I n s t r u m e n t s

a n d

M e t h o d s

[!]
[!]b^2[!]
p^{3[!][!]b-cosa+cotw[!]}
[!]^sinj+cotw[!]
[!]b-
V_p= 2R^[!][!][!]
[!]
are:^{[!]+b(sin2j-sin2a)}

sinj]-b}

A_wn=

and

whereb= cosa- cosj.

wheregis the interfacial tension between the wetting
and nonwetting^wn
fluids, so that r₁= rgives a condition for
maximumringsize.Thiscondition²
can beexpressedin
terms
0^of
=^ring
sin ^size
jcos (^jand
j^contact
+q) +^angle
b(sin(^q;j+q) -2)

whereb= 1-cosjforthe ideal medium andb= cosa-
cosjforthe flattened contact.

A good .japproxim =-0.588 ation qin +55.065the ideal case is

CHARACTERISTIC CURVES

The capillarypressure across thewetting-nonwettingphase
interfacecan be calculated by dividing the changein total
surface energy by the change in volume,Pc = dE/dV.
Letsdenote a surface tension or energy. The changein
total surface energy is given by

D
._{E=swn*DAwn+sws*DAws+sns*DAns}

Using Young's equation,

Fig 3 - Theoretical characteristic curve. An empirical relation given
by Colbeck is shown for comparison.

REFERENCES

1Walter Rose,J. Appl.Phys.29, 687 (1958).

2Willard GardnerandJohnHaleGardner,Soil Sci.76,135
(1953).

3J.M.Dallavalle,Micromeritics,2nded.(Pittman,1948),
p.288.

4 Haim Gvirtzman and Paul V. Roberts, Water Resour. Res. 27,
1167 (1991).

5JimFrankenfield,self-publishedontheworld-wide-web,
http://www.peak.org/~snow/papers/rings.

6S.C. Colbeck,J. Colloid InterfaceSci.72, 371(1979).

7S.C. Colbeck,Journal of Glaciology,Vol 13 #67, 1974.

s_ws=s_ns+s_wncosq

and the fact thatDA_ws= -DAis the changein surface en-
ergy it can be written.^ns
The saturation can be calculated as the ratio of the vol-
ume of the rings contained in a unit cell to the volume of
pore space in a unit cell. The resulting expression is

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