Surface tension

Surface tension:

A liquid at rest shows a property called surface tension. We have seen that water spider walks on the surface of steady water, greased needle floats on the steady surface of water, rain drops and soap bubbles always take spherical shape, etc. All these phenomena arise due to surface tension. 

Molecular Theory of Surface Tension:

To understand surface tension, we need to know the following terms:

a) Intermolecular force: 

Matter is made up of molecules. Any two molecules attract each other. This force between molecules is called intermolecular force. There are two types of intermolecular forces - i) Cohesive force and ii) Adhesive force.

i) Cohesive force:

The force of attraction between the molecules of the same substance is called cohesive force or force of cohesion. The force of attraction between two air molecules or that between two water molecules is a cohesive force. Cohesive force is strongest in solids and weakest in gases. This is the reason why solids have a definite shape and gases do not. Small droplets of liquid coalesce into one and form a drop due to this force.

ii) Adhesive force:

The force of attraction between the molecules of different substances is called adhesive force or force of adhesion. The force of attraction between glass and water molecule is a force of adhesion.

b) Range of molecular force:

The maximum distance from a molecule up to which the molecular force is effective is called the range of molecular force. Intermolecular forces are effective up to a distance of the order of few nanometers in solids and liquids. Therefore, they are short range forces.

c) Sphere of influence:

An imaginary sphere with a molecule at its center and radius equal to the molecular range is called the sphere of influence of the molecule. The intermolecular force is effective only within the sphere of influence.

d)Surface film:

The surface layer of a liquid with thickness equal to the range of intermolecular force is called the surface film.

e)Free surface of a liquid:

It is the surface of a fluid which does not experience any shear stress. For example, the interface between liquid water and the air above. 

f) Surface tension on the basis of molecular theory:

As shown in the figure above, XY is the free surface of liquid and X'Y' is the inner layer parallel to XY at distance equal to the range of molecular force. Hence, the section XX'-Y'Y near the surface of the liquid acts as the surface film. Consider three molecules A, B, and C such that molecule A is deep inside the liquid, molecule B within surface film and molecule C on the surface of the liquid. As molecule A is deep inside the liquid, its sphere of influence is also completely inside the liquid. As a result, molecule A is acted upon by equal cohesive forces in all directions. Thus, the net cohesive force acting on molecule A is zero.

Molecule B lies within the surface layer and below the free surface of the liquid. A larger part of its sphere of influence is inside the liquid and a smaller part is in air. Due to this, a strong downward cohesive force acts on the liquid molecule. The adhesive force acting on molecule B due to air molecules above it and within its sphere of influence is weak. It points upwards. As a result, the molecule B gets attracted inside the liquid.

The same holds for molecule C which lies exactly on the free surface of the liquid. Half of the sphere of influence is in air and half in the liquid. The number of air molecules within the sphere of influence of the molecule C, above the free surface of the liquid is much less than the number of liquid molecules within the sphere of influence that lies within the liquid. This is because, the density of air is less than that of a liquid. The adhesive force trying to pull the molecule above the liquid surface is much weaker than the cohesive force that tries to pull the molecule inside the liquid surface. As a result, the molecule C also gets attracted inside the liquid. Thus, all molecules in the surface film are acted upon by an unbalanced net cohesive force directed into the liquid.

Therefore, the molecules in the surface film are pulled inside the liquid. This minimizes the total number of molecules in the surface film and it remains under tension. The surface film of a liquid behaves like a stretched elastic membrane. This tension is known as surface tension.

Surface Tension and Surface Energy: 

Surface tension T is defined as, the tangential force acting per unit length on both sides of an imaginary line drawn on the free surface of liquid.

T = F/L 

SI unit of surface tension is N/m.

b) Surface Energy:

A molecule inside the volume of a liquid experiences no net cohesive force and the molecules B and C experience net inward cohesive force. Thus, work has to be done to bring any molecule from inside the liquid into the surface film. The surface molecules possess extra potential energy as compared to the molecules inside the liquid. The extra energy of the molecules in the surface layer is called the surface energy of the liquid. As any system always tries to attain a state of minimum potential energy, the liquid tries to reduce the area of its surface film. Energy has to be spent in order to increase the surface area of a liquid.