Diffusion of Zinc in Soil: II. The Influence of Soil Bulk Density and its

Interaction with Soil Moisture1

D. D. WARNCKE AND S. A. BARBER2

ABSTRACT

Effective Zn diffusion coefficients were determined at foursoil bulk densities and three moisture levels in five silt loamsoils. The tortuosity of the diffusion path, f1; for each set of soilconditions was estimated from 36C1 diffusion data. In each soiland for each soil moisture level the diffusion path was leasttortuous near 1.3 g/cm3. The observed order for the influenceof soil bulk density on tortuosity was 1.6 > 1.5 ;> 1.1 > 1.3g/cm3. Soil bulk density interacted significantly with soil mois-ture in affecting the Zn diffusion coefficients. The maximumrate of Zn diffusion did not always occur at a soil bulk densityof 1.3 g/cm3 where the diffusion path was least tortuous. At20 and 30% moisture the Zn diffusion rate reached a maximumnear 1.5 g/cm3 indicating that tortuosity was not the only factorinfluencing the rate of Zn diffusion. As the soil moisture wasincreased, a reduction in the effect of the interaction of Znwith the soil was greater than the effect of tortuosity in deter-mining the effective rate of Zn diffusion in each soil. When thebulk density was increased from 1.5 to 1.6 g/cm3, an increasein both the degree of interaction and toruosity combined tocause a sharp decrease in the Zn diffusion coefficient.

Additional Index Words: chloride diffusion, tortuosity.

IONS diffusing through soil are subject to the physical andchemical properties of the soil. A change in soil bulk

density affects the degree that these physical and chemicalcomponents influence the diffusion of ions. Phillips andBrown (1965, 1966) indicated that changes may occurin three ways. First, as soil bulk density of an unsaturatedsoil is increased from a low to a higher bulk density theincrease in volumetric moisture content accompanying theincrease in soil bulk density should act to increase thecontinuity of the liquid phase and hence, physically reducethe tortuosity of the diffusion path. Data on the effect ofvolumetric moisture reported by Warncke and Barber(1972) indicated that the rate of Zn diffusion in soil in-creased with increasing volumetric moisture. An increasein volumetric moisture will also increase the thickness ofthe water films about the soil particles which may reducethe chemical interaction of the ion with the soil.

WARNCKE & BARBER: DIFFUSION OF ZINC IN SOIL: n. SOIL BULK DENSITY AND MOISTURE 43

Second, with increased soil bulk density the fraction ofsolids per unit volume increases. Initially, at low soilbulk densities and low moisture, compaction may act toincrease the continuity of the liquid phase by bringingwater films into contact. Eventually, however, the increas-ing solids per unit volume may be expected to physicallyincrease the tortuosity of the diffusion path.

Third, the increasing closeness of the exchange sites withincreasing soil bulk density may allow more overlap of theoscillation volumes of the exchangeable ions. This wouldonly be significant if the amount of diffusion of ions inthe adsorbed phase was comparable to diffusion throughthe liquid phase. This may occur at low soil moisture con-tents (Van Schaik, Kemper and Olsen, 1966; and Mottand Nye, 1968).

The net effect which increasing soil bulk density hasupon the rate of ion diffusion in a soil should be relatedto the balance between changes in the relative influence ofthe physical and chemical components. Changes in thephysical soil component will be reflected in the tortuosityof the diffusion path whereas changes in the chemical soilcomponent will be reflected in the interaction of the dif-fusing ion with the solid phase. The interaction factor in-cludes effects due to changes in viscosity of the water,negative adsorption, and the effect of exchange adsorption.Hence, the effective rate of Zn diffusion in a soil may beexpressed by the relation:

Table 1—Properties of the soils investigated

4> [1]

whereDe(Zn) is the effective Zn diffusion coefficient for the soil

systemZ>Zn is the Zn diffusion coefficient in bulk solution f1 is/! is the tortuosity factor<j> is the interaction factor

Equation [1] assumes Zn diffuses through the liquid phase.This equation is similar to that used by Phillips and Brown(1968) for the diffusion of tritiated water. With water theinteraction factor, (/>, involved only changes in viscositynear soil particles whereas with ion diffusion, adsorptionand equilibrium with the exchange phase are also involved.

Generally, the tortuosity of the diffusion path may beestimated from the diffusion coefficient of a relativelynonadsorbed ion, such as Cl. In studying the self-diffusionof soil water, Kunze and Kirkham (1964) investigatedmethods for measuring the diffusion coefficient of soilwater and concluded that it could be estimated by multiply-ing the Cl diffusion coefficient by 1.24. Hence, we assumedthat /j can be estimated by measuring the rate of Cl dif-fusion in soil and calculating /j from equation [1] assum-ing </> equals one. If some negative adsorption shouldoccur, the effect would appear as an increase in the tortu-osity of the diffusion path (Van Schaik et al., 1966).

If changes in /j and <f> parallel each other or if <f> remainsconstant as soil bulk density is increased, the maximum Zndiffusion rate will coincide with the least tortuous diffusionpath. However, if this is not the case, then the maximumZn diffusion rate will depend upon the balance between /,and <j>, and will occur when the product of /t and <j> reaches

Soil

CincinnatiZanesvilleSidell (0-20 cm)FincastleSidell (20-40 cm)

PH

4.94.85.05.05.1

Displacedsolution Zn

NX 10s

41.252.521.420.280.09

ExchangeableZn

neq/100 g64.12

2.026.795.263.40

CECmeq/100 g

12.2612.2620.6914.8020.59

Organicmatter

%1.901.552.502.041.68

a maximum. Graham-Bryce (1963) found the bulk densitygiving the largest diffusion coefficient for Rb increasedfrom 1.4 to 1.65 g/cm3 in a low clay soil as the Rb con-centration in the soil was decreased. In a silt loam soil,Phillips and Brown (1965) obtained maximum Rb andSr self-diffusion coefficients with soil bulk densities of 1.30and 1.56 g/cm3, respectively; and in a clay soil the maxi-mum Sr self-diffusion coefficient occurred at 1.31 g/cm3.However, Phillips and Brown (1966) reported Rb andSr counter-diffusion coefficients to be linear functions ofbulk density up to 1.78 and 1.57 g/cm3 for silt loam andclay soils, respectively. Hence, the influence of soil bulkdensity on diffusion varies with the ion, ion concentration,and soil texture; all of which affect the tortuosity and/orinteraction factors.

The objective of this research was to investigate theinfluence of changing soil bulk density on the rate of Zndiffusion in soil at various initial soil moisture contentsand to relate changes in diffusion rate to changes in thetortuosity of the diffusion path and the degree of inter-action of the Zn with the soil.

MATERIALS AND METHODSCincinnati, Zanesville, Fincastle, Sidell surface (0-20 cm)

and Sidell subsurface (20-40 cm) silt loam soils were used inthis diffusion study. Their pertinent soil properties are given inTable 1. Twenty grams (air-dry) of each soil were labeledwith 40 ,uCi of carrier-free 65Zn to facilitate measuring Zn diffu-sion. For estimation of the tortuosity factor 20g of each soilwere labeled with 20 MCi of 36C1.

The procedure for labeling and packing the "labeled" soilinto plexiglas diffusion cells has been described (Warncke andBarber, 1972). Four soil bulk densities were used; 1.1, 1.3, 1.5,and 1.6 g/cm3. At each bulk density Zn and Cl effective dif-fusion coefficients were determined for moisture contents of10, 20, and 30% by weight. Thus, the volumetric soil mois-ture content increased with each increase in soil bulk density.A 48-hour equilibration period was allowed after adjusting thesoil conditions before the diffusion experiments were started.Three observations were taken on each of two replicates foreach soil, moisture, and bulk density combination.

Zinc-65 was allowed to diffuse from the soil into strips ofcation exchange resin (IR-120) paper for 48 hours, and 36C1was allowed to diffuse into anion exchange resin (IRH-400)paper for 5 hours (Vaidyanathan and Nye, 1966). Effective65Zn and 36C1 diffusion coefficients were calculated from equa-tion [2].

Zn) = Mt2/4C02? [2]

whereMt is the total amount of 65Zn which diffuses into the ex-

change resin paper in time /C0 is the initial uniform concentration of diffusible 65Zn in

the soilDe is the effective diffusion coefficient for the soil system

Equation [2] is a modification, for short time diffusion, of the

44

.4

.2

SOIL SCI. SOC. AMER. PROC., VOL. 36, 1972

12

10

8

1.3

10

De(Ci)c MO6

1.5 1.6Bulk Density (g/cm )

Fig. 1—Average influence of soil bulk density on the rate ofchloride diffusion and on the tortuosity of the diffusion pathin five silt loam soils at three moisture levels. The /i valueswere calculated from measured De(ci) values.

formula originally derived by Crank (1956) for diffusion to aplanar surface, and assumes the ion concentration at the soil-resin paper interface to be zero. In a preliminary experiment,effective Zn diffusion coefficients were found to remain con-stant with increasing diffusion time "indicating that the aboveassumption was valid.

The tortuosity of the diffusion path, /t, was estimated bysubstituting the data for Cl diffusion, Deic\-» into equation [1].De<.c\) and ^ci replaced De(Zn-, and DZn, respectively. jDcl wasassumed to be 2.03 X 10~5 cmVsec (Parsons, 1959) and </> wasassumed equal to 1.0. The interaction factor was estimated bysubstituting the diffusion data for Zn, De(Zny, into equation [1].DZn was assumed to be 7.20 X 10-6 cmVsec and the value of/! used was calculated from the results of Cl diffusion forsame soil and moisture conditions.

RESULTS AND DISCUSSIONInfluence on Tortuosity

An increase in soil bulk density above 1.1 g/cm3

affected tortuosity of the diffusion path in a similar mannerfor each soil. The /t and Z>e(C1) values, averaged for thefive soils, are shown in Fig. 1 plotted against soil bulkdensity for each moisture level. The maximum value foreach soil moisture level occurred near a bulk density of 1.3g/cm3. The values of /t at 10% moisture (w/w) werevery low indicating a very tortuous diffusion path. Evenwith increasing bulk density and the accompanying in-crease in volumetric moisture (11 to 16%) the change in/! was very small. At this low moisture level, increasing thebulk density from 1.3 to 1.5 and 1.6 g/cm3 increasedtortuosity only slightly.

With the increase of the soil moisture content from 10to 20% (w/w) the liquid phase became more continuousand the tortuosity of the diffusion path decreased. As at10% moisture, the maximum f1 value was obtained neara bulk density of 1.3 g/cm3. At a bulk density of 1.1g/cm3 all of the micropores and some of the larger poreswere probably filled giving a semicdntinuous liquid phase.Compaction of the soils caused many of the liquid discon-tinuities to be filled, resulting in a less tortuous diffusionpath. As the soil bulk density was increased from 1.3 to1.5 and then to 1.6 g/cm3 the soil particles were pushedmuch closer together. Hence, even though the liquid phase

id9

10

Cincinnati

1.2 1.3 1.4Bulk Density (g/cc)

1.5 1.6

Fig. 2—Influence of soil bulk density on the rate of Zn diffu-sion (log scale) at 10% moisture.

may have been more continuous, the diffusing ions wereforced to move around the particles thereby increasing thetortuosity of the diffusion path.

At 30% moisture (w/w) many of the larger pores werefilled and continuity of the liquid phase was greater thanat 20% moisture. This was reflected in higher observed/i values (a less tortuous diffusion path) at all bulk densi-ties for each soil. However, even at this moisture the tor-tuosity of the diffusion path was increased by increasingthe soil bulk density beyond 1.3 g/cm3. Compaction ofthe soils to higher bulk densities rapidly and noticeablyincreased the tortuosity of the diffusion path due to anincreased volume fraction of solids.

Looking at the results over all three moisture levels; soilbulk density had the same effect on /j regardless of the con-stant soil moisture (w/w) content. However, the effectwas more pronounced at 30% than at 10% moisture. Be-yond the critical soil bulk density of 1.3 g/cm3 the increas-ing fraction of solids per unit volume became the dominantfactor affecting f1 even though the continuity of the liquidphase was probably also increasing. The observed orderof tortuosity in each soil was 1.6 > 1.5 > 1.1 > 1.3 g/cm3.Hence, in these five silt loam soils the least tortuous dif-fusion path was obtained near a bulk density of 1.3 g/cm3

with the absolute tortuosity being determined by the soilmoisture content.

Influence on Zn Diffusion

The influence of changing the soil bulk density on therate of Zn diffusion in the five soils is shown in Figs. 2,3, and 4 for soil moisture contents of 10, 20, and 30%(w/w), respectively. The coefficients of variation for£>„ over all bulk densities were 12.5, 11.6, and 7.8%

WARNCKE & BARBER: DIFFUSION OF ZINC IN SOIL: 11. SOIL BULK DENSITY AND MOISTURE 45

10

10

(cmz/sec)

10"

ID1

10

Cincinnati

1.2 1.3 1.4Bulk Density (g/cc)

1.5 1.6

Fig. 3—Influence of soil bulk density on the rate of Zn diffu-sion (log scale) at 20% moisture.

for moisture contents of 10, 20, and 30% (w/w), respec-tively. An analysis of variance of the data (Table 2) showsthat £>e(Zn) did change significantly with changes in soilmoisture and with changes in soil bulk density. A highlysignificant interaction was found between soil moisturelevels and soil bulk densities.

Since soil bulk density was the primary variable in thisinvestigation, f1 may have been expected to be mainlyresponsible for the observed results. As has been pointedout, tortuosity reached a minimum near a bulk density of1.3 g/cm3 at each moisture level for each soil investigated.However, the maximum rate of Zn diffusion did not alwaysoccur at 1.3 g/cm3. Therefore, the interaction factor, <£,(equation 1) must be responsible for the differences.

Values of <f> calculated for each soil, soil moisture andbulk density combination are shown in Table 3. There wasa wide variation between soils and between bulk densitieswithin soils. The degree of interaction tended to decrease(i.e. increased <f> value) as bulk density was increasedfrom 1.1 to 1.5 g/cm3. On further increasing soil bulkdensity to 1.6, the degree of Zn interaction increasedsharply at all moisture levels.

At 10% soil moisture (Fig. 2), DeiZn) reached a maxi-mum near a bulk density of 1.3 g/cm3 for the Cincinnati,Zanesville, and Sidell (0-20 cm) soils; and near 1.5 g/cm3

for the Sidell (20-40 cm) and Fincastle soils. The differ-

Table 2—Analysis of variance of Zn diffusion coefficients atvarious soil bulk densities and moisture levels

Soil

CincinnatiZanesvilleSidell (0-20 cm)Sidell (20-40 cm)Fincastle

Moisture

811.3829.5330.5268.4659.4

Bulk density

1, 563. 71,105.3

124.7239. 9372.3

Moisture x bulk density

323.7304.463.810.781.7

10

"e(Zn)

10

10

10

CincinnatiZanesville

1.2 1.3 1.4Bulk Density (g/cc)

1.5 1.6

Fig. 4—Influence of soil bulk density on the rate of Zn diffu-sion (log scale) at 30% moisture.

ence between these two groups of soils may be related tothe level of Zn in solution. Apparently a considerably lowersoluble Zn concentration in the Sidell (20-40 cm) andFincastle soils (Table 1), reduced the degree of interactionas compared to the other three soils. With increasing soilbulk density and volumetric moisture the degree of inter-action became even less (Table 3) and was sufficient tooffset the increase in tortuosity such that the maximumZ)e(Zn) values were obtained near 1.5 g/cm3. With thehigher soluble Zn concentration in the Cincinnati, Zanes-ville, and Sidell (0-20 cm) soils, changes in <f> were similarto the changes in fv

With a 20% soil moisture content (Fig. 3) the maxi-mum £>e(zn) values were obtained near a soil bulk densityof 1.5 g/cm3 for all five soils. As a result of increased con-tinuity of the liquid phase at this moisture level the rate

Table 3—Influence of soil bulk density on the degree of inter-action of Zn with the soil for five soils at three moisture levels

Soil

Cincinnati

Zanesville

Sidell (0-20 cm)

Sidell (20-40 cm)

Fincastle

Bulkdensityg/cm3

1. 11.31. 51.61. 11.31.51.61. 11.31. 51.61. 11.31.51.61. 11.31. 51.6

110

5.9521.0419.670.418. 71

20.7411.910.120.0060.0630.0800.0010.950.90

17.561.880.0820. 21

13.97

£ moisture (w/w)20

_ p x 102 ——0.961.898.020.260. 810.542. 170.210.0030.0130.0230.0040.230.180.710.430.0450.0531.0520.018

30

0.770.563.310.441.050.792.170.210.0040.0160.0240.0040.310.200.680.340.390.300.700.01

* All values are significant at the 1% level. * Average of six observations.

46 SOIL SCI. SOC. AMER. PROC., VOL. 36, 1972

of Zn diffusion was significantly higher at all soil bulkdensities. With the increased moisture, the degree of inter-action was reduced sufficiently on increasing bulk densityfrom 1.3 to 1.5 g/cm3 that it offset the increase in tortu-osity and fairly constant £>e(Zn) values were observed forCincinnati, Zanesville, and Sidell (0-20 cm) soils. For theSidell (20-40 cm) and Fincastle soils the decrease in thedegree of interaction more than offset the increase in tor-tuosity resulting in a significant increase in De(Zn) at 1.5g/cm3 over that observed at 1.3 g/cm3.

The influence of increasing soil bulk density was ofmuch less importance in determining the rate of Zn diffu-sion at 30% moisture (Fig. 4). The value of De(Zn) wasalready quite high at 1.1 g/cm3 and increased only slightlyin each soil as the bulk density was increased to 1.3 g/cm3.As the soil was compacted further, tortuosity acted todecrease the value of £>e(Zn). However, at this moisturecontent, the decrease in the degree of Zn interaction withcompaction from 1.3 to 1.5 g/cm3 more than offset theinfluence of tortuosity, and maximum rates of Zn diffusionwere observed near a soil bulk density of 1.5 g/cm3.

When the soil bulk density was increased from 1.5 to1.6 g/cm3 the rate of Zn diffusion decreased sharply atall moisture levels. With the change in soil bulk densityin this range, both <j> and /t acted to reduce the rate of Zndiffusion.

The results obtained in this research make it question-able whether one can use adsorption isotherms to calculatea value of De as suggested by Nye. According to Nye(1968) the effective Zn diffusion coefficient as determinedin this paper should be related to the adsorption isothermby the expression:

^e(Zn) = £>Zn A dCJdC [3]

where Cl is the solution Zn concentration (,«,g/cm3 soil)and C is the labile Zn concentration (jug/cm3 soil); dC^/dCis related to the slope of the adsorption isotherm AC/AC;and the other terms have been defined. A comparison ofequations [1] and [3] indicates that the interaction factor,<j>, should equal the slope of the sorption isotherm AC]/AC.Adsorption isotherms were calculated for each soil bulkdensity for the Zanesville and two Sidell soils, assuming asoil moisture of 30% (w/w) and that the Zn concentrationin solution did not change appreciably with changing bulkdensity. (Data used for these calculations will be publishedin a subsequent paper by the authors.) With increasing bulkdensity both the solution Zn concentration/cm3 of soil aswell as the exchangeable Zn concentration increased by thesame proportion. Hence, the slope of the adsorption iso-therms remained constant as the soil bulk density wasincreased. The average values of AC/AC for the four bulkdensities were 0.132, 0.080, and 0.027 for the Zanesville,Sidell (0-20 cm), and Sidell (20-40 cm) soils, respectively.The interaction factor, <£, increased on the average withbulk density up to 1.5 g/cm3 (Table 3) and the <j> values at30% moisture were lower than the ACj/AC values byfactors of about 10', 102, and 101 for the Zanesville, Sidell(0-20 cm), and Sidell (20-40 cm) soils, respectively. In

determining the AC/AC values, Zn concentration in solu-tion was assumed to remain constant with increasing bulkdensity. If Zn concentration in solution decreased, the valueof ACj/AC would decrease and this may account for someof the difference between the <f> and AC/AC values.

The decrease in </> as bulk density was increased from1.1 to 1.5 g/cm3, while presumably AC,/AC remainedconstant, indicates that more may be involved in the inter-action factor than just ACjAC. Since the volumetric mois-ture increased as the soil bulk density was increased, themobility of the Zn in solution probably increased (VanSchaik et al., 1966) along with the mobility of the water(Kemper, Maasland, and Porter, 1964; Phillips andBrown, 1968). The change in the mobility or viscosity ofthe water was considered in determination of fv Since ananion, Cl, was used in determining flt the change in mobilityof Zn in solution was not necessarily accounted for by fvThus, any differences in Zn mobility as compared withCl would be included in </>.

In the field some initial compaction of the soil mayincrease the rate of Zn diffusion toward the plant root, butexcessive compaction will impede the supply of Zn to theroot by diffusion. As roots grow through the soil theytend to increase the bulk density of the soil immediatelysurrounding them. This increase in the soil bulk densityaround the roots may increase the rate of ion movementto the root for ions, such as Zn, which are supplied pri-marily by diffusion.