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Simulation of behavior of fertilizermaterials in soilEitaro Miwa aa Agriculture, Forestry and Fisheries Research Council , Ministry ofAgriculture, Forestry and Fisheries , Tokyo , 100 , JapanPublished online: 29 Mar 2012.

To cite this article: Eitaro Miwa (1980) Simulation of behavior of fertilizer materials in soil, SoilScience and Plant Nutrition, 26:3, 331-342, DOI: 10.1080/00380768.1980.10431218

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Soil Sci. Plant Nutr., 26 (3), 331-342, 1980

SIMULATION OF BEHAVIOR OF FERTILIZER MATERIALS IN SOIL

II. On Potassium Release from Slowly Soluble Potassium Silicates in Soil Column

Eitaro MIWA

Agriculture, Forestry and Fisheries Research Council, Ministry of Agriculture, Forestry and Fisheries, Tokyo, JOO Japan

Received July 30, 1979

As a trial of the quantitative evaluation of the availability of slow-release fertilizer, the dissolution and transport of K from slowly soluble potassium silicates (KSi) in soil columns were investigated by the simulation. The model of tri-ionic exchange chromatography was improved to include the source term of KSi. The column leaching experiments were carried out using K20·SSiOa (KSiS) and K20·6SiOa (KSi6). The results were compared with the computed ones. In the experiments, K+ released from these slowly soluble KSi accumulated in the exchanger phase of the soil at the layer of placement and the next 2 cm layer, while NH, + from NH,CI moved downwar9 to give broader distribution. These characteristic dis­tributions owing to the dissolution rate of the materials were reproduced well by the simu­lation of the each experiment. The effect of granule or particle size on the K dissolution from KSi was investigated by the simulation of the column leaching under the water flow of 30 mm/day and at 25°C. The abilities of KSiS and KSi6 to supply plenty of K, estimated by total K dissolved during 80 days in the soil (T sk), decreased with increasing granule or particle sizes of each material. The pattern of K release during a long term, estimated by the rate of decrease in the amount of K dissolved in each successive period of 10days (OrlO), decreased with increasing sizes. Tsk and DrlO were related to "Generalized Solubility Variable (GSV)" which was given by kCsSo (product of rate coefficient, k; solubility, Cs ; and initial total surface of the granules or particles, So). It was indicated that the desirable K released from KSi may be obtained by selecting the value of GSV within a certain limit. Additional Index Words: slow-release potassium, ion transport, cation exchange, potassium silicate.

In advanced fertilizer technology, slow-release fertilizers have been one of the main research targets. The availability of such fertilizer materials depend highly on their dissolution characteristics connected with the behavior of the nutrients released in the soil. The efforts to evaluate the availability from their dissolution character­istics have been made by routine methods like soil incubation test. However, the evaluation obtained by such methods is related only qualitatively with their avail,. ability, and rather useful in studying the comparative availability of a subject material with the others. The quantitative evaluation of the availability based on the disso-

331

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332 E. MIWA

lution characteristics in connection with the physico-chemical and biological prop­erties of the soil is required to estimate the usefulness of slow-release fertilizers.

The first trial was carried out on the dissolution and transport of K + from slowly soluble potassium silicates (KSi). Using K as an index nutrient made such trial readily approachable because of, i) the small biological effects, ii) the small involvement of redox reaction, and iii) few chance of reprecipitation. These permit to put the trans­formation of K out of consideration and make it reasonable to use the simple transport models of convective-dispersive flow for the theoretical investigation of its behavior. In this paper, the model of tri-ionic exchange chromatography proposed in a previous paper was improved to include the source term of KSi (1). Leaching of K + and NH" +

was investigated in the column previously saturated with Ca2 + and KSi was placed with NH"CI at a definite layer of the column. The experimental processes were simulated using the model and the results were compared with the experimental ones.

MATERIALS AND METHODS

Potassium silicates, K20· 5Si02(KSi5) and K20·6Si02(KSi6) were prepared by fusing the stoichiometric mixture of K2COa and Si02 at 1,200°C. Each glassy material was melted and sphered into bead-like granules of 1-4 nun in diameter at the time of cooling. A number of KSi granules of each selected diameter were immersed in 200 ml of water. The rate of dissolution was determined by the periodical analysis of the concentration of K and Si in the supernatant solution. The determination was made at the constant temperature of 10, 20, and 30°C.

The column leaching experiments were carried out using Arakawa clay-loam similar to the ones described in the previous paper (1), except that a number of KSi granules of a selected diameter were placed instead of KCl. KSi granules were put in the nylon net and removed from the soil after leaching, before the soil column was sectioned for analysis. The determination of Si was made by the colorimetric method by YOLK and WEINTRAUB (2). The other materials were determined by the methods described in the previous paper (1).

DESCRIPTION OF SIMULATION MODEL

The transport equation including the source term is

(1)

The last term was added as the source term to Eq. (1) of the previous paper. Q rep­resents the amount of material which is released from the source. The other symbols are common with the previous paper (1). The next Nernst-type equation is applicable to express the source term.

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where

Potassium Release from Potassium Silicates

aQ -=kS(C.-C) at

S = total surface of the granules or particles of the source, C. = saturated concentration of the source material, k = kinetic constant.

333

(2)

HIXSON and CROWELL reviewed the theoretical background of Eq. (2) with its integra­tion under various assumptions (3). The "cube root law" derived by the integration of Eq. (2) was verified experimentally by the dissolution of naphthalene in alcohol, CuS04 '5H20 in water, NaCi in water (4). MIWA and KURIHARA applied the "cube root law" to the dissolution of K from KSi and potassium polyphosphate granules in aqueous solutions (5). MILLINGTON and POWRIE calculated the dissolution of gypsum in the soil with particular attention to the effect of granule size in controlling the movement of sulphur using the equation similar to Eq. (I). In the paper they calculated the movement of sulphur by the model proposed by Day and Forsythe on the hydrodynamic flow of the ions which are not contrained by chemical forces (6). GLAS et al. constructed the model of dissolution and transport of gypsum in soils using the same equation but introducing F(m), a function of the mass of gypsum, m; instead of S because of the change in the shape of gypsum particles during disso­lution (7). In their model, the exchange complex was assumed to be saturated with Ca2

+ through the period of experiments and the precipitation-dissolution reaction of gypsum was taken as the dominant factor of the transport process (7).

On the dissolution of nutrient cations from fertilizer materials and their transport through the soil whose exchanger phase is usually occupied by the other cations, the exchange-type absorption and desorption of K + play a dominant role. For the in­vestigation of K + dissolution and transport from KSi in a soil column, the model of tri-ionic exchange chromatography was used with introduction of source term as described below. The explanation of the symbols was omitted since it is common with that described in the previous paper (1).

Initial values on KSi granules were given by the following equations.

VOLU = TWHT/DENK/PNUM

UDIA = 2.0*(3.0*VOLU/4.0/3. 14)**(1.0/3.0)

SUFU = 3.14* UDIA**2.0

TSUF=PNUM*SUFU

VOLU = mean volume of a KSi granule, mm3

TWHT=total weight of KSi added, mg DENK = density of KSi mg/mm3

(3)

(4)

(5)

(6)

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334 E. MIWA

PNUM = number of KSi granules UDIA=mean diameter of a KSi granule, mm SUFU = mean surface of a KSi granule, mm2

TSUF = total surface of KSi granules, mm2 •

Dissolution of KSi proceeds at the MFth layer. The rate of dissolution is com­puted by the next statement based on Eq. (2).

ZK=FF*TSUF*(SATK-CONK(MF» (7)

where

ZK = rate of K dissolution, FF=k, SATK=Cs .

With the addition of the rate of K dissolution, the net flow of K per unit time at MFth layer, TNFL(MF) is given by

TNFL(MF)=FLOW(MF -l)-FLOW(MF)+ZK.

The rate of change in the mass of undissolved KSi is,

where

DTWT = - ZK/CTIK

DTWT = rate of change in the weight of undissolved KSi granules, CTIK=K content of KSi, gig.

(8)

(9)

The rate of changes in volume, VOLU, and surface, SUFU, TSUF are computed by the similar process as shown by Eqs. (3)-(6). These computation of the changing rates are programmed at Al in the flow diagram given in Fig. 2 of the previous paper (1).

RESULTS AND DISCUSSION

As shown by MIWA and KURIHARA (5), the values of kC., the product of two constants in Eq. (2), is obtainable from the linear relationship between time and the amount of dissolved K per unit surface of KSi granules during the initial short time of dissolution. As the preliminary experiments indicated that the effect of agitation was quite small on the rate of K dissolution from KSi, the experimental measurement of kC. was made without agitation. Figure I shows the dissolution of K and Si from KSi, at lOoC. The dissolution at 20 and 30°C were similar in the linear increase of dissolved amounts and in the K dissolution overwhelming Si. K dissolution over­whelming Si suggests that the reaction,

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Potassium Release from Potassium Silicates 335

A) K Si 5 0.06 B) K Si 6

0.05

I-Z ::J 0.04 a: 0.3 w Q.

~

fa 0.03

~ 0.2

I/) 0.02 a l1.. 0 I- 0.01 Z Si a Si ~ «

10 20 30 10 20 30

TIME. days

Fig. 1. Dissolution of K and Si from potassium silicates at lQ'e.

(10)

is dominant compared with,

(11) and

pK=9.8. (12)

In the previous paper, KSi was assumed to be miscible with water (5). This assump­tion was based on the observation that the powdery KSi dissolved completely in a small quantity of water. This might be due to the high concentration of KOH which was kept in a small volume of solution, because the dissolution of Si02 proceeds at such high pH following Eqs. (II) and (12). When solution volume is large as in the experiments, however, K+ and OH- are quickly diluted by the diffusion to the bulk solution and the dissolution of Si by Eqs. (II) and (12) will be limited.

The high linearity of the dissolution curves in Fig. I suggests the little interference of resulted SiOI on the rate of K dissolution, as well as the validity of the method to estimate the kC. value from the slope of the line. Table I summarizes the kC. values thus obtained. According to the above consideration C. was given by the solubility of KOH at each temperature (8). The values of k were obtained by dividing kC. by Ca. These are also given in Table 1. As is obvious from Table I, kC., C., and k are functions of temperature (T) and each value increased with T. Interpolation of

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336 E. MIWA

Table 1. Values of kCs,lJ C.,!) and kl ) on the dissolution of KSi in H 20.

Temperature ("C)

Material 10 20

kC. C. k kC. C. k

KSi5 5. 18 x 10-· 3.53 X 10-1 1. 46x 10-3 1. 93 X 10-3 3. 68x 10-1 5. 24x 10-3

KSi6 7.22 x 10-& 3.53 X 10-1 2.05 x 10-t 3. 22x 10-' 3. 68x 10-1 8.75 x 10-'

Temperature eC)

Material 30

kC. C. k

KSi5 2. 54x 10-3 3. 89x 10-1 6. 53x 10-3

KSi6 5. 14x lO-t 3. 89x 10-1 1. 32 X 10-3

1) mg/mm2/day, 2) mg/mm8, 8) mm/day.

Arrhenius plots of the values of k in Table I, gives the following k-T relationship for each KSi.

For KSi5,

k(T)=2.69 x 1013 xexp(-1.06x 104fT) 283°K::;:T:::;293°K (13)

k(T)=4.16 x exp( -1.96 x 103fT) 293°K::;:T~303°K (14)

For KSi6,

k(T)=6.0x 1014 x exp(-1.2 x 104fT) 283°K<T::;:293°K (15)

k(T) = 2.25 X 102 x exp( - 3.65 x 103fT) 293°K;;:;;T:::303°K. (16)

Similarly, linear interpolation of the data in Table I gives the C.-T relationship,

C.(T) = 1.8 x 1O-3T -0.1574. (17)

Table 2 summarizes the experimental conditions of column leaching with the parameters used in the computations. The other conditions on the soil properties and column size are the same as listed in Tables I and 2 of the previous paper (1). The mean temperature of the experimental period was 32°C. k(T) and C.(T) for each experiment were given by extrapolating the relationship of Eqs. (14), (16), or (17).

Figure 2 shows the experimental and computed distributions of cations through columns 1,2, 3, and 4. The experimental results show that K+ dissolved from slowly soluble KSi did not move from the layer of placement compared with NH" + which was placed by soluble NH"CI at the same time, but accumulated in or around the layer of KSi placement. The less transport of K + released from slowly soluble KSi indicates

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Potassium Release from Potassium Silicates 337

Table 2. Experimental conditions of column leaching.

Column number

2 3 4

Material KSi5 KSi5 KSi6 KSi6

CITK (g/g) O. 192 O. 192 O. 165 O. 165

DENK (mg/mml) 2.38 2.38 2.38 2.38

TWHT(mg) 201. 8 231. 8 247.5 243.0

PNVM 18 6 7 30

VOlA (mm) 2.06 3.10 3.01 I. 84

TSVF (mm2) 238.8 181. 6 199.7 320.4

FERK (mgK) 38.7 44.5 40.8 40.1

FERN (mgN) 50.0 50.0 50.0 50.0

PERD (days) 8.0 14.0 14.0 14.0

V (mml/mm2/day) 136.0 76.0 101. 0 109.0

K: NH: -N.mg K~ mg NH;-N.mg 1 345 1234567 12345

2 E 4

* u 6 8. l

• 10' J: 12

14 I- 16

18 KSi5 K SIS

Q. 20 PNUM = 18 PNU M = 6

22 lJJ 24

26 0 28

30 A) Colum n B) Column 2

z * Fertilinr placement c:::::J Experimental r:::::J Computed

::J 2 4 ._) * * ~ 6 8

::J 10 12

...J 14

0 16 18

U ~~ KSi 6 KSi 6

24 PNUM=7 PNUM=30 i 26 I 28 j 30

C) column 3 D) Column 4 Fig. 2. Cationic distribution of each column.

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338 E. MIWA

the usefulness of such sources when the leaching of K is a matter of concern in the aspects of plant nutrition or soil-water relationship. The computed dissolution and distribution of K fitted well with the experimental ones at columns 1 and 4 (Fig. 2, A and D). At columns 2 and 3 the accumulation of K was found at the layer next to the one where KSi was placed. This may be due to the experimental error induced by incomplete filling of the soil at the layer of fertilizer placement.

The computation using the presented model thus gave the characteristic distribu­tion of K released from KSi precisely. Contrary, broad distribution of NH, + was also displayed by the computation.

Quantitatively, however, there is a large discrepancy between the experimental and computed distributions of NH, + and Ca2+ as shown in Fig. 2. The discrepancy is larger in the columns of KSi6 (Fig. 2, C and D) than in the columns of KSi5 (Fig. 2, A and B). The computed ionic distribution of exchanger phase is determined by exchange equilibrium. Parameters FKM and FNM playa decisive part in it. In the above computation, FKM and FNM were given the same values as were used in the previous paper, FKM =900 mm3, and FNM =350 mm3 (1). These values, used in the computation of the ionic distribution in the case where KCI and NH,Cl were placed in the column, successfully reproduced the experimental distribution (1). In the leaching of KCl and NH,CI, K + and NH, + transported at almost the same rate and most of the computation of exchange equilibrium were made in K+-NH,+-Ca2+ tri-ionic system. The above values of FKM and FNM were therefore suitable to compute the tri-ionic exchange equilibrium in Arakawa soil used in the experiments. In the case of KSi and NH,Cl, however K + concentration at each layer was extremely low as compared with NH, + at any instant. Furthermore, at many layers exchange involved only NH, + and Ca2 +, because of low rate of K+ dissolution from KSi. The computation of equilibrium composition at each layer thus is made in NH, +-Ca2+ di-ionic or NH, + -K + -Ca2+ tri-ionic exchange with quite low amount of K. The above discrepancy as to NH, + and Ca2 + distribution shows that the validity of FKM and FNM obtained in a certain tri-ionic composition is limited in the use for di-ionic or tri-ionic exchange of extremely different composition even at the same soil. The theoretical treatment of exchange in the model is based on the Donnan theory. These results suggest a limit of applicability of the Donnan theory, but the simplicity brought about by the use of it should be realized. Further investigation will be required on this point.

As were shown by the previous agronomic experiments on the availability of KSi and other slow-release sources of K, the granule sizes of the materials gave the clear effects on the K release and availability to crops (9, 10). To investigate the effect of granule or particle size on the dissolution and distribution of K from KSi in the soil column, a number of simulations were carried out under different conditions. Table 3 gives the conditions of simulated experiments with the parameters.

Figure 3 shows the distributions of K after to and 80 days at each column. The effect of granule size is clear for each material. At column 5, where 160 small gran-

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Potassium Release from Potassium Silicates

Table 3. Conditions of simulated column leaching.

Column number

5 6 7 8

Material KSi5

TWHT (mg) 216.0

FERK (mg K) 41. 5

PNUM 160 20 6 2,000

UOIA (mm) 1.0 2.0 3.0 0.46

V (mm8jmm'jday) 30.0

T"K

2 4 6 8

10

5 10 15

.. ] . 12 r' 14 rJ PNUM=160

~ 16 r UCIA= 1 mm

,18 COL U M N 5 ::I:

K, mg 5

.. .............. , •• r .... J

r .... ·J r'-

) : PNUM= 20 UDlA= 2 mm

COLUMN 6

298.0

00""""') • ............. i roo-"-"

J

PNUM = 6 UCIA= 3 mm

COLUMN 7

I­a.. UJ C

A) K Si 5, k=5.79xl0-3 mm/day

Z ;::[ :J ...J o U

2 4 .......... ] *' 6 r·····

,g J""" 12 -14 PNUM= 2000 16 UCIA=O.46mm

··········1 • roo···"--_·'

.j

PNUM =152 UCIA=I.lmm

PNUM= 24 UCIA= 2mm

9

KSi6

251. 0

41. 4

152

1. 1

18 COlUM N 8 COLUMN 9 COLUMN 10

B) K SiS, k=1.08xI0-3 mm/day

* Feortilizer plaCE'ment

D afhH 10 days

C::J af ter 80 days

Fig. 3. Computed distribution of K from potassium silicates of different sizes.

339

10

24

2.0

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340 E. MIWA

ules (diameter, 1 mm) were placed, all of the added K (41.5 mg) was dissolved during 80 days of simulation and detectable K front was found at the depth of 16-18 cm in the column. However, at column 7, where 6 granules (diameter, 3 mm) of the same material were placed, 24.3 mg of K was dissolved and distributed within 6 cm below the placed layer. The larger is the granule size, the more suppressed the dissolution and transport is (Fig. 3, A). The similar effect of the size is observed for KSi6 of which K dissolution is slower (Fig. 3, B). Thus, application of slow-release K sources in larger granules was shown to be effective also in preventing the leaching of released K. Figure 4 gives the amount of K dissolved at each column for each period of 10 days. At column 5, where KSi5 was placed in relatively soluble size, the largest amount of K was dissolved during the first 10 days, and the amount decreased gradually with time to the lowest one found in the last 10 days. The rate of decrease is lower at the columns, where KSi were added with less soluble material or size, namely, KSi6 < KSi5, small number of large granules < large number of small particles. The relationship between mean diameter of a granule or particle (d= VDIA) and total K dissolved during 80 days (Tsk) was obtained by regression.

For KSi5, Tsk = 57.53 -16.04d2/3, r= -0.9997,

for KSi6, Tsk=41.50-21.11d2/3, r= -0.973.

01 A) KSi5 E ci 15 * Tsk=31.8 mg lJ.I Tsk= 41.6mg

> 10 ..J 0 5 C/) C/)

I II m IV V VI VBVII I D m IV V VlVlIVIII C

COL U M N 5 CO L U M N 6

~

u. B) KSi6 0

~ 15

t : T".16.2mg I ~ ~.: o 10 ~ 4: 5

I D m IV VVIVDVID InmlVVVIVDWI

COlUM N 8 COLUMN 9

P E R 0

Tsk=24.3 mg

I II lIlV V VI VDVII COLUMN 7

I w...,m

g

,

I II II IV V VI VII VIII

COLUMN 10

0 I 0-10 D 10-20 m 20-30 IV 30-40 V 40-50 VI 50-60 VII 60-70 vm 70-80 days

Fig. 4. K dissolved at each simulated soil column for successive periods of 10 days. • Tsk: total amount of dissolved K during 80 days.

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Potassium Release from Potassium Silicates 341

Though these equations give the brief concept of the effect of granule or particle size, the dissolution pattern as shown in Fig. 4 may be related to a more general term. The dissolution of K in a certain time will increase with the total surface (S), solu­bility (Cs), and the rate coefficient of dissolution (k). The only value obtainable with the total surface of K source is the one at the initiation of the experiment (So). The product, kCsSo was thus selected as "Generalized Solubility Variable (GSV)." The rate of decrease in the amount of K dissolved in each successive period of 10 days, Dr10, was obtained by the slope of the stairs depicted in Fig. 4. DrlO and Tsk of each column plotted against kCsSo are shown in Fig. 5. The regressions of the plots give the next second degree relationships between kCsSo and Tsk or D rIO •

Tsk = -32.27(kCsSo)2+ 72.24kCsSo+ l.l529, R2=0.999

D r10 = 0.5707(kCsSO)2 + 0.5562kCsSo - 0.06416, R 2 = 0.999

It should be noted that the K dissolution (Tsk) and its pattern (Dr10) are satisfactorily expressed in the functions of the general term, kCsSo, no matter which of KSi5 or KSi6 is the K source. By selecting the value of kCsSo we may obtain the desirable K release from KSi. In many agronomic experiences including our previous experiments, the constant K releases through long terms were obtainable only with lower amounts of K supply sometimes deficient for complete growth of the crops in the earlier periods (9, 10). The ability of the fertilizer material to supply plenty of K in a constant manner through a long term has been always desired.

Figure 5, however, indicates the impossibility of meeting two requirements of plenty supply of K (large Tsk) and its constant release through the long term (small

z'" 0>­_0 .... "'0

o

:3 0 0.5 0-Vl­VlCl a E

1.0

~ 1.5 a:~ u W 0

o ~

~~ 2.0 W

~ a:

0.1 0.2 0.3 0.4 0.5 0.6 0.7 08 0.9 to 1.1

kCsSo mg/day

01 E

40 ":¥ '" ....

35 ';i; > oC(

30 0 o CD

25 (!) Z a:

20 :J o o

15 W ~ o

10 ~ a lC

~ o ....

Fig. S. K dissolution (Tsk) and its pattern (Dr l0) related to kCsSo.

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342 E. MIWA

Dr10) at the same time by any selection of the solubility and granule or particle size of KSi. This is an important point when we try the control of the availability of slowly soluble materials by the granule size selection. The validity of kCsSo as GSV will be extended over the materials which have smooth surfaces as KSi.

Acknowledgements. The author expresses the will of thanks to Dr. S. Iwata, Dr. K. Kurihara, and Dr. F. Yamazoe for useful discussion and review of the manuscript, The help of Computing Center for Research in Agriculture, Forestry and Fishery is greatly appreciated. The paper makes a part of Ph. D. Thesis of the author which was submitted to Tokyo University.

REFERENCES

1) MIWA, E., Simulation of behavior of fertilizer materials in soil. I. Model of tri-component ex­change chromatographic transport, Soil Sci. Plant Nutr .. 26, 175-184 (1980)

2) VOLK, R.J. and WEINTRAUB, R.L., Microdetermination of silicon in plants, Anal. Chern., 30, 1011-1014 (1958)

3) HIXSON, A.W. and CROWELL, J.H., Dependence of reaction velocity upon surface and agitation. I. Theoretical consideration, Ind. Eng. Chern., 23, 923-931 (1931)

4) HIXSON, A.W. and CROWELL, J.H., Dependence of reaction velocity upon surface and agitation. II. Experimental procedure in study of surface, ibid., 23, 1002-1009 (1931)

5) MIWA, E. and KURIHARA, K., Numerical evaluation of granljle size effect on dissolution rate of potassium silicates and potassium polyphosphate in aqueous solutions, Soil Sci. Soc. Am. J., 41, 637-640 (1977)

6) MILLINGTON, R.J. and POWRIE, J.K., Dissolution and leaching of fertilizer granules, 9th Int. Congr. Soil Sci. Trans. (Adalaide. Austr.), 3, 385-391 (1968)

7) GLAS, T.K., KLUTE, A., and MCWHORTER, D.B., Dissolution and transport of gypsum in soils. I. Theory, Soil Sci. Soc. Am. J., 43, 265-268 (1979)

8) Japan Chemical Society, Handbook of Chemistry: Basic Part I (1966) 9) MIWA, E. and KURIHARA, K., Studies on controlled potassium fertilizers. I. Relative effectiveness

of various hardly soluble potassium compounds as source of slow-release, Soil Sci. Plant Nutr.,

20,403-411 (1974) 10) MIWA, E. and KURIHARA, K., Studies on controlled potassium fertilizers. II. Evaluation of

potassium silicates as slow-release sources of potassium, ibid., 24, 103-111 (1978)

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