Applied Physics I: Chapter 2: Properties of Matter - Viscosity and Surface Tension
Surface Tension of liquid by Drop Weight Method
Theory, Principle, Description, Equation
This method is based on the principle that the weight of a drop falling slowly out of a capillary held vertically is directly proportional to its surface tension. The drop falls when its weight just exceeds surface tension.
SURFACE
TENSION OF LIQUID BY DROP WEIGHT METHOD
Theory
The
apparatus used for determining the surface tension of a liquid is known as stalagmometer. The drop weight method
is a technique used to determine the surface tension by measuring the weight of
a liquid drop falling from a capillary tube.
This
method provides a simple way to experimentally determine the surface tension of
liquids by balancing the gravitational force acting on the drop with the
surface tension force.
Principle
This
method is based on the principle that the weight of a drop falling slowly out
of a capillary held vertically is directly proportional to its surface tension.
The drop falls when its weight just exceeds surface tension.
Description
Let
us consider the capillary tube with liquid drop (or) bubble just about to fall,
as shown in Fig 2.5.
Here,
we can see that the upward pull due to surface tension forces keep the small
drop of the liquid in equilibrium, before its gets detached by overcoming the
downward force.
Downward force
The
excess pressure inside the drop when compared to outside atmospheric pressure =
σ / r
Here,
the area of cross section = πr2
∴ Downward force =
Excess pressure × Area of cross section
∴ Downward force = σ/r (πr2)
As
the weight (mg) of the drop is also acting vertically downwards we can write,
Downward
force = σ/r (πr2) + mg
Downward force = σπr + mg
Upward pull
The
upward pull due to surface tension = 2πrσ
Where
'r' is the radius of the liquid drop
Upward pull = 2πгσ
At equilibrium
Downward
force = Upward pull
i.e.,
Equation (1) = Equation (2)
∴ σπr + mg = 2πrσ
(oг)
2πrσ ‒ πrσ = mg
(oг)
πrσ (2‒1) = mg
∴
πгσ = mg
Surface
tension σ = mg / πr
The
equilibrium of the drop at the instant of its detachment is not static. Hence,
by considering the dynamical aspect of the drop into account, we can rewrite
the formula as
Surface
tension σ = mg / 3.8r .....
(4)
Note:
Lord Rayleigh arrived at equation (4) by taking the dynamical aspect into
account.
Applied Physics I: Chapter 2: Properties of Matter - Viscosity and Surface Tension : Tag: Applied Physics : Theory, Principle, Description, Equation - Surface Tension of liquid by Drop Weight Method
Applied Physics I: Chapter 2: Properties of Matter - Viscosity and Surface Tension
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