# Surface Tension

## What is known as surface tension?

Surface tension is the property of a liquid by virtue of which the free surface of liquid at rest behaves like an elastic stretched membrane tending to contract so as to occupy minimum surface area.

Consider about a liquid kept in a beaker as shown in figure. Imagine a line AB on the free surface of the liquid. The small elements of the surface on this line are in equilibrium because they are acted upon by equal and opposite forces, acting perpendicular to the line from either side. The force acting on this line is proportional to the length of this line.

If l is the length of the imaginary line and F is the total force on either side of the line, then

F \propto l

So, \quad F = \sigma l

Or, \quad \sigma = \frac {F}{l}

Or, \quad \text {Surface tension} = \left ( \frac {\text {Force}}{\text {Length}} \right )

Therefore, surface tension is measured as the force acting per unit length of an imaginary line drawn on the liquid surface, the direction of force being perpendicular to the line and tangential to the liquid surface.

### Units of surface tension

1. SI unit of surface tension is \text {N-m}^{-1}
2. CGS unit of surface tension is \text {dyne-cm}^{-1}

Its dimension will be \left ( \frac {\text {Dimension of force}}{\text {Dimension of length}} \right ) = \left ( \frac {\text {M L T}^{-2}}{\text {L}} \right ) = \left [ \text {MT}^{-2} \right ]

### Cause of surface tension

Phenomenon of surface tension is based upon two types of molecular forces. These are –

1. Cohesive force of molecular attraction.
2. Adhesive force of molecular attraction.

### Cohesive force

Cohesive force is the molecular force of attraction between the molecules of same substance.

• Surface tension is the phenomenon caused due to cohesive forces between molecules of liquid.
• Cohesiveness for solids is more than liquids and gas.
• Solids have definite shape and size due to their strong forces of cohesion between their molecules.

Adhesive force is the molecular force of attraction between the molecules of two different substances.

• Water wets the walls of its glass container because the force of adhesion between water and glass is greater than the force of cohesion between the water molecules.
• But, mercury does not wet glass because the force of cohesion between the mercury molecules is much greater than the force of adhesion between mercury and glass.
• It is due to the force of adhesion that ink sticks to paper while writing.

## Natural phenomenon based on surface tension

(1) Rain drops are generally spherical in shape. Due to surface tension, the rain drops tend to minimize their surface area. The surface area of a sphere is minimum for a given volume.

(2) Small mercury droplets are spherical and larger ones tend to flattened. Small mercury droplets are spherical because the forces of surface tension tend to reduce their area to a minimum value and a sphere has minimum surface area for a given volume.

Larger drops of mercury are flattened due to the large gravitational force acting on them.

(3) The hair of a painting brush cling together when taken out of water. This is because the water films formed on them tend to contract to maintain minimum area.

(4) A bug floats on water due to surface tension. As shown in figure, a bug bends its legs on the surface of water such that the deformed surface gives rise to forces of surface tension which act tangential to the deformed surfaces. The weight of the bug is balanced by the upward components of these forces of surface tension.

Beside the above phenomenon, following properties of liquid is also related to the effect of surface tension.

1. Pressure inside a liquid droplet.
2. Pressure intensity inside hollow bubble.
3. Pressure intensity inside a liquid jet.

These are explained as follows –

### 1.Pressure intensity inside a droplet

Consider about a small drop of a liquid having radius ( r ) as shown in figure.

Let, ( \sigma ) is the surface tensile force of the liquid and ( p ) is the pressure intensity inside the droplet.

Considering the equilibrium of one half of the droplet as shown in figure (A), we get –

\text {Pressure force} = \text {Surface tensile resistance}

Therefore, \quad p \times ( \pi r^2 ) = \sigma \times ( 2 \pi r )

So, \quad p = \frac {2 \sigma }{r}

### 2.Pressure intensity inside hollow bubble

A hollow bubble like a soap bubble has two surfaces subjected to surface tension. For a bubble of radius ( r ) , considering the equilibrium of one half of the bubble as shown in figure (A), we get –

p \times ( \pi r^2 ) = 2 \times \sigma \times ( 2 \pi r )

Or, \quad p = \frac {4 \sigma }{r}

### 3.Pressure intensity inside liquid jet

Let, ( p ) is the pressure intensity in a liquid jet of diameter ( d ) and length ( l ) as shown in figure (B).

Considering the semi jet and equating the bursting force to the resisting force, we get –

p l d = 2 \sigma l

Therefore, \quad p = \frac {2 \sigma}{d} = \frac {\sigma}{r}

Where ( r = \frac {d}{2} ) is the radius of the jet.