Surface tension | capillarity Effects

In this article we are going to discuss about surface tension and Capillarity Effects in brief.

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Surface tension:

Surface tension is defined as the property of liquid surface caused by the cohesion force( attraction between the molecule of same liquid) at free surface.
At a free surface of a liquid there is no any liquid molecules to balance the force of the liquid molecules below it.
The force is normal to the liquid surface. At the free surface a thin layer of molecules is formed
Surface tension is denoted by the σ
SI units of surface tension = N/m
MKS units of surface tension = kgf/m

Some examples of surface tension phenomenon-

1.Rain drop become spherical

2. Rise of sap wood in tree

3. Ants can flot in surface of water

4. Capillary rise and capillary fall

Fig. Surface tension

Surface tension on liquid droplet.

a droplet of liquid of radius ‘r’ on surface of droplet , the tensile force due to surface tension will be acting .

Let σ = Surface of liquid

p = Pressure intensity inside the liquid droplets (in excess of the outside pressure intensity )

d = Dia. Of droplet.

Let , droplet cut into 2 halves . the force acting on one half (say left half) will be

Fig.Surface tension on liquid droplet

1)Tensile force due to surface tension

Acting around the circumference of the cut portion as shown in fig. and this is equal to

= σ × Circumference

= σ × π d

2) pressure force on area

π/4 ×d^2 = p× π/4×d^2

These forces will be equal and opposite under equilibrium condition that is

p ×π/4 d^2 = σ × π d
p = σ × π d /π/4 ×d^2
= 4σ /d

So pressure intensity inside the droplet will increases with decrease in diameter of droplet.

2.Surface tension on hollow bubble.

Hollow bubble ( i.e soap bubble in air) has two surfaces in contact with air ,one inside and others outside.
These two surfaces are subjected to surface tension. In such case, we have

p × π/4 ×d^2 = 2×(σ × πd)
p = 2×(σ × πd) / π/4 d^2
= 8σ /d

Fig.Surface tension of hollow bubble

3.Surface tension on a liquid jet.

Consider a liquid jet of diameter 'd' and length 'l'

Let ,

p = Pressure intensity inside the liquid jet above the

Outside pressure.

σ = Surface tension of the liquid.

Consider equilibrium of the semi jet ,

force due to pressure = p × Area of semi jet

= p × L × d

Force due to surface tension = σ × 2L

Equating the forces, we have

p × L × d = σ × 2L
p = σ × 2L / L × d

Fig.Surface tension on a liquid jet

Capillarity

Capillarity is a phenomenon of rise or fall of liquid surface in small thin glass tube above or below general level of liquid when the tube is held vertically in the liquid .
the rise in liquid surface is known as capillary rise. the fall of the liquid surface is known as capillary depression/fall.
it is expressed in term of cm or mm of liquid .
its value depends upon the specific weight of the liquid , diameter of the tube and surface tension of the liquid .

Fig.Capillarity Effects

1. Expression for capillary rise

Consider glass tube of dia ‘d’ inserted in liquid & opened at both end .
the level of liquid will rise above in the tube .

Let, h =height of liquid in small tube .

In equilibrium state,

Fig.capillary rise

the wt of liquid of height h is balanced by the force at the surface of the liquid in the tube .but the force at the surface of the liquid in the tube is due to surface tension .

σ = Surface tension of liquid

θ = Angle of contact between liquid and glass tube .

The wt of height h in tube =(Area of tube × h) × p × g

= π/4 ×d^2 × h × g ×p …(i)

where p = Density of fluid

Vertical component of surface tension force

= ( σ × circumference ) × cos θ
= σ × π d × cos θ …(ii)

For equilibrium , equation (i) and (ii), we get

π /4× d^2 × h × g ×p = σ × π d × cos θ
h = σ × π d × cos θ / π/4× d^2 × g ×p
= 4 σ cos θ / g × p × d

The value of θ between water and clean glass tube is approximately = zero,

hence cos θ = unity .

The rise in water is given by -

h = 4 σ/ g × p × d

2. Expression for capillary fall

If glass tube dipped in mercury, the level of mercury in tube will be lower than general level of outside liquid .

let h = Height of depression In tube .

in equilibrium , two forces are acting on the mercury inside the tube .

1. due to surface tension acting in downward direction and equal to

= σ × π d × cos θ …(i)

2. due to hydrostatic force acting upward and is equal to intensity of pressure at a depth ‘h’ × Area

= p × π/4× d^2 = Pg × h × π/4 ×d^2 …(ii)

{ since, P = pgh }

Now equating equation (i) and (ii)

σ × π d × cos θ = P g h × π/4 d^2
h = 4 σ cos θ / p g d

Value of θ for Mercury and glass is 128°.

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