Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 61

of solubility of oxygen, nitrogen, and air in water for vari-
ous temperature conditions. All coefficients of solubility are
referenced to an absolute standard pressure of 101.3 kPa.
The ratio of the volume of dissolved gas, V d , in a liquid
to the volume of the liquid is called the volumetric coeffi-
cient of solubility, h , which varies slightly with temperature.
Values for the volumetric coefficient of solubility for air in
water under various temperatures are given in Table 2.12.
The volumetric coefficient of solubility of a gas in water is
approximately 2%. In other words, about 2% of water can
be considered to be voids that can be occupied by a gas.

Table 2.14 Coefficient of Diffusion for Air through
Different Materials

Water Content, Coefficient of

Diffusion, D( m 2 / s )

Material w (%)

10 − 9 Free water — 2 . 2 ×

10 − 10 Natural rubber — 1 . 1 ×

10 − 10 Kaolin consolidated

at 483 kPa

47 3 . 0 ×

10 − 10

Kaolin consolidated
at 34.5 kPa

75 6 . 2 ×

10 − 10

Derwent clay (Illite)
consolidated at
34.5 kPa

53 4 . 7 ×

2.3.8 Diffusion of Air through Water
The rate at which air can pass through water is described by
Fick's law of diffusion. The rate at which mass is transferred
across a unit area is equal to the product of the coefficient
of diffusion, D , and the concentration gradient. When con-
sidering the diffusion of air through water, the concentration
difference is equal to the difference in density between the free
air external to the water and the dissolved air in the water.
Under constant-temperature conditions, the density of air
is a function of the (absolute) air pressure (Eq. 2.19). An
increase in pressure in the free air will develop a pressure
difference between the free and dissolved air. The difference
in air pressures becomes the driving potential for the free
air to diffuse into (or dissolve in) water.
The gases composing air diffuse as individual components
into water. The coefficients of diffusion, D , for each com-
ponent of air through water are tabulated in Table 2.13. The
combined gases comprising air dissolve in water at a rate
of approximately 2 . 0

10 − 11

Jackson clay and 4%
bentonite
consolidated at
34.5 kPa

39 < 1 . 0 ×

10 − 11 Compacted

Westwater clay

16 1 . 0 ×

10 − 5

Saturated coarse
stone

21 2 . 5 ×

10 − 10 Saturated ceramic 49 1 . 6 ×

Source : From Barden and Sides, 1967.

2.3.9 Surface Tension
The air-water interface (i.e., contractile skin) possesses a
property called surface tension. The phenomenon of sur-
face tension results from intermolecular forces acting on
molecules in the contractile skin. These forces are different
from those that act on molecules in the interior of the water
(Fig. 2.38a).
A molecule in the interior of the water experiences equal
forces in all directions, which means there is no unbal-
anced force. A water molecule within the contractile skin
experiences an unbalanced force toward the interior of the
water. A tensile pull is generated along the contractile skin
in order for the contractile skin to be in equilibrium. The
property of the contractile skin that allows it to exert a
tensile pull is called its surface tension, T s . Surface ten-
sion is measured as the tensile force per unit length of
the contractile skin (i.e., units of mN/m). Surface tension
is tangential to the contractile skin surface. Its magnitude
decreases slightly as temperature increases. Table 2.15 gives
surface tension values for the contractile skin at different
temperatures.
The surface tension causes the contractile skin to behave
like an elastic membrane. The behavior of the contractile
skin is similar to an inflated balloon which has a greater
pressure inside the balloon than outside. If a flexible two-
dimensional membrane is subjected to different pressures

10 − 9 m 2 /s (U.S. Research Coun-

×

cil, 1933).
Barden and Sides (1967) measured the coefficient of dif-
fusion for air through the water phase of both saturated and
compacted clays and the results are presented in Table 2.14.
The study concluded that the coefficient of diffusion appears
to decrease with decreasing water content of the soil. The
coefficient of diffusion for air through the water in a soil
appears to differ by several orders of magnitude from the
coefficient of diffusion for air through free water.

Table 2.13 Coefficients of Diffusion for Certain Gases
in Water .......

Coefficient of

Temperature ( ◦ C) Diffusion, D (m 2 /s)

Gas

10 − 9

CO 2 20 1 . 7 ×

10 − 9

N 2 22 2 . 0 ×

10 − 9

5 . 2

×

H 2 21

10 − 9 O 2 25 2 . 92 ×

Source : From Kohn, 1965.