
J. Jpn. Soc. Soil Phys.
!"
No. +*,, p. 1320 ,**0   *Wettability Indices and Water Characteristics for Sands of Mixed Wettability
Takeyuki ANNAKA** Faculty of Agriculture, Yamagata University, +ῌ,- Wakaba-machi,
Tsuruoka, Yamagata 331ῌ2///, Japan
Abstract
Water-repellent soils have been known to cause ﬁnger-like wetting pattern.

The objectives ofthis study are to measure some wettability indices and water characteristics for sands of mixed
wettablity and to discuss relationships between the indices and the water characteristics.

The

WDPT (Water Drop Penetration Time) indicated the sands to be wettable or water-repellent, but
it did not correspond to the water-entry pressure which is considered to show the degree ofwater-repellency.

On the other hand, apparent contact angles measured by capillary rise method

and sessile drop method showed good correlation with the water-entry pressure.

Cassie’s equa-tion was found to give good estimations of the apparent contact angles for the sands of mixed
wettability. Soil water characteristic curves showed clear transitions from hydrophilic domains
to less hydrophilic or hydrophobic domains corresponding to the apparent contact angles.
Furthermore, it was found that magnitude of soil-water hysteresis for the sand was a#ected by its
wettability.
Key words : water-repellent sand, WDPT, contact angle, water-entry pressure, soil water characteristics+31* ; Bauters et al., +332, ,*** ; Ustohal et al., +332>?

+     

;"Ipqrst"u1 av" Aw
 

xy" z'% ῌ2efg%"{@Z !"#$%&'()*+ !

|I} &"~0 :

,)*+'"-. /0 1 !2345"+[% 0':?

"6%789:;%(</'89: =Wallis and1 "a98 9`A"%

Horne, +33,>? @(A <1B9A"" C

_ `A""cd  &'0"z'D =+3/+> Nakaya et al. =+311 a, b> EF =+32+>% `? &8 z'Nakaya =+32,> G 0 =+330> G"{ |I} z'% %"{ `?

Banyar =,**.>=+333> H ῌ

I78  !"#$(</', 

89:? JK1  !(LMN OPQ1
RNS "+TNPQU:%"VW(XYZ[,+[U: =DeBano, ,***>?

t1"a => UZ  *.-\] ^ IZ_ /'`a%b"_ a

mm*.0 mm, ,.0/gῌcm- U:? ¡¢`

%"cd 98 ( ,2efg ha£7`¤¥R¦ +*/§  ,.

ijk"lm(n@'8o` =Watson and Letey,¨©ª«/¬ ­®Y80 *.2/ mm ¯:9

* °±C]²] ³331ῌ2/// °±´µ¶·¸ +ῌ, : av WDPT ¹º» 2¢¼  OU V +*, ¼ ,**0

80    

Sessile Drop 8ῌE$8 0J950:;< OTS octadecyltrichlorosilane CH- CH,+1 SiCl- ;CD  y B

 !"#$ / kg %&'()* ,**- +,/῎  OTS -./01234

5 + kg 67839 / :;<= +>?

9  +*/@ 9+  Bauters et al.,+332  + > *.2/ mm  A 
OTS 

>3N ?@+ CA ,RSB0J  J5N





> qrmuvn)'



<=

DN Rqrmu319B#J!" OTS 

B <= *῎ ,/῎ /*῎ 1/῎ +**῎ CD EE

ZC Fj j  q῍3*V

 { k h

OTS kgH+**kgGOTS kg

9I JKL <= *῎ B +* ml C Cΐ+ MRSTU q Z 3*VDE { k h<=῎F":!J  MRSTU="9I Bachmann et al., ,*** 0Jlmn49

Fj r !"  EGR ¡NMRSTU=" ῏q¢3*V|= qF+2*V£, a

MC9IN <= +**῎  OTS  MC9I

q῍3*V|= qFbG3*V

sin bF,, 

OP

B Q:; WDPT ;J¤ H +* ml

j
h

ῐ

h£r
r

ῑ

tan aF¥  ,¦§

Water Drop Penetration Time MRSTU ap-ZI¨9{9I E|= 

parent contact angle 3*V NDST ; Ninety-

J{ ©¤ªF©«"

Degree Surface Tension QW water-entry pre-mm, +.1 mm

ssure JXYJPZ[B  \  +31+ ;Wallis and Horne, +33, ; Letey et al., ,***]^9 WDPT MRSTU QW!" 
,,+

gND 8

῍

E$8 !"K­OK BMRSTUZ
3*V J5 JKL 3*V gND 

!" 

WDPT

WDPT O

ZQῌ_`+

cosqFgNDῌgl , £+a9#:;E 9IN b"cP deB y¬Fj +.-Jῒet al.,RMRSTU q ="$89I Watson,*** f$ E:;%&g h'(Sand Letey, +31* ; Carrillo et al., +333 ; Feng et al.,Letey,+303 ; LeteyB )iI King, +32+ ; Bisdom et al., +33- ;,**+ EE gl 9IN gND  WDPT

Bauters et al., +332 ; * ῌBanyar, ,**.

Z/L+j, / cm, k , cm -.lmn4n)o+ Cp)%qrs3 Bt/ 0J > qrmuvn)'

B /* ml J5

BMe

Watson and Letey, +31*
WDPT C®

t/Nlmn4n)o+¯r°9J

>  Y ,p)wx -   EZ1BQ

weight῎ OP 01234 5a9:;!"  y WDPT

 5Z / L9Q



B 

Q  ±R8Sl

4 34²³Z´ B 01234 5,,,,  hµ Cΐ, 

09zRJ5Z9{|= JK
L2}1J|=  ΐ 5~R ΐ 5~

EGRB!U TU  PJ 3e 4ῌ 4 ,***

R  5t/609zR9J  EJTU
"9{J  7KN Y$89 MRST
U Z!"B 

C]^9  - $8

9MRSTU!" B gND ¶" ¡7

B cosq ·῎ T¸¹8E$8 T¸¹kh hµº» B Letey et al., +30, ; Emerson and Bond, +30- ; 4
ῌ 4 ,***©ªe :  5«¬­% p®῏ῌ+Fig. +

81

Sessile drop  ,Bachmann et al., ,***/ 2:;<A?j

Illustration of the sessile drop method developed by Bachmann et al. (,***) for measuringcontact angle.

&89:;<= * 012%>?(@?( B8C-.*+ r "DE23 F"A?( IDE

"A

"GH@

r "GH@&89:;<"JK723
0 HC "DE2
B"GHL72F,Emerson and Bond, +30-/3dxk ῌLMh ῎

M+
῏
dt
e῍ x

῍

 x NOPQRS dxῌdt   k
NOTU VW e  !X h NOPQY92Z [ L \]^_Z [0123 dxῌdt =+ῌx `a72%8C bcdefghQ"D
῏ῌ,


i¡¢%LV ,£¤¥¦§¨2/

Fig. ,

Relationships between surface tension
and weightῌ of ethanol-water solution.

E dxῌdt* %'2 x "DE23 HC i8C
'0
HCxML῎%'2 ,j῏-/3,ῌ,ῌ- ῐ῎ῑ῍HCkH lmn5opqHrZ =:(@s N,gl cosq
rgrῌ

tuv'H=

Z=wx y'z({H|"}~

2% =Nt(E23 ({H|" NtZ%

 HC  gl 



 r  g 

 r 

!"#$%&'(,-.*+/ 0123

)*+4 5672

% {   =  Z % ' 2 =012,Bauters et al., +332 ; Wang et al., ,***/3

h+ , mm "19" + -., cmkH \]""(@º>?B » +*, ¼ $,**0'82

 O1 PQ+ RSITUV WMXYZ
Bῌ[B \]^1 9 :_Z
F+ 5Z17 `abU Ec $ -* cm' 1d+ 1ef gZ7chijklm3 
nop*+ ,. 2qdJ rs  D1 lA :_ZF+ 5Z17 `abU c $ .* cm' 1d+ =>t1^+ 01567g Zc?@

31 PQ+ )uv

qwL -,xvqwy[-zv
Z]+ .* cm 7  , 2q?{|C}~1 1+ hi-}o!

BZ7

3Q+ "-fo @0-

C11^+ P0 #1^$%G . mm ῌFig. -nop¬­®D¸<4Illustration of the capillary rise method
for measuring contact angle.

RU *1 7o!& d+&7c?@ / cm c&

1 ,. 2qdJ rt+ s  D1
&Fnop;<& -'(123) *s  D +&F+
2q,. 2q 1, 2q12, vZ-Z.-/@01 $9 ῌA :X'

&+ (2q,. 2qD1 v;+ 7_Z - 01D + ,*01 ¡&
vC1

- 
-+ ¢0B£2D3l4 $ῌ+ ¤1 WDPT F+
hi *῍ $ ¥ZL7' & * 5+ hi ,/῍& - 5&C1?F+ ¦ -0** 5 §1 WDPTῌ.

,3Dg¹=

Fig. . Schematic illustration of instrument used
to measure water-entry pressure.



B¨

©0** 5Slightly water repellent, 0** 5©-0** 5+ / 567

Wettable, / 5

Severely water repellent, -0** 5 §X

Ex-

tremely water repellent -8ª0Z
$Bisdom et al., +33-' ¨ ?@+ hi,/῍ «c&F Wettable &-+ hi /*῍ «o&Extremely water repellent v L?{¬­®  

_ZF+ DCD3¯-L@01 °  ! "# $+ cmῌmin ±¬­®

%&' ()*+D3F?v9Zl: ¤1-+ gND D3F7

,-./012 !

,31 $4ῌ.'

D sessile drop nop²

q¯-³ , ,´x?C1

,3F,- 

sessile drop nop²D39}µjZ56789 :;< =>?@A : v¶f+ hi ,/῍ «c&F¬­®- 3*·67&B +CD1 7EF+,3F;3&+ hi /*῍ «o&F¬­®-G ..3/ cmῌ ,.* cm HIJ KLMN

3*· § ,3-m3vCZ v;+ hi¸¹º» : l¼§1de

83

ῑῌ+ F=l§1deSTX
Table +

Measured values of wettability indices for mixed sand

F=

WDPT

,LMNO¨
Sessile drop ©
gND ©
ª«©



῍
*
,/
/*
1/
+**

sec

῎῎῎῎῎῎῎ degree ῎῎῎῎῎῎῎
/-­.
®
/2­,
2-­0
3*
2,­+
3,­,
+*,
3-­+
+*/­1
+*.
++0­0
+,0­1
+*0
+-.­0

cm
¯2°
¯+°
+4,
-41
/42

*
¬-0**
¬-0**
¬-0**

¨

{|­e±²¢ W! ³´µ Sessile drop © - gND ©g ª«©F= *῍¶/*῍ & -  1/῍  +**῍ & 0  !
° 6PC/ $%& *.3/ '()·*!

*῍  ,/῍   

 ῌ/  ! "# $
%& *.3/ '()*'+,-./

! 01 23&456789

&:; <= >?@/AB6&/C D)
E !
F= /*῍ 1/῍ +**῍ <= WDPT CG1H-,0** I'() Extremely water repellent 6JK1!  ,LMNOPQRST

 "1A6UK6VC& 0&WK1/C ! XY F=& *῍ PQR ,/῍ Wettable JK1&01MNOPQR

STZ='W/C ! 010

WDPT & wettable  water-repellent VC[\9 & ,LMNO]^;_`
Ua'bc9de/fgC0'Wh

῍ῌ/
Fig. /

/C ! iSjC OTS klmg'9Bozer et al., +303 ; Watson and Letey, +31*

F=l& ,LMNO& 3*nQopq

Cr&s 'W9<=6t6 WDPT
& -,0** I'()

Extremely water repellent uv

K1D)1 !

^ 6 F=&pqg &s~6
/C ! 0<=6  gg./C H&E1 ! 01 PQRw  - xT
yz'{|H 'ῌ/ ῌ0 6W!

 

F= *῍ F=&7) 6}1/&s

~6/Cq &9 0&
WK1/C ! F=& /*῍ q

'W F= /*῍ 6}C/H a-ῌ, ῎ῒῐ῏

Water characteristic curves for wetting
precess.

6*w 9 MNO&g ED)
1 ! 9gc MNO w  MNO&9 &oKC06Q
MNO&MNOQ ) 

+32*! 010ῌw$% *./ 6 ¡9 * g'W/C ! "1*6F=s  qG6*¢'W/ & 0£¤¥¦¤

6WK1/C'W/C ! w H 

Ua'bc9HD)1 ! OTS klF=&bῌ,! bῌ, 6 , }¹ºlT » +*, ¼ P,**0R84

ῌ0Fig. 0=56

Water characteristic curves for drying
process.

ῌ1!"XY%9:; Cassie d#1
 P·SD¸ H sessile drop } ·CR¸ H~}R

Fig. 1

Apparent contact angles for mixed sandestimated by Cassie’s equation.

ῌ, -ῌ=±῏ *./ #² ³´µ¶Table ,

Di#erences in water pressure head between wetting and drying curves

!Z
-
῍
*
,/
/*
1/
+**

cosqjA+cos q+kA,cos q,ῌ# A+, A, H+,#$lm + ,nC o!

q+, q, Hlm + , 9:;JK  Ep , qῌl

³´µ
=

¶

mnr,sZJtXua3U [BWJK  v῎῎῎῎῎῎῎῎ cm ῎῎῎῎῎῎῎῎{++4{,*40
34{,4/{+34.
+14**4{+04,
+04/
-42
{+.42
+240
.43
{+-40
+24/

w x+y JQ" vw x,y J OTS ST"U+EV!Z m P῍Rj+**A,ῌPA+kA,R PA+, A, HQ"$1< OTS ST"mzR UO

Cassie dHid

J+ 
cosqjP+{mῌ+**Rcos q+kPmῌ+**Rq,῍|῎1 H sessile drop } ~}#1 #` Cassie dUOB  


!"#$%

&

'( ῐ'()῍*'(+, OTS -./0#
1 234

-56789:;$1<=56

>?9:;#@A BC DEF

GH2IJK --U q+, q,
BVBWJK!Z *῍ $1< +**῍ XY%9:;
V

!mzYb A +, A , U

!Z ,/῍ #`H Cb!Z /*῍ #`H4V 
Ustohal et al. P+332R H!" #V Cassie d OJ  UV 

Cassie 



LMNH 

LMNJOB !"H &'( PQ"R
ῐ'( POTS ST"R U !VBWJK "XY%9:;



4V

 VYV4

Bauters et al. P+332 ,***R H OTS ST"EY!

!Z#1[\]^_ Y#! P !Z /+*῍ 6RCῐUWBb

 U ¡V  LMN#$W OTS ST"` abc!,9:;U+E Cassie d Pe¢£}UghVB¤¥¦§¨J OTS

f +32*R UOghVX  Cassie dHidJ+>©#῎ª«VB ¬ª ­!JWQU

E 

V

Cassie dYbHXY%9:;

!ST

3*®¯°

23»¼ : CD 





85



(+33-) : Water repellency of sieve fractions from    OTS 

sandy soils and relationships with organic mate-     ! " 

 "#$%&' ()*"+ OTS ,- 
3rial and soil structure. Geoderma, /0 : +*/ῌ++2.
Bozer, K.B., Brandt, G.H. and Hemwall, J.B. (+303) : Ustohal et al. .+332/ 0%12

Chemistry of materials that make soils hydro-

Bauters et al. .+332/ 456&789phobic. In Proc. Symp. Water Rep. Soils, Univ.

" ):" OTS  ;<"=  Measurement of initial soil-water contact angle.    of water-repellent soils. Soil Sci. Soc. Am. J., 0- :>? .@ *.- mmA*.0 mm/   ./OTS " .OTS / B CD 
E  !FG .WDPT/  wettablewater-repellent H""=IJ#K

D ;$L"

Calif., Riverside, +23ῌ,*-.
Carrillo, M.L.K., Letey, J. and Yates, S.R. (+333) :.--ῌ.-0.
DeBano, L.F. (,***) : Water repellency in soils : a historical overview. J. Hydrol., ,-+ῌ,-, : .ῌ-,.

xyz{|} ῌ ~c ῌ  ῌ B

C D .,**-/ : #*E@Fj+

sessileK PU PG H I(Emerson, W.W. and Bond, R.D. (+30-) : The rate of"P9Q&'R(T

water entry into dry sand and calculation of the %MNOdrop"P9Q&'R

T

 gND!S

+  U )#*P9Q&advancing contact angle. Aust. J. Soil Res., + : 3ῌ'R#K

Cassie V&'R+#K+0.

9 (+W,XY-0%1./Z0

Feng, G.L., Letey, J. and Wu, L. (,**+) : Water pond-

9 1-'2[ \3' P9Qing depths a#ect temporal inﬁltration rates in a&'R'2[4E]56  U C

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