Surface tension and capillarity
What is surface tension?
It is often in daily life
that
For a liquid jet of radius r and length l.
If the jet is cut into two halves, then the forces acting on one half will be
those due to pressure intensity p on the projected area (2rl) and
the tensile force due to surface tension σ acting along the two sides (2l).
On equating these forces
- A blood drop forms a hump on a horizontal glass.
- Drop of mercury rolls like a spherical steel ball over a smooth surface.
- Water from rain or dew beads up into small drops on flower petals.
- A soap bubble released in to air forms a spherical shape.
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| Water on leaves |
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| Mercury on glass |
All the above observances
are the examples of surface tension. A liquid droplet (or bubble) behaves like
a small spherical balloon filled with liquid (or air). The surface of a liquid
acts like a stretched elastic membrane under tension. The tensile force acts
parallel to the surface and is due to the attractive forces between the
molecules of the liquid. The magnitude of this force per unit length is called
surface tension. It is denoted by Greek letter sigma with subscript “s” as “σs”.
It is usually expressed as N/m. This phenomenon is also known as surface energy
and is expressed in the equivalent unit of N.m/m2 or J/m2.
Values of surface tension of
water and mercury:
- The value of surface tension of water in contact with air varies from 0.0736 N/m at 19˚c to 0.0589 N/m at 100˚c.
- The value of surface tension of mercury with air in contact, is about 0.4944 N/m at normal temperature.
By
equating the force due to surface tension acting on the liquid with the force
due pressure, the pressure due to liquid can be
Determination of
pressure intensity inside a droplet
Taking a hemispherical
section of droplet, the pressure will act normal to the cross-section area of
droplet and surface tension will act along the circumference.
Determination of pressure intensity
inside a soap bubble
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. The
pressure acting on the hemispherical section of the soap bubble is same as in
the case of droplet. Thus, equating these two forces for equilibrium, we have
Determination of pressure intensity
inside a liquid jet
For a liquid jet of radius r and length l.
If the jet is cut into two halves, then the forces acting on one half will be
those due to pressure intensity p on the projected area (2rl) and
the tensile force due to surface tension σ acting along the two sides (2l).
On equating these forces
What is cohesion and adhesion?
The inter-molecular attraction force
between the molecules of the same liquid, is cohesive force and the phenomenon
is called cohesion.
The inter-molecular attraction forces between
the molecules of liquid and the molecules of solid surface is called adhesive
force and the phenomenon is called adhesion.
Another interesting effect due to
cohesion and adhesion or surface tension is capillary effect.
There are various examples of capillary
effect in nature around us.
Capillarity in plant: water from underground
and roots of plants rise in the tree due to capillary effect.
Capillary rise in soil: there are many
sources of water in nature in which water comes to ground from the very depth
without any pumping action.
What is capillary rise or capillary
effect?
When the molecules of certain liquid comparatively
possess greater affinity for solid molecules or in other words when a liquid
has greater adhesion than cohesion, then the capillary rise will be observed. And
when cohesion is greater than adhesion then capillary fall will be observed.
Capillary action of water and mercury
When the water is placed inside a glass
container, water slightly curves up at edges where it touches the glass surface.
This happens because for glass, water has greater adhesion than cohesion. This effect
is expressed by saying that water wets the glass (sticking to it).
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| Capillary rise of water and capillary fall of mercury |
Whereas, when mercury is placed inside a
glass container, mercury curves down at the edges because for glass, mercury has
greater cohesion than adhesion so in other words mercury does not wet the
glass.
Contact angle (or wetting angle) Φ: the
angle that the tangent to the liquid surface makes with the solid surface at
the point of contact is defined as contact angle or the wetting angle. It denoted
by Geek capital letter Φ. The surface tension force acts along this tangent
line toward the solid surface.
A liquid will wet the surface if Φ < 90º;
And will not wet the surface if Φ > 90º.
Determination of surface tension by
capillary rise method:
The magnitude of the capillary rise in a
circular tube can be determined from a force balance on the cylindrical liquid
column of height h in the tube.
Weight of the liquid column = force due
to surface tension
Weight of liquid column = mg = ρ.V.g = ρ.g.(π.R2.h)
Force due to surface tension = 2.π.R.σs.cosΦ
(vertical component of surface tension =
σ.cosΦ)
On equating these forces, we get
Where R = radius of tube
Formula for capillary
rise and fall
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