Chemistry Reference
In-Depth Information
The fundamental property of liquid surfaces is that they tend to contract to the
smallest possible area. This property is observed in the spherical form of small
drops of liquid, in the tension exerted by soap films as they tend to become less
extended, and in many other properties of liquid surfaces. In the absence of gravity
effects, these curved surfaces are described by the Laplace equation, which relates
the mechanical forces as (Adamson and Gast, 1997; Chattoraj and Birdi, 1984;
Birdi, 1997):
p
−
p
′ = γ (1/r
1
+ 1/r
2
)
(2.11)
= 2 (γ/r)
(2.12)
where r
1
and r
2
are the radii of curvature (in the case of an ellipse), while r is the radius
of curvature of a spherical-shaped interface. It is a geometric fact that surfaces for
which Equation 2.11 hold are surfaces of minimum area. These equations thus give
dW =
p
d(V + V′) − γ d
A
(2.13)
=
p
dV
t
− γ d
A
(2.14)
where
p
=
p
′ for a plane surface, and V
t
is the total volume of the system.
It will be shown here that, due to the presence of surface tension in liquids, a
pressure difference exists across the curved interfaces of liquids (such as drops or
bubbles). This
capillary force
will be analyzed later.
If one dips a tubing into water (or any fluid) and applies a suitable pressure, then
a bubble is formed (Figure 2.4). This means that the pressure inside the bubble is
greater than the atmospheric pressure. Thus, curved liquid surfaces induce effects
that need special physicochemical analyses in comparison to flat liquid surfaces. It
must be noted that, in this system, a mechanical force has induced a change on the
Air
Liquid
Bubble
FIGure 2.4
Formation of an air bubble in a liquid.
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