Page 348 - Mechanical Engineers' Handbook (Volume 4)
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2 Fundamentals 337
2 FUNDAMENTALS
2.1 Surface Tension
Surface tension is a force that operates on a surface and acts perpendicular and inward from
the boundaries of the surface, tending to decrease the area of the interface. As a result, a
liquid will tend to take up a shape having minimum area. In the case of zero gravity in
vacuum this liquid drop will be a perfect sphere. Surface tension can be viewed as a con-
sequence of attractive and repulsive forces among molecules near the interface. From a
thermodynamic point of view, it may be interpreted in terms of energy stored in the molecules
near the interface. Surface tension consists of the dispersion force and other specific forces
such as metallic or hydrogen bonding, i.e., . Surface tension in nonpolar liquids
d
m
is entirely caused by dispersion forces. In hydrogen-bonded liquids, both dispersion forces
and hydrogen bonding have contributions resulting in relatively larger values of surface
tension. In liquid metals, the metallic force combining with the dispersion force results in
higher values of surface tension. And it is easy to understand that the surface tensions of
liquid metals are higher than those of hydrogen-bonded liquid such as water, which in turn
are higher than those of nonpolar liquids such as pure hydrocarbons. The surface tension
significantly depends on the temperature. As temperature increases, the surface tension de-
creases. The surface tension of water, for example, decreases almost linearly with tempera-
ture, 75.83 0.1477T (mN/m), where T is temperature ( C).
2.2 Contact Angle
A physical property that is closely related to the surface tension is the contact angle. The
contact angle is defined as the angle (measured in the liquid) formed between the liquid–
vapor interface and the solid–liquid interface as shown in Fig. 2, which may be expressed
as
cos sv sl (1)
where is the surface tension between the solid and vapor, and is the surface tension
sl
sv
between the solid and liquid. The surface tension between the liquid and vapor is a function
of temperature and decreases as the temperature increases. For a given solid surface and
liquid, when the surface tension between the solid and liquid is a fixed constant, the contact
angle will decrease as the temperature increases. When the temperature increases, the wetting
characteristic of a liquid on a given solid surface becomes better.
σ
vapor
σ sv liquid
α
σ sl
solid
Figure 2 Contact angle.