Capillarity and its derivations for capillary height and capillary fall

1. Capillarity
By
Rampal Singh Ojha
Assistant Professor
Department of Mechanical Engineering, Rai University
B.E.(Mechanical),M.tech(Production)
GATE 2011,2012,2015

2. Kerosene Lamp Lamp
Wetting of sponge

4.  Ability of a liquid to flow in narrow spaces without the
assistance of, and in opposition to, external forces like gravity
 Capillary action is sometimes called capillarity, capillary
motion, or wicking

6. REASON
Capillarity occurs because of
intermolecular forces between the liquid and
surrounding solid surface. And due to thepressure
of cohesion and adhesion which cause the liquid
work against gravity.

7.  Capillarities are of two types
Capillarity rise (adhesion > cohesion)
Capillarity fall (adhesion < cohesion)

8. Capillary Rise
Let σ = Surface tension of
liquid.
ϴ = Angle of contact between
the glass tube and the liquid
surface.
h = Height of liquid column in
glass tube.
The weight of liquid of height h
in the tube = Volume x ρ x g
= (π/4)d2 x h x ρ x g
Here ρ = density of liquid
g = acceleration due to gravity.

9. Capillary Rise
The vertical component of surface
tensile force = surface tension x
circumference x cosϴ
= σ x πd x cosϴ
At equilibrium, the weight of liquid
balanced by the vertical component of
tensile force.
For water and glass tube, the angle ϴ is almost zero. ie
cosϴ ≈ 1
Then the equation for capillary rise of water in the glass
tube is h = 4 σ /(ρgd)

10. Capillarity Fall
Let h = height of capillary depression.
The hydrostatic force on liquid =
Intensity of pressure at depth h x Area
= ρ x g x h x (π/4)d2
Surface tension acting downward =
Surface tension x circumference x
cosϴ
= σ x πd x cosϴ
Equating two forces, we get

11. Lubricating oil spread easily on all parts because of their low
surface tension.
Cotton dresses are preferred in summer because cotton dresses
have fine pores which act as capillaries for sweat.
Dirt get removed when detergents are added while washing
clothes because surface tension of water is reduced.

12. The absorption of ink by a blotting paper is due to
capillary action, as the blotting paper is porous. When
it is placed over the ink, the ink raises into the pores.
Also rise of oil in the wick of a lamp is due to capillary
action.
If one end of a towel is dipped into a bucket of water
and the other end hangs over the bucket, the entire
towel soon becomes wet due to capillary action.
Supply of water to the leaves at the top of even a tall
tree is through capillary rise.