Surface Tension :
We will learn that A liquid has the property that its free surface tends to attain minimum possible area and is therefore, in a state of tension, somewhat like a stretched membrane. It is a molecular phenomenon based on electromagnetic inter-action between the molecules. The force of contraction at right angles to an imaginary line of unit length, tangential to the surface of liquid, is called its surface tension.
Surface Tension Introduction
Surface tension of a liquid is measured by the force acting per unit length on either side of an imaginary line drawn on the free surface of liquid. The direction of this force being perpendicular to the imaginary line and tangential to the free surface of liquid. So, if
F
is the force acting on one side of imaginary line
AB
of length
l
, then mathematically surface tension is
T
=
F
/
l
The S.I. unit of surface tension is newton per metre (Nm
−1
) and dynecm
−1
. The Dimensional formula of surface tension is MT
−2
which is same as that of force constant or spring constant.
Surface Tension depends only on the nature of liquid and is independent of the area of surface or length of line considered. It is a scalar as it has a unique direction which is not to be specified.
Small liquid drops tend to be spherical due to surface tension, because for a given volume, sphere has the minimum surface area. It follows that in order to increase the surface area of liquid, work has to be done against this force of contraction. This work is stored in the surface as its potential energy.
Explanation To Surface Tension
Laplace explained the phenomenon of surface-tension on the basis of inter-molecular forces. We know that if the distance between two molecules is less than the molecular range
c
(≈ 10
−9
meter) then they attract each other, but if the distance is more than this range, then attraction becomes negligible.
Therefore, if we draw a sphere of radius
c
with a molecule as center, then only those molecules which are enclosed within this sphere can attract, or be attracted by, the molecule at the center of the sphere. This is called ‘sphere of molecular activity’.
In order to understand the tension existing in the free surface of a liquid, let us consider four liquid molecules like
A
,
B
,
C
and
D
along with their spheres of molecular activity as shown in Figure.
-
The molecule
D
is well inside the liquid and so it is attracted equally in all directions. Hence the resultant force acting on molecule
D
is zero.
-
The sphere of molecule
C
is just below the liquid surface and the resultant force on it is also zero.
-
The molecule
B
which is a little below the liquid surface has its sphere of molecular activity partly outside the liquid. Thus, the number of liquid molecules in upper half (attracting in downward). Hence the molecule
B
experience a resultant downward force.
-
The molecule
A
is at the surface of the liquid, so that its sphere of molecular activity is half outside the liquid and half inside. So it experiences a maximum downward force.
-
Hence all the molecules situated between the surface and a plane
XY
, distance c below the surface, experience a resultant downward cohesive force.
-
When the surface area of liquid is increased, molecules from the interior of the liquid rise to the surface.
-
As these molecules reach near the surface, work is done against the (downward) cohesive force. This work is stored in the molecule in the form of potential energy.
-
Thus, the potential energy of the molecules lying at the surface is greater than that of the molecules in the interior of the liquid.
Since we know that a system is in stable equilibrium when it has minimum potential energy. So, in order to have minimum potential energy, the liquid surface tends to have minimum number of molecules in it (which is possible if the free surface tries to attain the minimum surface area). In other words, the surface tends to contract to a minimum possible area. This tendency of the free surface of the liquid is exhibited as surface tension.
Surface Tension Example
Example 1:
Take a ring of wire and dip it in a soap solution. When the ring is taken out, a soap film is formed. Place a loop of thread gently on the soap film. Now, prick a hole inside the loop. The thread is radially pulled by the film surface outside and it takes a circular shape.
Ans.
Before the pricking, there were surfaces both inside and outside the thread loop. Surfaces on both sides pull it equally and the net force is zero. Once the surface inside was punctured, the outside surface pulled the thread to take the circular shape so that area outside the loop becomes minimum (because for given perimeter area of circle is maximum).
Example 2:
A piece of wire is bent into a
U
-shape and a second piece of wire slides on the arms of the
U
. When the apparatus is dipped into a soap solution and removed, a liquid film is formed.
Ans.
The film exerts a surface tension force on the slider and if the frame is kept in a horizontal position, the slider quickly slides towards the closing arm of the frame. If the frame is kept vertical, one can have some weight to keep it in equilibrium. This shows that the soap surface in contact with the slider pulls it parallel to the surface.
Example 3:
Needle supported on water surface
Ans.
Take a greased needle of steel on a piece of blotting paper and place it gently over the water surface. Blotting paper soaks water and soon sinks down but the needle keeps floating. The floating needle causes a little depression. The forces
F
and
F
due to surface tension of the curved surface are inclined as shown in Fig. The vertical components of these two forces support the weight of the needle.
Example 4:
Small mercury droplets are spherical and larger ones tend to flatten.
Ans.
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. Here the shape is such that the sum of the gravitational potential energy and the surface potential energy must be minimum. Hence the centre of gravity moves down as low as possible. This explains flattening of the larger drops.
Surface Energy
A liquid molecule completely inside the liquid is surrounded by similar molecules on all sides and hence experiences no resultant force on it, whereas a molecule at the free surface of liquid is surrounded by similar liquid molecules on one side of the free surface (while on the other side it may be surrounded by air molecules or the molecules of the vapour of the liquid etc). Since air or liquid vapours have negligible density compared to liquid, so they exert only a small force on the molecules at the free surface. Hence, a resultant inward force acts on molecule lying at the surface. This inward force tries to pull the molecule into the liquid due to which the free surface layer remains in microscopic turbulence in which the molecules are pulled back from the free surface layer to the liquid bulk and hence new molecules from the liquid bulk come to the surface in an attempt to fill the empty space.
When a molecule is taken from inside the liquid to the free surface, then work has to be done against the inward resultant force for moving the molecule up to the free surface. The potential energy is increased due to this work. A molecule at the free surface has greater potential energy than a molecule completely inside the liquid. This extra energy possessed by the free surface layer is called the surface energy
Relation Between Surface Energy And Surface Tension
Tension, let us consider a
U
-shaped frame that guides a sliding wire on its arm. Let the arrangement be dipped in a soap solution, then taken out and placed in a horizontal position as shown in Figure.
We may think that the soap film formed is extremely thin, however at the molecular scale its thickness is not ignorable as it may possess several hundred thousand molecular layers. So, we say that the soap film has two free surfaces both of which are in contact with the sliding wire and hence exert forces of surface tension on the wire.
If
T
be the surface tension of the soap solution and
l
be the length of the sliding wire, then each surface will pull the wire parallel to itself with a force
Tl
and hence the net force of pull
F
on the wire due to both the surfaces is order to keep the wire in equilibrium, we have to apply a constant external force
F
ext
equal and opposite to
F
.
Now, let the wire be slowly pulled out (so that change in kinetic energy is zero) with the help of external force through a distance
x
so that the area of the frame is increased by Δ
A
=
lx
. Since the film has two free surfaces of the soap solution, hence total change in surface area of the film is 2Δ
A
= 2
lx
.
The work done by the external force in moving the wire through
x
is
W
ext
=
F
ext
x
= (2
Tl
)
x
=
T
(2
l
x
) = 2
T
Δ
A
Since there is no change in kinetic energy, so the work f done by external force is stored as the change in potential energy Δ
U
of the surface, so we have
Δ
U
=
W
ext
= 2
T
Δ
A
…(1)
where, Δ
A
=
lx
is the change in surface area of each free surface.
So, we observe that the surface tension of a liquid is equal to the surface energy per unit change in surface area.
So, from equation (1), we observe that the work done by an external force to increase the surface area of the film by Δ
A
total
is
W
ext
=
T
Δ
A
total
= 2
T
Δ
A
each surface
However, for the case where we may have only one free surface, then Δ
A
total
= Δ
A
and hence
W
ext
=
T
Δ
A
total
=
T
Δ
A
The SI unit of surface tension is also written as Jm
–2
and it can also be verified that 1 Nm
–1
= 1 Jm
–2
.
Force Of Cohesion
The force of attraction between the molecules of the same substance is called cohesion. In case of solids, the force of cohesion is very large and due to this solids have definite shape and size. On the other hand, the force of cohesion in case of liquids is weaker than that of solids. Hence, liquids do not have definite shape but have definite volume. The force of cohesion is negligible in case of gases. Because of this, gases have neither fixed shape nor fixed volume.
Force Of Cohesion Examples
(i)
Two drops of a liquid coalesce into one when brought in mutual contact because of the cohesive force.
(ii)
It is difficult to separate two sticky plates of glass wetted with water because a large force has to be applied against the cohesive force between the molecules of water.
(iii)
It is very difficult to break a drop of mercury into small droplets because of large cohesive force between mercury molecules.
Force Of Adhesion
The force of attraction between molecules of different substances is called adhesion.
Force Of Adhesion Examples
(i)
Adhesive force enables us to write on the black board with a chalk.
(ii)
Adhesive force helps us to write on the paper with ink.
(iii)
Large force of adhesion between cement and bricks helps us in construction work.
(iv)
Due to force of adhesion, water wets the glass plate.
(v)
Fevicol and gum are used in gluing two surfaces together because of adhesive force.
