Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 33

(b)

(a)

Air

Air

Water

Water

/molecules.m -3

r

FIGURE 2.4 (a) Isotropic forces on a bulk water molecule and anisotropic forces on a surface
water molecule. (b) Number density of water molecules as a function of distance from the
interface.

pressure forces on the surface will be negative, that is, the surface is said to experience
atension.Thesurfaceissaidtohaveacontractiletendency,thatis,itseekstominimize
the area, and is describable in thermodynamics in terms of a property called surface
or interfacial tension and is designated by the symbol

.Itisthe force per unit length
on the surface (N/m or, more commonly, mN/m) or, equivalently, the free energy per
unit surface area (J/m 2 ) .
The molecular picture of surface tension given above explains the variation in sur-
face tension between different liquids (Table 2.3). It is clear that surface tension is a
property that depends on the strength of the intermolecular forces between molecules.
Metals such as Hg, Na, andAg in their liquid form have strong intermolecular attrac-
tive forces resulting from metallic bonds, ionic bonds, and hydrogen bonds. They
therefore have very high surface tension values. Molecules such as gases and liquid
hydrocarbons have relatively weak van der Waals forces between the molecules and
therefore have low surface tensions. Water, on the other hand, is conspicuous in its
strange behavior since it has an unusually high surface tension. The entire concept
of hydrophobicity , and its attendant consequences with respect to a wide variety of
compounds in the environment, is a topic of relevance to environmental engineering
and will be discussed in Chapter 3.

σ

2.6.2 C URVED I NTERFACES AND THE Y OUNG -L APLACE E QUATION
Curvedinterfacesarefrequentlyencounteredinenvironmentalengineering.Examples
are air bubbles in water, soap bubbles in water, fog droplets in air, aerosols, colloids,
and particulates in air and water environments. Consider a curved interface such as
an air bubble in water as shown in Figure 2.5. Surface tension is itself independent of
surfacecurvaturesolongastheradiusofcurvatureofthebubbleislargeincomparison
to the thickness of the surface layer (a few angstroms). Young (1805) argued that in