Surface Tension

 

Molecules interact with each other resulting in forces of attraction. n-Heptane is a liquid at ambient temperatures because the molecules attract one another and become a cohesive bulk liquid and not a vapor. In a similar way water is a liquid at room temperature but the forces holding the water molecules together are polar as opposed to those that hold heptane molecules together which are dispersive. However, irrespective of the type, interactive forces exist between molecules. The energy of the molecules cover a wide range and take the form of the bell shaped curve of energies typically but not necessarily Gaussian in form. At any time a molecule approaching the surface of a liquid may (randomly) have sufficient kinetic energy to overcome the interactive forces with its neighbors and leave the surface. This results in the liquid having a finite vapor pressure at any given temperature. In the bulk liquid every molecule has interactive forces from its neighbors in three dimensions but those at the surface will only have two-dimensional interactions with their neighbors. Thus, there is a lateral force in the surface of a liquid and this force is called surface tension.  The dimensions of surface tension will be +1 in mass an -2 in time and its classical definition is the force per unit length in the surface of a liquid.

 

There is an interesting relationship between surface tension and surface energy. As a result of surface tension the surface tends to make the surface area as small as possible (cf the spherical shape of a drop of liquid).  A system is in stable equilibrium when its potential energy is at a minimum. Thus the surface of a liquid can be considered as possessing potential energy each sq. cm. containing a certain amount of energy independent of the configuration. Consider the film of soapy water depicted in figure 13. 

 

 

Figure 13. Surface Tension and Surface Energy

 

Let (T) be the surface tension on each side of the film abs (S) the energy associated with each square centimeter of film. Suppose that the film is contained in a rectangular wire frame (ABCD) formed in such a manner that the cross wire (BC) can slide along (AB) and (DC). Let the wire be displaced to (B’C’) through a distance (x). Then if (a) is the length (BC) the work done in stretching the film will be (2Tax).  The potential energy of the film has consequently been increased by an amount (2Tax). Now each side of the film has been increased by an area (ax). Hence the increase in energy per unit area (S) is given by,

 

Thus the dimensions of both the surface tension (T) and the surface energy (S) are 1 in mass and  –2 in time.

 

Rise of Liquid in a Narrow Vertical Cylindrical Tube (contact angle not zero)

 

Consider the section of a tube dipping into a liquid as depicted in figure 14 with an angle of contact (). The profile of the liquid curve is given by LMN. As the tube is considered narrow the profile of this curve can be considered as spherical.  Now the rise in liquid displaces some air and so there is a buoyancy effect and this can be accounted for by assuming the density () of the liquid above the main surface is given by,

 

 

           where () and () are the densities of air and liquid respectively.

 

 

Figure 14. Rise of Liquid in Cylindrical Capillary Tube

 

Let (r) and (R) be the radii if the tube and meniscus respectively, and let (H) be the height of (M) the lowest part of the meniscus above the level of the bulk liquid. Now since the system is in equilibrium, the weight of the liquid is equal to the upward force due to surface tension around the circle whose section is LN.

Consequently,

 

 

Assuming the weight of the liquid lens to be negligible,

 

 

or,          

 

If the volume of the lens (V) is not neglected, then it can be calculated that,

 

 

Consequently, 

And thus,

 

          It is clear that when     

 

From the point of view of molecular interactions in physical chemistry, the surface tension of a liquid will be directly related to the inter-molecular force between one molecule of the liquid and another.

 

The subjects discussed in this book have been selected to be of interest to physical chemists and analytical chemists but much of the contents have evolved in the field of physics. Many important technical studies are common to both physics and physical chemistry and the two subjects tend, in part, to be synergistic.