Capillarity and Surface Forces (Liquids) - Surface and Colloid Chemistry: Principles and Applications - page 20

particular case where the contact angle, θ, is not zero, a correction will be needed,
and the equation will become

γ = 2 R ρ L g h (1/cos (θ)) (2.27)

It is seen that, when the liquid wets the capillary wall, the magnitude of is 0, and
cos(0) = 1. In the case of Hg, the contact angle is 180° since it is a nonwetting fluid
(see Figure 2.8). Because cos(180) = −1, the sign of h in the equation will be nega-
tive. This means that Hg will show a drop in height in a glass tubing. Hence, the rise
or fall of a liquid in a tubing will be governed by the sign of Cos (θ). Thus, capillary
forces will play an important factor in all systems where liquids are present in a
porous environment.
Similar results can also be derived by using the Laplace equation (Equation 2.21)
(1/radius = 1/R):

Δ P = 2 γ/ R (2.28)

The liquid rises to a height h and the system achieves equilibrium, and the following
relation is found:

2 γ/ R = h g g ρ L (2.29)

This can be rewritten as

γ = 2 R ρ L g g h (2.30)

The various surface forces are seen to be responsible for capillary rise. The lower
the surface tension, the lower the height of the column in the capillary. The magni-
tude of γ is determined from the measured value h for a fluid with known ρ L . The
magnitude of h can be measured directly by using a suitable device (e.g., a photo-
graph image).
Further, it is known that real-world capillaries or pores are not always circular
shaped. In fact, in oil reservoirs, the pores are more triangular shaped or square
shaped than circular. In this case, the rise in capillaries of other shapes, such as rect-
angular or triangular (Birdi et al., 1988; Birdi, 1997, 2002) can be measured. These
studies have much significance in oil recovery or water treatment systems. In any
system in which the fluid flows through porous material, it would be expected that
capillary forces would be one of the most dominant factors.
Also, the vegetable world is known to be dependent on capillary pressure (and
osmotic pressure) to bring water up to the higher parts of plants. Using these
forces, some trees succeed in bringing the essential liquid (water) up to 120 m
above the ground.

2.5 bubble FormatIon
There is one phenomenon that everyone can quickly recognize—soap bubbles—that
one has observed since childhood. The formation of foam bubbles along the coasts