

J. Jpn. Soc. Soil Phys.

No. +*-, p. +*/ ++, ,**0

J.R. Philip and D.A. de Vries   *ῌ*
Reviewing classical studies in soil physics“Moisture Movement in Porous Materials under Temperature Gradients”
By J.R. Philip and D.A. de Vries
Transactions, American Geophysical Union, Vol. -2, No. ,, ,,,῍,-, (+3/1)
Masaru SAKAI* and Nobuo TORIDE*

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 [,2%U£¤¥¦C \],-.xlL§¨©1ª3.I«%& Philip {µ¶ : J. R. Philip and D. A. de Vries · w o{ ¸¹=¬&fΐῌ+He¨ !f" |},
©Fª~«z" , A C  B C
z " 2Philip and de Vries +3/1, Figure ,3

Fig. +

Water ﬂow through a liquid island. The
arrow indicates the ﬂow direction due tothe temperature gradient. Vapor condenses
on one side A and evaporates from theother side B. (Philip and de Vries +3/1,
Figure ,)

9^x

107

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 ,  !".ῌ+ ῒ῔ῐ῏ῑ#$%&'()*+, -./01 2CS,3 45678 2CH-COCH-3 9:!/;<=>?@AB
CD " EFG<=, %&HIJKIJLMΐῌ,

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2±Tῌ±z3a %²³ 2±Tῌ±z3 ´" 2c3 

®¢
h" ¯°, Philip and de Vries )*+" t°, Cass )*+"Fig. ,(a) Apparent available porosity for vapor
di#usion as a function of volumetricwater content (qK῍*.,). The solid line
represents the liquid island model and thedashed line is based on the conventional
theory. (b) Ratio of the temperature
gradient of air phase (῎T/῎z)a and thesoil average temperature gradient (῎T/῎z).
(c) The enhancement factor h for thethermal vapor transport. The solid line
and the dashed line represent the Philipand de Vries model and the Cass model,
respectively.

N9" Philip G, EO !/;<=PQ 
RSTU!E VW

XYZ[ @D \U!" ] ^H_I`ab\cdF!He)*+ !"
%&fg@hi H_jkl@m9_n o9^, H_,p +  O %qrst uv  wH
ex  ^$yz " p +@$yz S A

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dF!N:!" zN ῍ &I a
 af 2a3 q

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(h !" Philip G, f2a3 ¡¢ ^£b9!"

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f2a3¤ῌ῎aaῌ
K 2a¥aK3῍῏῎EEC aK ,H_jkl@miN ¦§ICD

108]®¯J, ° +*- ± ,**0ῌ-©ª`Zab>«¬$  DTvap ()DTliq !
ab>«¬$Dqvap ()Dqliq !
 ! ­ HIJK DTvap Fig. -

Thermal vapor (DTvap), thermal liquid water (DTliq), isothermal vapor (Dqvap), and isothermal liquidwater (Dqliq) di#usivities for a loam soil as a function of volumetric water content. The dashedline indicates DTvap based on the conventional theory.

   , aqK

qῐqK $&' aῑaK() *+, -.

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>LA4 (MNO>PQRSTU VW

qTvap%;<=>&q BC>DEFG$ HIJK

4jkl$ /mno p/ (/>q3

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E wxdhikl"6ryz${|  , b > Philip 1]}~ mnoPA?`Zabq"#$ /`Zab"NOA?>PYZ[ BC$QRSTU+.- X01 - X

cTῌcza > [x ! enhancement factor Pxhh%  hi> /`Zab>P@

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῎

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῍ cz ῏arww Z a ., 

f"gE?  ,  "NO>x4 ῌ \ /(/012$34"56  78 q9qK $&' a:aK.-  !"#$ qK%*.,

afaq cTῌczaaa
cTῌczῐ῎ , c h  ! h q !

 ,  h >Pkl"QRSTU- X01 1 XYZ[BC$

ῐ \"&  A?`Z
 HIJK> ῎

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ῐ \u`Zabq cTῌczaῌcTῌcz "A §¨Z /*ῒ YZ

ª« : J. R. Philip and D. A. de Vries  ¬}~­a/®¯°@ KL`±ῌ.
Fig. .

 B$n *.*1. *.+-. *.-+- [¡¢a/ / £q¦§ ST/N ¨[©¥N¤ ¥H Philip

109

 pH

Volumetric water content proﬁles for the initial water content of *.*1., *.+-., and *.-+- for aloam soil after / days. The solid lines and dashed line represent simulated results with the Philipand de Vries model and the conventional theory, respectively, and the plots are observed data.

 Philip+./ ,h  Cary +313    q  Tq K
:
DT
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;
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z  zz zh ! Cass et al. +32.   "#$00= DT:DTvap;DTliq, Dq:Dqvap;Dqliq =D/ %&'() *+,-./01

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2 q de Vries +3/2  ,BMKLh F , c GH=IJ Cass et al.

9 h  *+KLBM7NOPQ34
5/ Noborio et al., +330 ; Scanlon et al., ,**-
R( STUVWX YZ[\]^_`a
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=D// 
 E 
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0
KLE KLE4@k\7Nd\01= Philipn9 . , Z¹º » +*- ¼ ,**0

1100ῌ, ῒΐ῍῏!)* q h K h - van GenuchtenMualem WXY van Genuchten, +32* Z[1\!
qr=*.*+ qs=*..1, a=*.*1. cm]+ n=+.-3 Ks=--.1
cm day]+ l=+ ^_`" h  Philip (WXY qK=*.,aTῌazaῌaTῌaz=+.1-! b -ΐ ῏῔ ῏῕ cdefg`" DTvap, ῍ ῎ ῏DTliq, Dqvap, Dqliq &' hijb + kl Lmnopq'fg`" qr*.,/ Ostufg DTvap

vw- q῍*.,/ Ks 

xyfg DTliq

vw' z! Philip ( DTvap

 {s|} DTvap GD~ nopq'fg`" {s xyfg Dqliq~   qr*.*/Fs|  tufg Dqvap~ $%  >  aKῌaz=*

ῑ
-! ῐ

-UV!  T:; qi  :;Lm ,*6 Lm +*6,/6-! z! . tu xy *-!/! "#$%tu< HYDRUS-+D * Simunek et al., +332 
! U| B?1RJ>b .  OL. x=*- 8  -!

 / BAHI# $%#&' O
ῑῌ/

:;<
*.*1. *.+-. *.-+- )*|¸ / BALmnoGtu qTvap xy qTliq  noGtu qqvap xy qqliq H

Fig. /

Thermal vapor (qTvap), thermal liquid water(qTliq), isothermal vapor (qqvap), and isothermal
liquid water (qqliq) ﬂux proﬁles for the
initial water content of *.*1., *.+-., and*.-+- for a loam soil after / days.

 qi=*.*1.

OLMP
H   Gurr etal. +3/,  ῐῑ ῒ  !"#$%&'ῐ

KLMN(ST K qi=*.-+- -U qi =*.*1. *.+-.  ^_`" h U}G$% ¡¢£-! }

 Philip (WXY¤¥ KLMN(OLMP ¦1e I#
KLM §~¨© OLM §¦¨©' Philip (WXY } DTvap  . ª«m^_'b - $%I#Ge¬­'ῌ

 qi=*.+-.

ῒ GD  . ®῏-¯&'  1(°-e­' b /  / BA . ®&'OLMN(KLMP&0ῌ+ ῐ ῎- ±OLMP&' L

Gurr ( )*+,- ./-!01 +*mnoGOLMPST 7 ¡ 

cm 

2345. +*6 7-8.

noGD KLMP ST O,/6  9! :;<  qi=*.*1. *.+-. *.-+-

qi=*.*1.

2

D qTvap xy qTliq  fg`" DTliq> ?@A / B CDE- 

FGDHIJ-! qi=*.*1. *.+-.



KLMN(OLMP Q(R!  qi=*.-+STUNV!

 OLMPtu -²¦1!³´¦1 z!KLMP
xῌ0 cm  q῍*.*/¤µ¶R!s xy

-- qqliq x·0 cm F-!s  t¶· : J. R. Philip and D. A. de Vries ¸ ¹8JK~.XY§º»}3'.¢¼ qqvap

 xῌ0 cm   Dqliq  x0 cm    ` . / 0111

 789:'p78g.XY]^p@89:'p@8g 7Dqvap   ! x0 cm    lm .XY pq\789:'"#$%&' , ( qTvap  qqvap

rs8lm''tuvwxyz.h)*+ ,-./0 12 34' qi5*.+-.
6 qi5*.*1.  789:' ;<'=>  qTvap

? @89:'  AB/0 qqliq

C @


'Ir. . ('"#$%&{ _Jx|}z.
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+*- ¡ S,**0T_`a S+33+T : b DX pp. 23ῌ30 YZ[D\]^X$%&'()*+,-"./0.#+1 Philip

Nassar, I.N. and Horton, R. (+323) : Water transport in23 4567,-897#:;< =

unsaturated nonisothermal salty soil : II. theore->?<*@A B,- CD=EF

tical development. Soil Sci. Soc. Am. J., /- : +--*ῌ

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+--1.

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Noborio, K., McInnes, K. J. and Heilman, J.L. (+330) :ῌ ῐ ῏ ῍Two-dimensional model for water, heat, andCary, J.W. (+313) : Soil heat transducers and water

evaluation. Soil Sci. Soc. Am. J., 0* : +*+*ῌ+*,+.

vapor ﬂow. Soil Sci. Soc. Am. J., .- : 2-/ῌ2-3.

Penman, H.L. (+3.*) : Gas and vapor movement in soil :solute transport in furrow-irrigated soil : II. ﬁeld

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in soil. Soil Sci. Soc. Am. J., .2 : ,/ῌ-,.

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Scanlon, B., Keese, K., Reedy, R.C., Simunek, J. andde Vries, D.A. (+3/2) : Simultaneous transfer of heatAndraski, B. J. (,**-) : Variations in ﬂow andand moisture in porous media. Trans. Am. Geo-transport in thick desert vadose zones in re-phys. Union, -3 : 3*3ῌ3+0.

sponse to paleoclimatic forcing (*ῌ3* kyr) : Field

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measurements,

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anduncertainties.

Water Resour. Res., No. 1, ++13, doi : +*.+*,3/,**,
WR**+0*.. -.+ῌ-.1.

Jury, W.A., and Letey, J. (+313) : Water vapor move-

Simunek, J., Sejna, M. and van Genuchten, M.Th.

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simulating the one-dimensional movement ofMilly, P.C.D. (+32,) : Moisture and heat transport inhysteretic,

inhomogeneous porous

water, heat, and multiple solutes in variably-

media : asaturated media. Version ,.*. IGWMC-TPS-1*. In-

matric head-based formulation and a numericalternational Ground Water Modeling Center, Col-model. Water Resour. Res., +2 : .23ῌ.32.

orado School of Mines, Golden, CO.

Miyazaki, T., Hasegawa, S. and Kasubuchi, T. (+33-) :van Genuchten, M.Th. (+32*) : A closed-form equa-

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tion for predicting the hydraulic conductivity ofInc., New York.

unsaturated soils. Soil Sci. Soc. Am. J., .. : 23,ῌQῌ R S,***T : UVW DX pp. 20ῌ3, YZ[D\]

232.

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