Soil Water Flow - Transport in the Atmosphere-Vegetation-Soil Continuum - page 142

σ cos ϕ

ϕ

σ

r
R

z c

Figure 4.7 Capillary rise of water in a glass tube.

face water tension σ (N m -1 ). In combination with the adhesive forces (expressed in
a so-called wetting angle φ ), σ determines the maximum height. At equilibrium, the
vertical component of the surface water tension is equal to the gravitational force of
the lifted water column in the glass tube:

2
πσ ϕπ ρ 2 r cos = r zg

(4.6) c

were r is the radius of the tube (m), ρ is the water density (kg m -3 ) and g is the gravi-
tational acceleration (m s -2 ). This gives for the maximum height z c :

c = 2 σϕ
ρ

cos

z

(4.7)

gr

A general igure for surface water tension σ is 0.07 N m -1 . In case of clean glass,
adhesion is maximum and the wetting angle φ = 0º (cos φ = 1). In case of clean steel,
no adhesion occurs and the wetting angle φ = 90º (cos φ = 0). Some materials and
soils repel water and are called hydrophobic. At these materials wetting angle φ > 90º
and cos φ < 0.

Question 4.5: How much is the capillary rise (mm) of water in a clean glass tube with
a radius of 1 mm? And how much for a tube with radius 0.1 mm? Take σ = 0.07 N m -1
and g = 9.81 m s -2 .