The principle of capillary rise in soils can be related to the rise of water in glass capillary tubes in the laboratory. When the end of a vertical capillary tube is inserted into a source of water, the water rises in the tube and remains there. This rise is attributed to the attraction between the water and the glass and to surface tension which develops at the air-water interface at the top of the water column in the capillary tube.
The surface tension is analogous to a stretched membrane, or a very thin but tough film. The water is “pulled up” in the capillary tube to a height, dependent upon the diameter of the tube, the magnitude of surface tension, and the unit weight of water.
The attraction between the water and capillary tube, or the tendency of water to wet the walls of the tube affects the shape of the air-water interface at the top of the column of water. For water and glass, the shape is concave as seen from top, that is, the water surface is lower at the centre of the column than at the walls of the tube. The resulting curved liquid surface is called the ‘meniscus’. The surface of the liquid meets that of the tube at a definite angle, known as the ‘contact angle’. This angle, incidentally, is zero for water and glass (Fig. 5.12).
Capillary rise hhcc Ts Ts dc Meni scus a: Contact angle
(zero for water and glass)
Glass capillary tube
Free water surface
Fig. 5.12 Capillary rise of water in a glass-tube
The column of water in the capillary tube rises, against the pull of gravity, above the surface of the water source. For equilibrium, the effect of the downward pull of gravity on the capillary column of water has to be resisted by surface tension of the water film adhering to the wall of the tube to hold the water column.
If Ts is the surface tension, in force units per unit length, the vertical component of the force is given by πdc . Ts . cos α where α is the contact angle and dc is the diameter of the capillary tube. With water and glass, the meniscus is tangent to the wall surface, so that the contact angle, α, is zero.
Therefore, the weight of a column of water, that is capable of being supported by the surface tension, is πdc . Ts. But the weight of water column in the capillary tube is πdc2
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where γw is the unit weight of water and hc is the capillary rise.
∴ πdc . Ts = π γ 4 d hc2 c. w or hc = 4T d s w c γ . ...(Eq. 5.36)
This equation helps one in computing the capillary rise of water in a glass capillary tube.
The value of Ts for water varies with temperature. At ordinary or room temperature, Ts is nearly 7.3 dynes/mm or 73 × 10–6 N/mm and γ
w may be taken as 9.81 × 10–6 N/mm3. ∴ hc = 4 73 10 9 81 10 30 6 6 × × × ≈ − − . dc dc ...(Eq. 5.37)
where dc is the diameter of the glass capillary in mm, and hc is the capillary rise of water in the glass tube in mm.
There are situations, however, in which the temperature effects should be considered. Generally, as temperature increases, surface tension decreases, indicating a decrease in capil- lary rise under warm conditions or an increase in capillary rise under cold conditions. The effect of this on soil will be discussed in a later sub-section.
As the column of water stands in the capillary tube, supported by the surface tension at the meniscus, the weight of the column is transmitted to the walls of the capillary tube creat- ing a compressive force on the walls. The effect of such an action on soil is also discussed in a later sub-section.
The height of the capillary rise is not dependent on the orientation of the capillary tube, or on variations in the shape and size of the tube at levels below the meniscus as shown in Fig. 5.13.
dc dc dc dc dc dc
hc hc
Fig. 5.13 Capillary heights of capillary tubes of various shapes (These are equal if the diameters of their menisci are the same)
However, for water migrating up a capillary tube, a large opening can prevent further movement up an otherwise smaller diameter tube. The determining factor is the relation be- tween the size of the opening and the particular height of its occurrence above the source of water.
In case the capillary rise computed on the basis of a larger opening is more than the height of this section of the tube, the water would rise further, and the final level will depend upon the capillary rise, computed and based upon the smaller opening above. In other words, the capillary rise would be dependent upon the diameter of the meniscus in such cases. How- ever, in case the capillary rise computed on the basis of a larger opening is less than the height of this section, the water would rise no further, even if the section above is of a smaller size.
SOIL MOISTURE–PERMEABILITY AND CAPILLARITY 139 The hydrostatic pressure in the capillary tube at the level of the free surface of the water supply is zero, that is, it is equal to the atmospheric pressure. It is known that below the free water surface hydrostatic pressure u increases linearly with depth :
u = γw . z where γm = Unit weight of water.
Conversely, hydrostatic pressure measured in the capillary column above the free water surface is considered to be negative, that is, below atmospheric. This negative pressure, called capillary tension, is given by :
u = – γw . h
where h is the height measured from the free water surface. The maximum value of the capil- lary tension uc is :
uc = γw . hc = 4T
dcs ...(Eq. 5.38)
Capillary rise is not limited to tubes. If two vertical glass plates are placed so that they touch along one end and form a ‘V’ in plan, a wedge of water will rise in the V because of the phenomenon of capillarity (Fig. 5.14).
Meniscus Capillary rise Water level Pictorial view Capillary wedge Glass plates Plan
Fig. 5.14 Capillary rise in the corner formed by glass plates
The height of such rise is related not only to the attraction between the water and plates and the physical properties of water, as in tubes, but also to the angle formed by the ‘V’.
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