Capillarity and Surface Forces (Liquids) - Surface and Colloid Chemistry: Principles and Applications - page 16

Pgas

Pliquid

FIGure 2.5 Liquid drop and Δ P (= P LIQUID − P GAS) (at a curved liquid-gas interface).

phase), the Laplace pressure would be the difference between the pressure inside the
drop, p L , and the gas pressure, p G (Figure 2.5):

p L − p G = Δ P (2.20)

= 2 γ/radius (2.21)

In the case of a water drop with radius 2 μ, there will be Δ P of magnitude

Δ P = 2 (72 mN/m)/ 2 10 −6 m

= 72000 Nm −2 = 0.72 atm (2.22)

It is known that the difference between pressure inside the drop and the gas pressure
changes the vapor pressure of a liquid. Thus, ΔP will affect the vapor pressure and
lead to many consequences in different systems.
The Laplace equation is useful for analyses in a variety of systems:

1. Bubbles or drops (raindrops or combustion engines, sprays, fog)

2. Blood cells (flow of blood cells through arteries)

3. Oil or groundwater movement in rocks

4. Lung vesicles

2.3.1 T h e I m p o r T a n T r of l e of f l a p l a c e e q u a T I o n I n V a r I o u S a p p l I c aT I of n S
Another important conclusion one may draw is that Δ P is larger inside a small bub-
ble than in a larger bubble with the same γ. This means that, when bubbles meet,
the smaller bubble will enter the larger bubble to create a new bubble (Figure 2.6.)
This phenomenon will have much important consequences in various systems (such
as emulsion stability, lung alveoli, oil recovery, bubble characteristics [as in cham-
pagne; beer]). The same consequences will be observed when two liquid drops con-
tact each other: the smaller will merge into the larger drop.
Figure 2.7 shows a system that initially shows two bubbles of different curvature.
After the tap is opened, the smaller bubble is found to shrink, while the larger bubble
(with lower Δ P ) increases in size until equilibrium is reached (when the curvature
of the two bubbles become equal in magnitude). This type of equilibrium is the