Environmental Engineering Reference
In-Depth Information
Up to now, capillarity has been intuitively introduced in the basics of physical or
mechanical schematics. This is actually a broader thermodynamic notion related to
the energy - or potential - of water inside the stone's porous matrix. In other terms,
capillary pressure
P
c
is the expression of a
matric potential
Ψ
c
that exists inside the
porous structure because, due to wettability, water in these conditions has less
energy than free water. This new point of view is useful when interpreting water
transfer phenomena: if water is wetting a stone, it will naturally penetrate inside the
porous structure because it will have a lower potential. The difference will be
dissipated in potential energy (the water is getting “higher”) or heat: wetting heat or
viscous dissipation. On the contrary, if for some reason water acts as a non-wetting
fluid, such as in mercury intrusion porosimetry (MIP) [DAI 96, LAU 98, MET 92],
mechanical energy should be provided to enable it to penetrate the porous network.
Like any energy, Ψ
c
's unit is the Joule [J] ≡ [N.m]. Expressed per unit volume, it
becomes identical
4
to capillary pressure
P
c
: [J.m
-3
] ≡ [N.m
-2
] ≡ [Pa]. In the field of
soil physics
5
, matric potentials are expressed in meters and generally denoted
h
,
since they represent hydraulic heads. With these conventions:
-3
ψ
[J.m
]
= ρ
gh
[m]
=
−
P
[Pa]
[9.8]
c
l
c
where
g
is the acceleration of gravity (≈ 9.81 m.s
-2
) and ρ
l
the density of water
(≈ 1,000 kg.m
-3
at 20°C).
h
is often called
capillary suction
because it represents the
water depression expressed in terms of water column height.
Other potentials can add themselves to matric potential:
- gravity potential
ψ
g
, which represents the potential energy of water at a given
height z:
-3
ψ
[J.m
]
=
ρ
gz
[m]
[9.9]
g
l
- osmotic potential
ψ
o
when salts are dissolved into pore water (see Chapter 8,
section 8.2):
-3
ψ
[J.m
]
=
ycRT
[9.10]
o
with:
y
: osmotic activity coefficient;
4 Actually following [9.7]
P
c
is normally positive, although matric potentials and suctions are
normally negative by convention. This is why there is a negative sign in equation [9.8].
5 Many notions presented in this chapter have initially been developed in this field. This
explains many of our references.
