Physical Chemistry , 1st ed.

exists at the liquid-vapor interface will act according to the Laplace-Young

equation:

p

2

r





That is, there will be a pressure differential on either side of the liquid surface.

Depending on the wettability of the surface, one of three things will happen.

First, if surface tensions are balanced, nothing might happen; we will not con-

sider this possibility further. Second, if the liquid wets the capillary surface,

then the surface of the liquid in the capillary is curved as shown in Figure

22.9a, and the level of the liquid inside the capillary rises due to p, the pres-

sure differential across the curved liquid surface. In fact, the liquid will rise

until its height inside the capillary exerts a pressure equal to the pvalue from

the Laplace-Young equation. This pressure is related to the force due to grav-

ity of the column of liquid divided by the circular area of the capillary. This

pressure is equal to the product of the liquid’s density , the gravitational con-

stant g, and the height of the column in the capillary h:

pgh

It is therefore easy to determine how high this capillary risewill be:

gh

2

r





or, rearranging for the height of the capillary rise:

h



2

g



r

 (22.18)

The close-up in Figure 22.9b also shows that we can rewrite equation 22.18 in

terms of the inner radius of the capillary, defined as R. If the surface of the

liquid is spherical, then the radius of the curved meniscus and the radius of

the capillary are related by

Rrcos 

where is the contact angle. Substituting into equation 22.18:

h

2 



c

g

o

R

s

 (22.19)

If surface tensions are known from other measurements, equation 22.19 is an

easy way to determine contact angles of liquids. It also shows that capillary rise

will be larger if the capillary radius Ris smaller.

The third possibility is that the liquid does not wet the surface. In that case,

the meniscus of the liquid surface is inverted, as shown in Figure 22.10. Here,

we see that the contact angle is greater than 90° and the cosine of that angle is

negative. Therefore, the height of the column is negative and the liquid expe-

riences a capillary depression.Mercury is a liquid that shows a capillary de-

pression.

Capillary action, either rise or depression, is significant only for cylinders

having small radii. If the capillary is wide enough to provide sufficient flat sur-

face for the liquid, then capillary action is negligible.

Capillary action is found in many everyday settings. Paper towels, coffee fil-

ters, and tea bags work because of capillary action. Certain synthetic fabrics are

uncomfortable in humid weather due to a lack of capillary action. Waterproofed

776 CHAPTER 22 Surfaces

Liquid

Capillary

(a)

(b)

r

R 



h

Figure 22.9 If a liquid wets a solid, then it will
rise inside a small cylindrical tube of the solid
material. (a) The net effect of capillary action. (b)
The liquid inside the capillary forms a meniscus
that makes a certain contact angle with the wall.
See text for definitions of the variables.

r

R



Figure 22.10 Capillary depression is seen
when a liquid does not wet the solid material of
a capillary. In this case, the diagram in Figure
22.9a would show the liquid in the capillary be-
lowthe level of the liquid in the container. The
meniscus in this case is inverted.