Consider a rectangular wire frame ABCD in which the wire AB is movable. Dip the wire frame in soap solution. A film is formed which pulls the wire AB inward due to surface tension by a force ( σ × 2l ).
Here σ is the surface tension of the film and l is the length of the wire AB. The length is taken twice because the soap film touches the wire above as well as below.
If the film is stretched by a small distance x to the position A’ B’ keeping the temperature constant, then the work done is given by
σ × 2l × x
Now 2l × x is the total increase in area of the soap film on both the sides.
∴ Work done = σ × Increase in area
or , Work done per unit area = σ
The wetting of surfaces – the meniscus
The behaviour of water on glass is different when glass surface is greasy than when glass surface is clean. On the greasy surface water tends to gather in blobs.
On the other hand on degreased glass surface water wets the whole of glass surface smoothly. In a related phenomenon aqueous solutions in glass tubes adopt a u shape called a meniscus, which is clearly not a minimum surface area.
It all depends upon intermolecular forces between the liquid and glass surface. A clean glass surface offers oxygen atom from material of glass itself, so water can hydrogen bond to the glass.
This tendency can be sufficiently strong to cause the water molecules to prefer contact with the glass to contact with their own kind and thus the minimum surface area criterion is overridden i.e. inter-substance hydrogen bonding (between glass and water molecules) wins over intra-substance hydrogen bonding (between water molecules).
In case of mercury strong metallic bonds are present among the atoms. These atoms do not have any attraction for glass surface. Therefore, they in an effort to acquire minimum surface area acquire the shape of inverted hemisphere.