J. Jpn. Soc. Soil Phys.
lm)¢£
No. 32, p. -+* ,**.

 *ῌ**ῌ**ῌ

**Latent Heat Transfer in a Salt-a#ected Nonswelling Clay
Iwao SAKAGUCHI*, Hidetoshi MOCHIZUKI**, Mitsuhiro INOUE** and Shinobu INANAGA*** The United Graduate School of Agricultural Sciences, Iwate University** Arid Land Research Center, Tottori University, +-3* Hamasaka, Tottori 02*ῌ***+, JapanAbstract
Latent heat transfer (LHT) with phase-change from liquid to gas occurs, when there is atemperature gradient in the porous media. LHT is a characteristic of porous media like soils, butthere are few studies on the relationship between LHT and solutes. Although Philip and de Vries
model was often used to analyze LHT, solutes have never been taken into consideration in themodel. In this study, LHT was analyzed theoretically and experimentally with an assumption thatthe e#ects of temperature and salt concentration on thermal conductivity are caused by LHT.
Thermal conductivities of Kaolin were measured under several conditions of water content, NaCl
concentration and temperature.

The LHT component of thermal conductivity was separated

from the apparent one according to its temperature dependence, and analyzed by the extended
method of Hiraiwa and Kasubuchi to estimate the phenomenological coe$cient which contains
tortuosity factor.
As a result, the phenomenological coe$cient never exceeded unity even at the maximum. The
coe$cient was expected to show a constant value under the ﬁxed water content. However, it
decreased with NaCl concentration. Further research is required on the tortuosity factor andmodiﬁcation of Philip and de Vries model, or introduction of other coe$cients into the model todeal with solutes.
Key words : latent heat transfer, salt-a#ected nonswelling clay, thermal conductivity, watervapor di#usion, phenomenological coe$cient+      ῌ  !"#$et al., +3/, ; Jackson et al., +30/u$lmvEFGH(w#xyΐ>zghpq {|&N[JK_Y#$ 3v! >QRgh}~%&% '()*+,-./012 34'.

f9Z[_rs$ TK lmv>QR5῎6#789"#$ ῐ:; <=>.?@ABC*D . %_Y#Rv>QR ((EFGH9IJK LEM&NOEMP>QR

._%sf!"#$ s T

9ST#12!"#$ <=> LEM!QU4'.

FZR+Z!"#tPenman,VW&NXY >QRZ[#$ >QR OEM!\]+3.* ; Rollins et al., +3/.u$ 6[ Tf l'.^%_ <=>Z[#$ 3` >abcdefmv>QRgh. lmv>QRZlm

OYLEMP<=>9gh6#$ T'iDZ

(|Z%_ %_Y#$ Philip and[#>jk lm(nY_opqJK_rs tGurr

de Vries t+3/1u  l῍( ¡JKs<=> t<* ¤¥¦§¦§¨ῑ2©§pqª** «¬¦§­®¯pq°c±² ³02*ῌ***+ «¬´µ +-3*: >QR4' ¶῏.·:s¸¹º£»l ' >QR ῒ¼E>4Z ¨ 32 ¼ ,**.4  y"4@K[\" Ve  Philip and de Vries Hiraiwa and Kasubuchi ,*** "%5 /    !" " *+)C 34 y" 6#$%&'( #)*+ ,!'( #$ '

-. / $ 01%& 234  ' !5-6 ,'( # )7 89 34 "

Jury andLetey +313 $ 01%& !5:;34!

,ῌ ῍

῎FGHIJ$D*+ deVries, +3/2
Js¡¢lc£T¤LJv¤CpT¢T*Jv¤CLT¢T*Jl<=> Philip and de Vries 89 3

ῌ

4? Cary @A4 Cary, +30/ B=5 Js $¥FGHIJ W m¢, lc $78

 )C 34 D Cass et al., +32.

U W m¢+ K¢+ T $

E < FGHIJ$ E

K L $ T J kg¢+ Jv $ FGHI

MNO+ 7,J kg m¢, s-+ Cp $ W J kg¢+ K¢+PQ K*+RS5SO TUT* $[¦ K CL $'(  J kg¢+ K¢+

7/ V$ RS5

Jl $'( FGHIJ kg m¢, s¢+ / ῌ/"$WXYZ [\" !] ^XYZD

9¨ + ©$ ¨ , ©$ T' ¨ -7_` a©$K7 6L

TU

/

[\""

7 v.

Cass et al., +32. ; bO +332
Hiraiwa and Kasubuchi ,*** $ E

XYZSOTU c 
TU d !5 FGHIJ!<=
T? )C 34 Ve$fg4/h ij7E>jki 7,PQlmª'Dª'$:« ¬*"N ¨ - ©

$;­® c '( #;­®¯°¬*"±² ¨ . ©$;­® ³  <Js¡¢lc£T¤LJv¡¢lc¤lv£T¡¢l£T

῍"," ,! E lv $TU W m¢+ K¢+ l $R"," x!opqrsS5 W m¢+ K¢+ / .  nHIopqrsi$t
u vwt

ª' ¨ . ©$'(§i y" $z+ "," v" bO +332 $u #{ <$|}%~$ WXYZSOTU%~ < h "¢lv£T¡LJv

῎TU%~$ u #{ <E6 ´µ "d FGHIJ$  D*&%~+</"  u

+33+ $ K [\" *+ 

# <T'$

(*+ ")ZJv¡¢Da£r

῏/ * " V Dh Da $d %&34 m, s¢+ r $$ +, -/ kg m¢- / ῏ !" $T'V E !<=WXYZD*_`/ O+ " ST'Eu g3t $," c E
T'

v.

/"O+"

 Philip and de Vries $ Eu t"," V0$ E!
<=u 1XYZD7_`$TU /] VTU$ TE FGHIJ?D*+h 23 T'¶=/7  < Penman, +3.* ; Rollins et al., +3/.
Jv¡¢taDa£rῐ t $:;34 a $> m- m¢- /
lJF·¸F¹Iº¸ Philip and de Vries, +3/1 $«$ +»"N;­®r $ 8 ¢-r* kg m  >jk hr ?D*+ ῑr¡r*hrhr opqrs yw m g3$ ῑ

D*+J : m/0sL)(bc&: 8¼K5Mgyw
hrexp RT ῏ M    *.*+2 kg mol +  g  3.2+ m s ,  R  2.-+ J mol + K +  yw   ym m yom$%& '(!"#)*+ywym,yoῐ

῎ ῏ ῐ )-./)0 MgymMgyo
rr* exp RT exp RT 
Nassar and Horton +331 $2$3 ῍ )0 ῌ )1ῑ
ῑῌ+1 r 0 T, ym, yo

Fig. +% 456 h ῍|}T2c

Soil water retention curve of Kaolin foreach temperature ﬁtted with Eq. (+,).

)1 789:;< =6 ; Philip andde Vries, +3/1 $>?6 bhta Jury and Letey,z{D)(bc&|}~0%L |}+313 0 %& @3$'( )A .+0Q$%L
Fig. + 1 |} T2c 0%L ]BrBr Bym
Br ByolvhtaLDa
BT , Bym BT , Byo BT 
BrBr Bym
Br Byo,,BTBym BT
Byo BT 

bLDa
 H31j4%L5678)ΐῒ]4 WP. Decagon  09P& H1yP&nL :  1 Campbell +31.

)

W q 0W; w kg kg + 14EsL /ῑ ῒΐ )-./)0 )09PLw bymya
wsatMgywdr*lvbLDa exp RT  dT,,Byo
r*MgBym,T yw
BT RT,  BT
Byo
r*MgBym,RT  BTBT ῕ῒ ya   m  wsat +W῔ῒ; D  bkg kg +!" ya 0 9:$%L
m/1 _PA<D NaCl 09PL SL῔ ) lvῒ)$CD3$AE

 >

v

1?P!(3$A ¡¢ FG Abdullaev et al., +332 ; Magome--ῌ ῏῔῍ῐ῎ῒΐdov, +332 *+&P-ῌ, ῐ῎ῒΐ-ῌ+ ῏ ῔FG HI( 8J1!K1
3LM  N lc

NaCl =O*PQAT Decagon @c] KD,09P& )k8 D- £¤¥¦8 A§.

R SL TUVAO*P  !WX1,**- b ]%L ]: ¤¥¦ HB¨ ©

P&Y "Z#A[\ ]$?%XA^A_

ª +« '(_ ¬CY ,« d­nL Shio ]® HB¨A

Q$%&`S%PLM &0a'%L &1(zawa and Campbellbc$)(bcAA de*+f,g

,« 0DsDP!¯°E%& _ KD, 1!]±²hi- jA)k1l._ *.1m/0

1FGDP$rs.+ ³¤:1 ´

+33*

1!n&opAq$Ars.+LM FG

µH|:¶ 3· .0 mm, [* 0/ mm 09P HQ$%&tu%\DP 'v01Ss& wx-y

31j4%L¸¹3I1º4%L ] - »;  32  ,**.

6Table +ῌ+ ./01
Experimental conditionw kg kg+C mol kg+
T K.*+, .*/, .+*, .,*, .-*, ..**.*, *.+, *./, +.*, ,.*, -.*, ..*,12, ,22, ,32, -*2, -+-ῌ,456&Kwxyz789:;

Fig. ,

Thermal conductivity of Kaolin withmass basis water content.

 

ῌ-456&Kwxyz NaCl 9:; w*.+* kg kg+

Fig. -

Thermal conductivity of Kaolin foreach temperature with NaCl concentration at w!*.+* kg kg"+.

ῌ.

456&Kwxyz NaCl 9:; T,32 K

Fig. .

Thermal conductivity of Kaolin foreach mass basis water content with
NaCl concentration at T!,32 K.

--  w  NaCl  C mol kg+  !"# +.,* Mg m- $%&'()*+,  -./012 Table + *3 . .+Fig. , * 456& l 789:; 3  NaCl

*< l 278=>?*@ABCD  l 789:;EF2 NaCl G?HI JKLA M
456& NOP ,**- a *QRB STU2 VWL 3  XY2STU$Z!"#[\$] ^_Y] M`78= $2abcd l 2ef[ CDg2hi

Fig. - * w*.+* kg kg+ *K] l  NaCl 978=$efj \ῌa78=$2VWA XY2:;  b *3  Bb$ l 2 NaCl klLmn*oB Hiraiwa and Kasubu-CD*@\  abcdEf2efjLAchi ,*** EF Mp$A l 78 kqr

 C,.* mol kg+ l$ Q ]  OP ,**- a

NaClstuv*K]wxyzb{|EF }~+32-` .,NaCl 

MpEF[Y
Fig. . * ,32K *K] l  NaCl 9:;  k7Q*3

 w*.*/*.-* kg kg+ $2 NaCl¡¢ : £¤F:;¥¦§¨©ª<=>)*+

ῌ/l>)
mol kg6+BFig. / AC5*.*

ῌ0lv of Kaolin without NaCl for eachtemperature with mass basis water content.

Fig. 0lv of Kaolin for each temperature withNaCl concentration at w*.+* kg kg+.

ῌ1l LDaP qL AC5*.* mol kg6+BFig. 1

Calculated LDaP of Kaolin without NaClfor each temperature with mass basis
water content.

 ll>)
5*.+* kg kg6+B7

 NaCl  Aw

 Figs. ,, .   l NaCl  !"#$%& '()*+,-. 
/01 2!34 w5*.*/6*.-* kg kg6+ 789:;<=>)*+?#"$@;&1".-



NaCl Hiraiwa and Kasubuchi A,***B CDE

l%& lv FG  ,1- K HI l FJKL$  M
1NO l $JKL$.F
QRS71P lv $ ,12 K 7TU01 l FJKL$  #VWX2" lc VW[0#$$

7 lvlv VWYZ\] ^"_`[0#$ Ja" b de Vries cdeJafghijfklFm Tarnawski et al. A,***Bn opCD7 l %& lv FG " qr01
lv F

Fig. /   lvxyzF
1s"tuvLFwO_`MuvLv{|! #HiraiwaandKasubuchiA,***B

Tarnawski et al. A,***B $ }~  b F| LDaP AP῍  exp ῌ

F2B  C5*.* mol kg6+ "qLF Fig. 0  C5*.* mol kg6+  lv uvLF

 Fig. 1 7s" ##7 r* X2"VW w5*.+* kg kg6+  lv  NaCl F

Campbell A+32/B N ym  lv n l op NaCl Flv x

n & A,**- aB $op&1.. ῍ Fb VWx ῌ῍ ῌ῎ "Hῌ῍  b F|q ym LF ῌX2"VW7H  b

 yo Fqr2"

Lang A+301B N Fig. 1   LDaP7

%&¹ºc » 32 ¼ ,**.

8

῎ῌ2°±²³ LDaP ´µ NaCl >?abc
wD*.+* kg kgE+

Fig. 2

Calculated LDaP of Kaolin for eachtemperature with NaCl concentration atw῍*.+* kg kgῌ+.

῎ῌ+*°±²³·¸῎LU{abc
b of Kaolin for each NaCl concentration with mass basis water content.

Fig. +*

[ JK\]:S  CD*.* mol kgE+

 b :9 R^ Hiraiwa and Kasubuchi ,***:_` b  P?I : lv  NaCl >?abc d O>?QJK\]e?MN:;<$9 b  _ῌF CD*.*

mol kgE+ ![ :f NaCl >?GHg MN

h9 NaCl >?abc

 b D hta i b NaCl >?abc h  NaCl >?abc!j9:;<$9

i  Philip and de Vries klmn῍ op qrs#$9 d n῍ ;tu$ klmvw p klmxn῍56 yzU{| }<9~3 j9:;<$9 NaCl >?F89 b :ῌTU  Fig.
+* ῎ῌ3°±²³*+¶: LDaP ´µTU
wD*.+* kg kgE+

Fig. 3

Relationship between lv and calculated
LDaP of Kaolin at w῍*.+* kg kgῌ+.

 ῌIh9 b F lv Fig.

/  _`S

 lv Fig. /  ῌ

   b !"#$ %&'()*+,- %&./0123456789:;<$9i  ! b [ + f#2

D*.+* kg kgw

F89 LDaP  NaCl >?GHI

JKLMN OPQRS2

Fig. 2 wD*.+* kg kgE+ F89 lv : LDaP

TU  Fig. 3 

LDaP Fig. 1 Nd!j9 4:  !%  9: ;<$9 ! $
9%&f %9i#2
?U{ t h9:;<$9 %&'῍ A BC= NaCl >?@  ῌE+

#$  F  b [ + f29 $ lv Fig. / %&'()*+,-  b 8$9: ! VP?WXYZF)'U{!j9 IU{:)
Fa f t  #$9£

$i  %&¡¢9 tD*.00 ! a ¤¥34 %c ¦§¨? ©ª῏«ῌ¬­« ®Q 56 ¯;t#$   R d %&0 : 7 +y0,¶ -  h    !"#$%&'()* t +,- ./0123,6 !"#7< = -.>?*

De Vries, D.A. (+3/2) : Simultaneous transfer of heatand moisture in porous media. Trans. Amer.
Geophys. Union., -3 (/) : 3*3ῌ3+0.
Gurr, C.G., Marshall, T. J. and Hutton, J.T. (+3/,) :/    459Movement of water in soil due to a temperature

89 +:;@AB5gradient. Soil Sci., 1. : --/ῌ-./.

Jackson, R.D., Rose, D.A. and Penman, H.L. (+30/) :6 89 C1*=. DE

Circulation of water in soil under a temperature

FGHI JK+ .$L JKMN*3 OP Hiraiwa and Kasubuchi Q,***R +ST*3

gradient. Nature., +0 : -+.ῌ-+0.
Jury, W.A. and Letey, J., Jr. (+313) : Water vapor
movement in soil : reconciliation of theory andOUV WXYZ.[\] YZ^_experiment. Soil Sci. Soc. Am. J., .- (/) : 2,-ῌ2,1.

 `abc + +d0e f? !Hiraiwa, Y. and Kasubuchi, T. (,***) : Temperaturegh  ij*3 O dependence of thermal conductivity of soil overNaCl!"#$%&' ()*kl +,a wide range of temperature (/ῌ1/¡). European-m. 7 +/ 2 Philip and de Vries n

Journal of Soil Sci., /+ : ,++ῌ,+2.

opqrs mnop7 tu+vw

¢#£$ Q+32-R : 5¤¥ %¦& '§¥+x y0,-m. ,1C.\z3Lang, A.R.G. (+301) : Osmotic coe$cients and waterYZ?{6 |jb-] C Philip andde Vries nop+}* ~6

potentials of sodium solutions from * to .*¡.
Aust. J. Chem., ,* : ,*+1ῌ,*,-.

 b\3 m+s

Magomedov, U.B. (+332) : Thermal conductivity of0 YZ ?{6 |jbinary and multicomponent aqueous solutionsb\2b-]

b-3

of inorganic substances. High Temperature, -0 :..ῌ/*.

(¨©ªῌ«¬"# ,+  COE F: FQ!AR +3 * +"3­ῌ)®¯ Q+332R : *°±57 89 ¥ +² +32 : .+ῌ.0.

YZf YZ Q  +-.0*+*.R !

(¨©ªῌ³´ µῌ«¬ ­ Q,**- aR : ,¶ !"#,¶-5 ῌNaCl89¥ +² ,,/ : //ῌ0+.

(¨©ªῌ·´ ¸ῌ¹gº» Q,**- bR : 45L?.¼¥ 4/  3- : .1ῌ/*.

Abdullaev, K.M., El’darov, V.S. and Mustafaev, A.M.

Nassar, I.N. and Horton, R. (+331) : Heat, water, and(+332) : Thermal conductivity of aqueous solu-solute transfer in unsaturated porous media. I-tions of NaCl-CaCl, system. High Temperature,

Theory development and transport coe$cient-0 : -1/ῌ-12.

evaluation. Trans. in Porous Media., ,1 : +1ῌ-2.

Campbell, G.S. (+31.) : A simple method for determin-Penman, H.L. (+3.*) : Gas and vapor movements ining unsaturated conductivity from moisture

the soil. I-The di#usion of vapors throughretension data. Soil Sci., ++1 : -++ῌ-+..

porous solids. J, Agric. Sci., -* : .-1ῌ.0,.

Campbell, G.S. (+32/) : Soil Physics with BASIC,Elsevier, Amsterdam.
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