Environmental Engineering Reference
In-Depth Information
2r
air
h
water
α
Figure 9.3.
Schematics of a meniscus at equilibrium in a cylindrical pore
Wetting of solid surfaces by water creates a force resulting from surface tension
(equation [9.6]), which is upwards oriented if the liquid comes from the bottom and
applied on the circumference of the meniscus 2π
r
. To compensate for that force, a
pressure difference ∆
P
must exist between the air and water phases. This pressure is
applied on the meniscus projected surface π
r
2
. Writing down the equilibrium
between these two forces gives Laplace's law:
2
σcos
α
∆
P
=
P
−
P
=
=
P
[9.7]
air
water
c
r
where σ in this case is the air/water surface tension: 0.072 N.m
-1
at 20°C [GUE 92].
9.2.2.3
. Capillary pressure and related variables
This pressure difference ∆
P
that exists in a wet porous medium between the
gaseous phase (air) and liquid phase (water) because of the wetting phenomenon
creates what is called
capillary pressure
noted here as
P
c
. Air inside the porous
structure is connected to the outer atmosphere and will then be at atmospheric
pressure. From [9.7], this implies that water should be at a lower pressure, i.e. in
depression
. For
P
c
values below 0.1 MPa (1 bar) this can be verified experimentally
by introducing a specific pressure sensor inside the medium. Such a device for
measuring capillary pressure involves a pressure sensor placed in a tube full of de-
aerated water connected to the outer liquid phase through a saturated porous cup.
This is known as a
tensiometer
[MAR 96, MUS 91]. A depression above 0.1 MPa
can no longer be transmitted through water, so other devices such as
micro-
psychrometers
3
should be used to measure the capillary pressure. In this last case,
the relative air phase humidity is measured, from which the capillary pressure can
be calculated, as will be shown in section 9.2.3.1.
3 To get more information on the principle of psychrometry, see [CAM 98], Chapter 11 or for
information on its application to non-saturated porous media: see [HIL 98], pp. 164-166.
