Capillarity and Surface Forces (Liquids) - Surface and Colloid Chemistry: Principles and Applications - page 18

ln (p cur /p lat ) = (v L / R T ) (2 γ/R cur ) (2.23)

where p cur and p lat are the vapor pressures over curved and flat surfaces, respectively.
R cur is the radius of curvature, and v L is the molar volume. The Kelvin equation thus
suggests that, if liquid is present in a porous material, such as cement, then the dif-
ference in vapor pressure exits between two pores of different radii due to the high
vapor pressure. Similar consequences of vapor press exists when two solid crystals
of different size are considered. The smaller-sized crystal will exhibit higher vapor
pressure and will also result in a faster solubility rate.
Further, the transition from water vapor in clouds to rain drops is not as straight-
forward as it might seem. The formation of a large liquid raindrop requires that a
certain number of water molecules in the clouds form a nuclei. The nuclei or embryo
will grow, and the Kelvin relation will be the determining factor.

2.4 caPIllary rISe (or Fall) oF lIquIdS
The behavior of liquids in narrow tubes is one of the most common examples in
which capillary forces are involved. It will be shown later how important this phe-
nomenon is in many different parts of everyday life and technology. In fact, liquid
curvature is one of the most important physical surface properties that requires atten-
tion in most of the application areas of this science. The range of these applications
is from blood flow in the veins to oil recovery in the reservoir. Properties of fabrics
are also governed by capillary forces (i.e., wetting, etc.). The sponge absorbs water
or other fluids where the capillary forces push the fluid into the many pores of the
sponge. This is also called wicking process (as in candlewicks).
Let us analyze the system in which a narrow capillary circular tube is dipped into
a liquid. The liquid is found to rise in the capillary when it wets the capillary (like
water and glass or water and metal). The curvature of the liquid inside the capil-
lary will lead to pressure difference between this state and the relatively flat surface
outside the capillary (Figure 2.8). The fluid with surface tension, γ, wets the inside
of the tubing, which brings about an equilibrium of capillary forces. However, if
the fluid is nonwetting (such as Hg in glass), then one finds that the fluid falls . This
arises because Hg does not wet the tube. Capillary forces arise from the difference
in attraction of the liquid molecules to each other and the attraction of the liquid mol-
ecule to those of the capillary tube. The fluid rises inside the narrow tube to a height
h until the surface tension forces balance the weight of the fluid. This equilibrium
gives following relation:

γ 2 π R = surface tension force (2.24)

= ρ L g g h π R 2 = fluid weight (2.25)

where γ is the surface tension of the liquid, and R is the radius of curvature. In the
case of narrow capillary tubes (less than 0.5 mm), the curvature can be safely set
equal to the radius of the capillary tubing. The fluid will rise inside the tube to com-
pensate for surface tension force, and thus, at equilibrium, we get