Surface Tension and Capillarity
Introduction
Due to molecular attraction, liquids possess certain properties such as cohesion and
adhesion. Cohesion means inter-molecular attraction between molecules of the same
liquid. Adhesion means attraction between the molecules of a liquid and the molecules
of a solid boundary surface in contact with the liquid. The property of cohesion enables
a liquid to resist to tensile stress, while adhesion enables it to stick to another body.
Surface Tension
Surface tension is due to unbalanced cohesive forces at the interface of liquid, gases or
between two immiscible liquids.
A liquid molecule on the interior of the liquid body has other molecules on all sides of
it, so that the forces of attraction are in equilibrium and the molecule remain equally
attracted on all the sides. On the other hand a liquid molecule at the surface of the
liquid i.e. at the interface between a liquid and a gas (air) does not have any liquid
molecule above it and consequently there exit a net downward force on the molecule
due to the attraction of the molecules below it.
Liquid
surface
Molecule A which is below the free surface of liquid is surrounded by various
corresponding molecules and consequently under the influence of balanced cohesive
forces on all sides and hence in equilibrium while molecule B is on the surface of the
liquid due to which it is under the influence of net downward force (unbalanced
cohesive force). This force on the molecules at the liquid surface is normal to the liquid
surface. Due to the attraction of liquid molecules below the surface, a film or a
membrane is formed at the surface which can resist small tensile load. For example: A
small needle placed gently upon the water surface will not sink but will be supported
by the tension at the water surface.
This property of the liquid surface film to exert a tension is called surface tension. It is
denoted by .
Fs
=L
Surface tension is the force required to maintain unit length of the film in equilibrium. It
is a line force and it is expressed as force per unit length. Its SI unit is N/m. It acts
normal to the line drawn on liquid surface.
Note:
1. Surface tension for air water interface at 20°C is 0.0736 N/m.
2. Surface energy per unit area is numerically equal to surface tension.
3. Surface tension is directly dependent on intermolecular cohesive forces.
4. As the temperature rises, cohesive forces decreases and hence the surface tension
decreases.
Applications of Surface tension: The effect of surface tension can be seen in a rain drop
or a liquid droplet (spherical shape of liquid drop is due to surface tension), soap
bubble, floating of leaves on the fluid and liquid jet.
Reason of pressure rise / spherical shape in a liquid droplet: When a droplet is
separated initially from the surface of the main body of liquid, then due to surface
tension there is a net inward force exerted over the entire surface of the droplet which
causes the surface of the droplet to contract from all the sides and results in increasing
the internal pressure within the droplet. This contraction of the droplet continues till the
inward force due to surface tension is in balance with the internal pressure and the
droplet forms in to sphere which is the shape for minimum surface area.
Patm
d
P
P
Patm
Due to the surface tension pressure intensity within a liquid drop, soap bubble and
within a liquid jet increases. This internal pressure which is in excess to the outside
pressure can be determined using following expressions.
1. Pressure inside a liquid drop in excess of atmospheric pressure.
Surface tension,
Fs
=L
Fp
Pressure, P = A
Fs =
L
Fs =
(
FP = P A
)
FP = P
d2
For equilibrium of a liquid drop, Surface tension force = pressure force
Fs = FP
(
P
=
)
=P
d2
Here, p is pressure above atmospheric pressure.
In a liquid drop, surface tension resists pressure force whereas pressure force tries to
burst the droplet.
2. Pressure inside a soap bubble in excess of atmospheric pressure.
A spherical soap bubble has two surfaces in contact with air, one inside and the other
outside, each one of which contributes the same amount of tensile force due to surface
tension. Therefore,
Total surface tension force,
Fs =
L
Fs = 2
(
)
For equilibrium of a soap bubble, Surface tension force = pressure force
Fs = FP
2
P
(
)
=P
d2
=
3. Pressure inside a liquid jet in excess of atmospheric pressure.
Surface tension,
Fp
Pressure, P = A
=
Fs =
(2L)
FP = P A
FP = P
Ld
For equilibrium of a soap bubble, Surface tension force = pressure force
Fs = FP
2
P
( )
=P
Ld
=
Note: Liquid drop : bubble : jet =
:
:
= 2:4:1
Capillarity
Non- Wetting and wetting liquids
Solid body
When a liquid possess, relatively, greater affinity for solid molecules or the liquid which
have greater adhesion than cohesion, then it will wet a solid surface in contact and tend
to rise at the point of contact. Such liquids are called wetting liquids. In this case, the
angle of contact between liquid and the solid surface is less than 90°. An example of
such liquid is water.
For example: If a glass tube of small diameter is partially immersed in water, the water
will wet the surface of the tube and it will rise in the tube to some height, above the
normal water surface. In this case, the water surface is concave upward.
The wetting of solid boundary of tube by water results in creating decrease of pressure
within the water due to which rise in the water surface (within the tube) takes place in
order to maintain the same exact pressure as that in outside surrounding water.
On the other hand, if a liquid has less attraction for solid molecule or in other words the
cohesion predominates over adhesion, then the liquid will not wet the solid surface and
the liquid surface will be depressed at the point of contact. In this case, the angle of
contact between liquid and solid surface is more than 90°. Example of such liquid is
Mercury.
For example: If a glass tube of small diameter is partially immersed in mercury, the
mercury will not wet the surface of the tube in contact and the level of mercury inside
the tube will be depressed or it will be lower than the normal mercury level. In this
case, the mercury surface is concave downward.
The tendency of the mercury to not adhere to the solid surface (tube) results in creating
an increase of pressure across the mercury surface due to which the elevation of the
meniscus (curved mercury surface) in the tube is lowered to the level where the
pressure is same as that in surrounding mercury.
This rise or fall of a liquid when a small diameter tube is immersed in it is known as
capillarity.
Capillary rise is due to adhesion and capillary fall is due to cohesion therefore
capillarity is due to both adhesion and cohesion.
Expression for capillary rise
Weight of risen fluid in tube = specific weight
=ρg(
volume of risen fluid
D2 h )
where, ρ = density of liquid
g = acceleration due to gravity
D = diameter of tube
h= capillary rise
Vertical component of surface tension force, Fs =
For equilibrium,
Vertical component of surface tension force = weight of risen fluid
= ρg(
h=
D2 h )
Note:
1. Lighter liquid experience greater capillary rise.
2. As diameter of tube increases, capillary rise decreases. Hence in order to avoid
capillary effect in manometer tubes, the diameter of the tubes should be more.
Expression for capillary fall
Total internal pressure force = pressure
=ρgh(
Area
D2 )
where, ρ = density of liquid
g = acceleration due to gravity
D = diameter of tube
h= capillary fall
Vertical component of surface tension force, Fs = For equilibrium,
Vertical component of surface tension force = total internal pressure force
-
h=-
= ρgh(
D2 )
Note:
1. Here negative sign in expression indicates fall in liquid mercury.
2. As diameter of tube increases, capillary fall decreases.
References
1. Fluid mechanics by RK Bansal
2. Fluid mechanics by Modi and Seth