PHY-1201 AAA

Surface Tension
Surface tension is measured as the energy required to increase the surface area of a liquid by a
unit of area. The surface tension of a liquid results from an imbalance of intermolecular
attractive forces, the cohesive forces between molecules:
• A molecule in the bulk liquid experiences cohesive forces with other molecules in all
directions.
• A molecule at the surface of a liquid experiences only net inward cohesive forces.
A microscopic view of water illustrates the difference between molecules at the surface of a
liquid and water molecules within a liquid.

The molecules at the surface of this The unbalanced attraction of molecules

sample of liquid water are not at the surface of a liquid tends to pull
surrounded by other water molecules. the molecules back into the bulk liquid
The molecules inside the sample are leaving the minimum number of
surrounded by other molecules. molecules on the surface. It required
energy to increase the surface area of a
liquid because a larger surface area
contains more molecules in the
unbalanced situation.
Adhesive Forces
Forces of attraction between a liquid and a solid surface are called adhesive forces. The
difference in strength between cohesive forces and adhesive forces determine the behavior of
a liquid in contact with a solid surface.
• Water does not wet waxed surfaces because the cohesive forces within the drops are
stronger than the adhesive forces between the drops and the wax.
• Water wets glass and spreads out on it because the adhesive forces between the liquid
and the glass are stronger than the cohesive forces within the water.
Cohesive Forces
Cohesion, also known as cohesive attraction or cohesive force, is the action or property of
molecules adhering to one another due to mutual attraction.

1
PHY-1201 AAA

The force of attraction between two comparable substances or molecules is known as the
cohesion force. Cohesion is exemplified by water. Each water molecule makes hydrogen bonds
with molecules next to it.
Formation of a Meniscus

When liquid water is confined in a tube, Mercury does not wet glass - the
its surface (meniscus) has a concave cohesive forces within the drops are
shape because water wets the surface stronger than the adhesive forces
and creeps up the side. between the drops and glass. When
liquid mercury is confined in a tube, its
surface (meniscus) has a convex shape
because the cohesive forces in liquid
mercury tend to draw it into a drop.

Capillary Action
• Capillary action is the rise of a liquid that wets a tube up the inside of a small diameter
tube (i.e., a capillary) immersed in the liquid.
• The liquid creeps up the inside of the tube (as a result of adhesive forces between the
liquid and the inner walls of the tube) until the adhesive and cohesive forces of the
liquid are balanced by the weight of the liquid.
• The smaller the diameter of the tube, the higher the liquid rises.
Formula for Surface Tension
Mathematically, the surface tension is defined as the force (F) acting on the surface and the
length (l) of the surface, so is given as:
T=F/l
Also, the ratio of the work done (W) and the change in the area of the surface (A) is termed
surface tension.
T=W/A

2
PHY-1201 AAA

Unit and Dimension of Surface Tension

Its SI unit is N/m or J/m.
The dimensional formula of Surface Tension is [MT-2].
Causes of Surface Tension
The effect known as surface tension is caused by the cohesive forces between liquid molecules.
Since the molecules at the surface lack like molecules in both directions, they cohere more
closely to those specifically aligned with them on the surface. This creates a surface “film” that
makes moving an object across the surface more difficult than moving it while fully submerged.

Assume a jar is filled with water; the water molecules can be found in two positions in this jar:
First, beneath the water, and second, on the surface of the water. Since there are no molecules
above these molecules, the molecules at the water’s surface are unbalanced. As a result, only
the molecules below will be attracted. As a result, a thin crust will form on the liquid’s upper
surface. Because of this thick layer, a form of stress is generated, which is known as Surface
Tension. These phenomena can also be explained in terms of energy.
What is Surface Energy?
Surface energy measures the breakdown of intermolecular bonds caused by the formation of a
surface. Surface free energy and interfacial free energy are other names for it. Surface energy
is defined as the work done per unit area by the force that forms the new surface.
When the free surface area of a liquid is increased, effort must be done against the force of
surface tension. This work is stored as potential energy on the liquid surface. This increased
potential energy per unit area of the free surface of the liquid is referred to as surface energy.
Mathematically, the surface energy is defined as:
Surface energy = Surface tension × Change in the surface area
Or, ES = T × ΔA
Where, T denotes surface tension and ΔA denotes an increase in surface area.
Therefore, the SI unit of surface energy is Nm-2 and the dimensional formula is [MT– 2].

3
PHY-1201 AAA

What is Angle of Contact?

The angle of contact is defined as the angle subtended between the tangents drawn at the liquid
surface and the solid surface within the liquid at the point of contact, or it is defined as the
angle subtended between the tangents drawn at the liquid surface and the solid surface within
the liquid at the angle of contact (θ).

The angle of contact depends on the following factors:

• The nature of the liquid, the solid with which it comes into contact.
• The medium that exists above the free surface of the liquid.
• As the temperature of the liquid rises, so does the angle of contact.
• When soluble impurities are added to a liquid, the angle of contact drops.
Applications of Surface Tension
1. The spherical shape of droplets: The small droplets of fluid are spherical due to
surface tension. The molecules of water tend to stick together due to intramolecular
force, and the energy of molecules which are located on the surface of droplets contains
higher energy and try to push the other molecule to the center of the droplet. Due to this
the drop makes the shape that contains the least surface area and the spherical shape is
best for the least surface area, that’s why the droplets of water and raindrops are
spherical.
2. Fire polishing of glass: The method of polishing glass or thermoplastic with the help
of fire or flame is called Fire Polishing. When we heat a glass material in flames, the
glass surface starts melting. But due to surface tension, it starts to become soft and
smooth which makes the glass very flat and smooth. This method is most applicable to
flat external surfaces. Flame polishing is frequently in acrylic plastic fabrication
because of its high speed compared to abrasive methods. In this application, an
oxyhydrogen torch is typically used, one reason being that the flame chemistry is
unlikely to contaminate the plastic.
3. The rise of liquids in Capillary Tubes: A tube whose radius is very short and uniform
is called a capillary tube. When an open capillary is dipped in water. The water rises to
some height in the capillary tube.

4
PHY-1201 AAA

Factors affecting Surface Tension

• If the solute is highly soluble in the fluid, the surface tension of the fluid would increase.
And if the solute is less soluble in the fluid, then the surface tension of the fluid would
decrease.
• If there are dust particles or any lubricant present on the surface of the fluid, the surface
tension of the fluid decreases.
• Increasing the temperature reduces the surface tension of the fluid. And decreasing the
temperature increases the surface tension.
FAQs on Surface Tension
Question 1: What is the Unit of Surface Tension?
Answer: The Unit of Surface Tension is N/m or J/m.
Question 2: What is the cause of Surface Tension?
Answer: The effect known as surface tension is caused by the cohesive forces between liquid
molecules. Since the molecules at the surface lack like molecules in both directions, they
cohere more closely to those specifically aligned with them on the surface. This creates a
surface “film” that makes moving an object across the surface more difficult than moving it
while fully submerged.
Question 3: Why soap is helpful in cleaning clothes?
Answer: Soap reduces the surface tension of water. So, water penetrates into small areas of
clothing and removes stains. So, soap is helpful for washing clothes.
Question 4: Why do we use Toothpaste to clean teeth?
Answer: Toothpaste froth reduces surface tension. Hence, it clears the teeth by failing over a
large area of teeth.
Question 5: Why are small drops of mercury flat and big drops flattened?
Answer: There are two types of forces acting on mercury droplets. On small droplets, the
surface tension is higher than the gravitational force, so it is rounded but on big droplets, the
surface tension is lower than gravitational force, so it is flattened.
Examples of Surface Tension
• Drops of water: When using a water dropper, the water does not flow in a continuous
stream, but rather in a series of drops. The shape of the drops is caused by the surface
tension of the water. The only reason the drop of water isn't completely spherical is that
the force of gravity pulling down on it. In the absence of gravity, the drop would
minimize the surface area in order to minimize tension, which would result in a
perfectly spherical shape.
• Insects walking on water: Several insects are able to walk on water, such as the water
strider. Their legs are formed to distribute their weight, causing the surface of the liquid
to become depressed, minimizing the potential energy to create a balance of forces so
that the strider can move across the surface of the water without breaking through the

5
PHY-1201 AAA

surface. This is similar in concept to wearing snowshoes to walk across deep snowdrifts
without your feet sinking.
• Needle (or paper clip) floating on water: Even though the density of these objects is
greater than water, the surface tension along the depression is enough to counteract the
force of gravity pulling down on the metal object. Click on the picture to the right, then
click "Next," to view a force diagram of this situation or try out the Floating Needle
trick for yourself.
Anatomy of a Soap Bubble
When you blow a soap bubble, you are creating a pressurized bubble of air which is contained
within a thin, elastic surface of liquid. Most liquids cannot maintain a stable surface tension to
create a bubble, which is why soap is generally used in the process ... it stabilizes the surface
tension through something called the Marangoni effect.
When the bubble is blown, the surface film tends to contract. This causes the pressure inside
the bubble to increase. The size of the bubble stabilizes at a size where the gas inside the bubble
won't contract any further, at least without popping the bubble.
In fact, there are two liquid-gas interfaces on a soap bubble - the one on the inside of the bubble
and the one on the outside of the bubble. In between the two surfaces is a thin film of liquid.
The spherical shape of a soap bubble is caused by the minimization of the surface area - for a
given volume, a sphere is always the form which has the least surface area.
Excess of pressure inside a liquid drop, a soap bubble, and an air bubble
As it is discussed earlier, the free surface of a liquid becomes curved when it has contact with
a solid. Depending upon the nature of liquid-air or liquid-gas interface, the magnitude of
interfacial surface tension varies. In other words, as a consequence of surface tension, the above
such interfaces have energy and for a given volume, the surface will have a minimum energy
with least area. Due to this reason, the liquid drop becomes spherical (for a smaller radius).
When the free surface of the liquid is curved, there is a difference in pressure between the inner
and outer the side of the surface (Figure 7.27).
i) When the liquid surface is plane, the forces due to surface tension (T, T) act
tangentially to the liquid surface in opposite directions. Hence, the resultant force
on the molecule is zero. Therefore, in the case of a plane liquid surface, the pressure
on the liquid side is equal to the pressure on the vapor side.
ii) When the liquid surface is curved, every molecule on the liquid surface experiences
forces (FT, FT) due to surface tension along the tangent to the surface. Resolving
these forces into rectangular components, we find that horizontal components
cancel out each other while vertical components get added up. Therefore, the
resultant force normal to the surface acts on the curved surface of the liquid.
Similarly, for a convex surface, the resultant force is directed inwards towards the
center of curvature, whereas the resultant force is directed outwards from the center
of curvature for a concave surface. Thus, for a curved liquid surface in equilibrium,
the pressure on its concave side is greater than the pressure on its convex side.

6
PHY-1201 AAA

Excess of pressure inside a bubble and a liquid drop:

The small bubbles and liquid drops are spherical because of the forces of surface tension. The
fact that a bubble or a liquid drop does not collapse due to the combined effect indicates that
the pressure inside a bubble or a drop is greater than that outside it.

1) Excess of pressure inside air bubble in a liquid

Consider an air bubble of radius R inside a liquid having surface tension T as shown in Figure
7.28 (a). Let P1 and P2 be the pressures outside and inside the air bubble, respectively. Now,
the excess pressure inside the air bubble is ΔP = P1 − P2.

In order to find the excess pressure inside the air bubble, let us consider the forces acting on
the air bubble. For the hemispherical portion of the bubble, considering the forces acting on it,
we get,
i. The force due to surface tension acting towards right around the rim of length 2πR is
FT = 2πRT
ii. The force due to outside pressure P1 is to the right acting across a cross sectional area
of πR2 is FP1= P1πR2
iii. The force due to pressure P2 inside the bubble, acting to the left is FP2= P2πR2.
As the air bubble is in equilibrium under the action of these forces, FP2= FT + FP1

7
PHY-1201 AAA

P2πR2 = 2πRT + P1πR2

(P2 − P1) πR2 = 2πRT

2) Excess pressure inside a soap bubble

Consider a soap bubble of radius R and the surface tension of the soap bubble be T as shown
in Figure 7.28 (b). A soap bubble has two liquid surfaces in contact with air, one inside the
bubble and other outside the bubble. Therefore, the force on the soap bubble due to surface
tension is 2×2πRT. The various forces acting on the soap bubble are,
i. Force due to surface tension FT=4πRT towards right
ii. Force due to outside pressure, FP1= P1πR2 towards right
iii. Force due to inside pressure, FP2= P2πR2 towards left
As the bubble is in equilibrium, FP2= FT + FP1
P2πR2 = 4πRT + P1πR2
(P2 − P1) πR2 = 4πRT

3) Excess pressure inside the liquid drop

Consider a liquid drop of radius R and the surface tension of the liquid is T as shown in Figure
7.28 (c).

8
PHY-1201 AAA

The various forces acting on the liquid drop are,

i. Force due to surface tension FT=2πRT towards right
ii. Force due to outside pressure, FP1= P1πR2 towards right
iii. Force due to inside pressure, FP2= P2πR2 towards left
As the drop is in equilibrium,
FP2= FT + FP1
P2πR2 = 2πRT + P1πR2
= > (P2 − P1) πR2 = 2πRT

Example 7.11 If excess pressure is balanced by a column of oil (with specific gravity 0.8)
4 mm high, where R = 2.0 cm, find the surface tension of the soap bubble.
Solution: The excess of pressure inside the soap bubble is