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# Surface Tension

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 Sub Topics The attractive force between substances that are alike is known as cohesion, while the attraction between unlike substances is called adhesion. Cohesive forces are responsible for surface tension. Surface tension is a property of liquid surfaces resulting from inter-molecular bonding which causes the liquid to minimize its surface area and resist deformation of its surface. It is useful analogy to visualize the behavior of liquids. In this section we will learn more about surface tension.

## Definition

A liquid behaves as if its surface was covered with a stretchy skin. The effect is called surface tension; this is the another result of the force of attraction between the molecules.

The surface tension is defined as the force per unit length acting on either side of a line imagined to be drawn on the liquid surface in equilibrium, the direction of the force being tangential to the surface and normal to the line.

Factors Affecting the Surface Tension

1. Temperature Effects : The surface tension of a liquid in contact with its own vapor or air depends only on nature of liquid and temperature. Surface tension decreases with the raise of temperature. It represents the variation of surface tension and surface energy of water with temperature. Clearly the Surface tension decreases with raise of high temperature.And becomes zero at 374⁰C which is the critical temperature of water.
2. Effects of Solute: If the solute is less soluble in liquid, the factors affecting surface tension of liquid decreases. For example ,by mixing soap, detergent powder or phenol in water, the surface tension of water decreases, but if the solute is very soluble in liquid, the surface tension of liquid increases. For example, if salt is mixed in water, the surface tension of the water increases.
3. Contamination Effects: The presence of dust, oil or grease on the surface of water, reduces the surface tension of water. Factors affecting surface tension decreases with rise of temperature and becomes zero at the critical temperature. Critical temperature of water is 374⁰C. The surface of a liquid acts like a stretched membrane and tends to occupy the minimum surface area. This property of the liquid is called the surface tension.

## Cohesion and Surface Tension

Cohesion means intermolecular attraction between molecules of the same liquid. It enables a liquid to resist small amount of tensile stresses. Cohesion is a tendency of the liquid to remain as one assemblage of particles. "Surface tension" is due to the cohesion between particles at the free surface.
Surface tension is caused by the force of cohesion at the free surface. A liquid molecule in the interior of the liquid mass is surrounded by other molecules all around and is in equilibrium. At the free surface of the liquid, there are no liquid molecules above the surface to balance the force of the molecules below it. Consequently, there is a net inward force on the molecule. The force is normal to the liquid surface. At the free surface a thin layer of molecules is formed. This is because of this film that a thin, small needle can float on the free surface.

## Causes

Surface tension is essentially a molecule phenomenon. In order to know how it affects the behavior of liquids in contact with solids, it is necessary to know the force that operates among molecules. These can be of two types

1. Adhesion: It is a force of attraction that acts between molecules of different substances. It differs from pair to pair of substances.
2. Cohesion: It is the force of attraction that acts between molecules of the same substances

## Formula

The surface tension is defined as the force per unit length along a line where the force is parallel to the surface and perpendicular to the line

$T$ = $\frac{F}{L}$

The alternative description of surface tension is often used in thermodynamics. It can also be thought of as an energy per unit area and the shape is formed which minimises the energy.

The surface tension of liquids decreases with rise of temperature. It is zero at boiling point and vanishes at critical temperature. For small temperature difference the variation in surface tension with temperature is linear and is given by

$T_{t} = T_{0}(1 - \alpha t)$

Where,

$T_{t}$ = Surface tension at $t ^{0}C$
$T_{0}$ = Surface tension at $0 ^{0}C$
$\alpha$ = Temperature coefficient of surface tension.

## How to Measure Surface Tension ?

A number of commonly used methods of measuring surface tension exist. The choice of a method depends on the system to be studied, the degree of accuracy required and possibly with the ability to automate the measurements. One important method among them is described here.

Capillary Rise Method:
If a glass capillary tube is brought into contact with a liquid surface and if the liquid wets the glass with a contact angle of less than 90, then the liquid is drawn up into the tube. The surface tension is directly proportional to the height of rise, h, of the liquid in the tube relative to the flat liquid surface of the larger container. Then the relationship between radius, density and surface tension is given as,

where b is the radius of curvature at the center of the meniscus
Δ$\rho$ is the density difference between liquid and gas

For small capillary tubes, b is well approximated by the radius of the tube itself, assuming that the contact angle of the liquid on the tube is zero. For larger tubes or for increased accuracy, the value of b must be corrected for gravitational deformation of the meniscus. Obtaining accurate results with the capillary rise method requires using a thoroughly clean glass capillary tube with a very uniform diameter of less than 1 mm. The container for the liquid should be at 8 cm in diameter and the liquid must wet the capillary tube with a contact angle zero. This method is primarily useful for pure liquids and is capable of high accuracy at relatively low cost.

## Capillary Action

Capillary action is due to surface tension. When a vertical capillary tube, open at each end, is lowered partially into water, water rises up the tube. The level of water in the tube becomes higher than the level outside. The water rises up to a level which can just be supported by surface tension. The water in the tube in contact with the glass is acted on by the force of the glass molecule which is equal to the surface tension force.

The height $h$ of liquid column is given by

$h$ = $\frac{2T \cos \theta}{\rho g r }$

Where,

$T$ - Surface tension
$g$ - Acceleration due to gravity
$\rho$ - Density of the liquid
$\theta$ - Constant angle
$r$ - Radius of the tube

## Units

The SI unit of the surface tension is N/m. In the C.G.S system the unit is dyne/cm. The dimensional formula of surface tension is calculated as follows.

T = $\frac{Force}{Length}$

By using dimensional notations,

T = $\frac{MLT^{-2}}{L}$

T = $MLT^{-2} \times L^{-1}$
T = $MT^{-2}$

## Examples

Some important examples of phenomenon of surface tension are as follows.

• Rain drops
• Rise of sap in a tree
• Capillary rise and capillary siphoning
• Collection of dust particles on water surface
• Break up of liquid jets

## How to Determine Surface Tension?

Let us discuss some problems of surface tension.

### Solved Examples

Question 1: Calculate the surface tension of water with density 1000 kg/m3 and the radius and capillary rise is 1 mm and 6.2 cm respectively?

Solution:

Given parameters are,
$\rho$ = 1000 kg/m3, g = 9.8m/s, h = 6.2 cm and b = 1 mm
Equation of surface tension in capillary method is,

$\Delta \rho gh$ = $\frac{2\gamma }{b}$

$\gamma$ = $\frac{b\Delta \rho gh}{2}$

$\gamma$ = $\frac{1\times10^{-3}\times1000\times9.8\times6.2\times10^{-2}}{2}$ = 0.3038N/m

Question 2: Calculate the surface tension of a liquid with density 13534 kg/m3 and the radius and capillary rise is 0.5 mm and 8 cm respectively?
Solution:

Given parameters are,
$\rho$ = 13534 kg/m3, g = 9.8m/s, h = 8 cm and b = 0.5 mm
Equation of surface tension in capillary method is,

$\Delta \rho gh$ = $\frac{2\gamma }{b}$

$\gamma$ = $\frac{b\Delta \rho gh}{2}$

$\gamma$ = $\frac{0.5\times10^{-3}\times13534\times9.8\times8\times10^{-2}}{2}$ = 2.652N/m