its quasi-steadystate. The mass of the retained water at t = tstop is labeledas ∆mstop. During the drainage, the water table remainsstable. The mass of the drainage water (∆m − ∆mstop) isscaled by the water density ρ and the cross-sectional area Aof the packing. More water drains out when hydrogel particlesare placed in deeper location under the soil surface.

tstop and that drains out after rain stops, we find thateven after hours of free draining, there is still more waterremaining in packings when larger H ′ value is applied.

10

V. CONCLUSION

In conclusion, we built a 3D laboratory set-up to studyhow rain water is transported and stored in a modelsandy soil when hydrogel particles are applied into thesoil by different methods. The set-up mimics a heavyrain condition in nature and measures the mass of theretained water in a soil packing during the rainfall andafter rain stops. The sample column we used is trans-parent and allow us to also observe certain experimentalphenomena by eye. The data and the visual observationsare combined to determine the principle mechanisms thatcontrol the transport and storage of rain water in sandsoils with commercial superabsorbent additives.

The model sandy soil we chosen has a well-known porestructure and very hydrophilic grain surfaces. It showsextremely poor water-holding capacity under rain – thatamount of the retained water in a pure soil packing is 30times less than what is required to wet the whole pack-ing. Our study shows that rain water only uniformlywets a shallow top layer of the soil packing and then aninstability occur on the wetting front and grow into afingered flows that finally penetrates through the pack-ing and forms a narrow water channel. Since the satu-rated hydraulic conductivity of the model sandy soil isfar larger than the rain rate, both the wet top layer andthe water channel in the soil packing maintain a low sat-uration level during the rainfall. Once the water channelis fully formed, rain water follows this path to drain outand the rest of the soil remains dry.

When dry hydrogel particles are uniformly mixed intothe model sandy soil, under the same raining conditionthe amount of the retained water in the packing increasesand the increment strongly depends on the mixing depthsand the gel number ratio in the mixture region. Not allthe hydrogel particle additives can have contact with therain water; only those lucky ones located in the wet toplayer or in the water channel are able to absorb water.Within the gel number ratio range we tested, the pres-ence of hydrogel particle additives cannot prevent the fullformation of the water channel but only delay it a bit intime. The reason is that their water supply is limitedand their swelling is time-consuming. The swelling ofthese hydrogel particles slowly modifies the size and theshape of the water channel so that rain water may bedirected to flow through their dry neighbors. Here themajor mechanism that enhances the soil water retentionis to lock as much rain water as possible into the hydro-gel particles rather than increase the capillary storage ofwater in sandy soil by modifying soil pore structure. Ourstudy on the drainage behavior of these packings furtherconfirms this conclusion. Therefore, the key of optimiz-ing the method is to maximize the percentage of addedhydrogel particles that can contact and absorb rain wa-ter by carefully choosing the mixing depths and the gel

number ratio in the soil.

When dry hydrogel particles are placed in a layerdeeply under ground, in the same raining condition theamount of the retained water in the packing increaseseven more significantly than that in the uniformly mixingcases. The hydrogel particles applied by this method nei-ther prevent the fingered flow to penetrate nor stronglyslow down the flow speed in the water channel until theoptic-clear wet gel layers are well-built across the soilpacking under the rainfall. Beside locking rain water inhydrogel particles, a new rain water storage mechanism isinduced here using the clogging effects of the wet gel lay-ers to enhance the capillary storage of water in sandy soilpores. The building of wet gel layers is time-consumingand their efficiency largely depends on the forming loca-tion and the number of the wet gel layers. Wet gel layersformed deeply under ground are very efficient in cloggingrain water thus creating large temporary water reservoirsin sandy soils above them; wet gel layers formed in a shal-low location are not so efficient in clogging rain water butmay absorb more water inside the gel layers. For wet gellayers formed at the same depth, increasing the numberof the wet gel layers enhances the clogging effects andthe water-holding capacity in a packing. We also moni-tor the drainage behaviors in these cases after rain stopsand find that it is far more complex than that obtainedin the mixing ones. The reason is that the drainage be-havior here is not only controlled by the efficiency of thewet gel layers in slowing down draining speed but also de-cided by the total drainable rain water retained in eachpacking at the time rain stops.

Our study has elucidated many interesting features inrain water transport and storage in a sandy soils with andwithout superabsorbent additives. And it shows how theadditives may be efficiently used, in light of the formationof fingered flows. Furthermore it brings new questionsinto focus: how exactly does the presence of the hydro-gel particles modify the fingered flowing paths of rainwater in sandy soils? How does particle swelling disturbsthe pore structure of sandy soils? If there is more thanone channel, what sets the separation length? To helpanswer such questions, a quasi two-dimensional versionof our set-up has been constructed in order to to directlyvisualize channel morphology and kinetics [31, 32].

Acknowledgments

We thank Jean-Christophe Castaing, Zhiyun Chen,Cesare M. Cejas, and Remi Dreyfus for helpful discus-sions. We also thank Degussa Inc. for kindly pro-viding us the hydrogel particle samples. This work issupported by the National Science Foundation throughGrants MRSEC/DMR-112090 and DMR-1305199.

11

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I ExperimentA MaterialsB Procedures

II Pure model sandy soilIII Hydrogel particles mixed in uniformlyA Drainage after rainfall

IV Hydrogel particles placed in a layer under the ground A Drainage after rainfallB Depth of gel particle layer

V Conclusion Acknowledgments References