92168.pdf

Liquid-gas and liquid-liquid interfaces 67

phase by oil-oil dispersion forces and to the water phase by oil-water

dispersion forces. In a simple approach proposed by Fowkes^42 the

oil-water dispersion interactions are considered to be the geometric

mean of the oil-oil and water-water dispersion interactions. Hence,

the interfacial tension is given by

Tow = 7& + ("Xw + Tw) - 2 x (dw x i&)* (4.3)

Substituting values from Table 4.1 for the n-hexane-water interface,

51.1 = 18.4 + 72.8 - 2 X (yw x 18.4)**

which gives

yw = 21.8 mNnr^1

and

yw = 72.8 - 21.8 = 51.0 mNm"^1

Using surface and interfacial tension data for a range of alkanes,

Fowkes calculated that -y4 = 21.8 ± 0.7 mN m"^1.

Phenomena at curved interfaces - the Kelvin equation

As a consequence of surface tension, there is a balancing pressure
difference across any curved surface, the pressure being greater on
the concave side. For a curved surface with principal radii of
curvature r\ and r 2 this pressure difference is given by the Young-
Laplace equation, Ap = y(llri + l/r 2 ), which reduces to A/? = 2y/r
for a spherical surface.
The vapour pressure over a small droplet (where there is a high
surface/volume ratio) is higher than that over the corresponding flat
surface. The transfer of liquid from a plane surface to a droplet
requires the expenditure of energy, since the area and, hence, the
surface free energy of the droplet will increase.
If the radius of a droplet increases from r to r + dr, the surface area
will increase from 4-nr^2 to 4tr(r + dr)^2 (i.e. by 8irr dr) and the increase
in surface free energy will be Siryr dr. If this process involves the
transfer of dn moles of liquid from the plane surface with a vapour