Properties of Matter - U4 - Surface Tension -PPT 1

Unit IV – Surface Tension
Ms Dhivya R
Assistant Professor
Department of Physics
Sri Ramakrishna College of Arts and Science
Coimbatore - 641 006
Tamil Nadu, India
1

Surface Tension
Surface Tension:
The tension of the surface film of a liquid caused by
the attraction of the particles in the surface layer
by the bulk of the liquid, which tends to minimize
surface area.
2

Surface Tension
Definition:
It may be defined as the force per unit length of a
line drawn in the liquid surface, acting
perpendicular to it at every point and tending to
pull the surface apart along the line.
Unit: Nm-1
Dimension: MLT-2/L = MT-2
3

Molecular Forces
Intermolecular forces are responsible for most of
the physical and chemical properties of matter.
Adhesive Forces
Force of attraction between molecules of the
different substances is called adhesive force.
Cohesive Forces
Force of attraction between molecules of the same
substance is called cohesive force.
4

Molecular Forces
Range of Molecular Attraction:
The Maximum distance up to which a molecule
exerts a force of attraction on another is called
the range of molecular attraction and is generally
of the order of 10-9m.
Sphere of Influence:
A Sphere with the molecule as centre and the range
of molecular attraction as radius is called the
sphere of influence.
5

Explanation of ST on Kinetic
Theory
6

Explanation of ST on Kinetic
Theory
Molecules A,B,C
Surface Film: Layer of Liquid between PQ & RS
Surface Energy: PE Per unit area of the surface film
7
P Q
R S

Pressure Difference Across a
Liquid Surface
8

Upward force = Downward force
Upward Force = 𝑝𝜋𝑟2
Downward force =𝜎2𝜋𝑟
𝑝𝜋𝑟2 = 𝜎2𝜋𝑟
𝑝 = 2𝜎/𝑟
Soap Bubble
Two surface in contact with air
Downward force =2 × 𝜎2𝜋𝑟 = 4𝜎𝜋𝑟
𝑝 = 4𝜎/𝑟
Excess Pressure inside a liquid
drop
9

Experimental Determination of ST
YouTube Video tutorial Link - Jaegar's Method
10

JAEGAR’S METHOD
Pressure inside Bubble = 𝑝1 = 𝐻 + ℎ1𝜌1𝑔
Pressure outside Bubble = 𝑝2 = 𝐻 + ℎ2𝜌2𝑔
Excess Pressure = p = 𝐻 + ℎ1𝜌1𝑔 − 𝐻 + ℎ2𝜌2𝑔
𝑝 = (ℎ1𝜌1 − ℎ2𝜌2)𝑔
WKT Excess Pressure 𝑝 = 2𝜎/𝑟
2𝜎/𝑟 = (ℎ1𝜌1 − ℎ2𝜌2)𝑔
𝜎 =
1
2
ℎ1𝜌1 − ℎ2𝜌2 𝑟𝑔
11

Adv & Dis Adv
Advantages:
• Angle of contact need not be known
• No Contamination
• No need for large quantity of Liquid
• ST can be determined at various temperatures
Disadvantages:
• Exact Value of radius of bubble when it breaks
cannot be determined
• Drop may not be hemispherical/ size of E
12

Variation of ST with Temp
Unassociated - Individual Molecules and
Associated Liquids – Groups of molecules
Unassociated Liquid – ST Decreases – Temp
increases
𝜎𝑡 = 𝜎0(1 − 𝛼𝑡)
𝜎𝑡 = ST at Temp t deg C
𝜎0 = ST at Temp 0 Deg C
13

Quincke’s Method
14

Quincke’s Method
Under equilibrium, Two Forces acts
1. Due to ST from left to right Horizontally = 𝜎𝑙
2. Hydrostatic thrust from right to left
i. Average Pressure =
0+ℎ1𝜌𝑔
2
=
1
2
ℎ1𝜌𝑔
ii. ∴ 𝑡𝑜𝑡𝑎𝑙 ℎ𝑦𝑑𝑟𝑜𝑠𝑡𝑎𝑡𝑖𝑐 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =
1
2
ℎ1𝜌𝑔 × ℎ1𝑙
=
1
2
ℎ1
2
𝜌𝑔𝑙
3. The ST at G acting vertically upward
15

Quincke’s Method
Since the drop is in equilibrium.
Horizontal force must be equal
𝜎𝑙 =
1
2
ℎ1
2
𝜌𝑔𝑙
∴ 𝜎 =
1
2
ℎ1
2
𝜌𝑔
16

Determination of Angle of
Contact
Surface tension pull along KS = 𝜎. 𝑙
Horizontal component of this force along KC
= 𝜎. 𝑙𝑐𝑜𝑠𝛼
Where 𝛼 = (180 − 𝜃)
In Equilibrium, 𝜎. 𝑙 + 𝜎. 𝑙𝑐𝑜𝑠𝛼 =
1
2
ℎ2
2
𝜌𝑔𝑙
𝜎(1 + 𝑐𝑜𝑠𝛼) =
1
2
ℎ2
2
𝜌𝑔
Or
1
2
ℎ1
2
𝜌𝑔(1 + 𝑐𝑜𝑠𝛼) =
1
2
ℎ2
2
𝜌𝑔
17

Determination of Angle of
Contact
Or ℎ1
2
(1 + 𝑐𝑜𝑠𝛼) = ℎ2
2
(1 + 𝑐𝑜𝑠𝛼) =
ℎ2
2
ℎ1
2
𝑐𝑜𝑠𝛼 =
ℎ2
2
ℎ1
2 − 1
𝑐𝑜𝑠𝛼 =
ℎ2
2
− ℎ1
2
ℎ1
2
Angle of contact 𝜃 = (180 − 𝛼)
18

Ripples Method / Rayleigh’s
Method
Velocity of Harmonic Disturbance = ν =
𝜆𝑔
2𝜋
+
2𝜋𝜎
𝜆𝜌
For long waves
2𝜋𝜎
𝜆𝜌
can be neglected
ν =
𝜆
2𝜋
𝑔 +
4𝜋2
𝜆2𝜌
𝜎
If 𝜆 < 𝜆𝑐Waves are called ripples
ν =
2𝜋𝜎
𝜆𝜌
19

Method
Equ 1 shows that ν = ∞ when 𝜆 = 0 and when 𝜆=
∞.
𝜆 has a critical value 𝜆𝑐 for which ν is minimum. For
ν min the two terms must be equal.
The product of the two terms if
𝑔𝜎
𝜌
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.
Hence their sum will be minimum when they are
equal.
𝜆𝑐𝑔
2𝜋
=
2𝜋𝜎
𝜆𝑐𝜌
20

Method
𝜆𝑐
2 =
4𝜋2𝜎
𝑔𝜌
𝜆𝑐 = 2𝜋
𝜎
𝑔𝜌
For water 𝜎 = 17 × 10−3𝑁𝑚−1;𝜌 = 1000Kg𝑚−3;
𝜆𝑐 = 0.017 m
If the wavelength is less than this value, the waves
are called ripples
21

Experiment
Principle: Measurement of Wavelength of Ripples
𝜈 = 𝑛𝜆 =
𝜆𝑔
2𝜋
+
2𝜋𝜎
𝜆𝜌
𝜎 =
𝑛2𝜆3𝜌
2𝜋
−
𝜆2𝜌𝑔
4𝜋2
22

Drop Weight Method
𝜎 =
𝑚𝑔
3 ⋅ 8𝑟
Excess Pressure p =
𝜎
𝑟
Downward force = π𝑟2 𝜎
𝑟
Weight of the drop 𝑚𝑔
also acts Downwards
Total DW Force =
π𝑟2 𝜎
𝑟
+ 𝑚𝑔
Upward Force = 2π𝑟𝜎
23

Drop Weight Method
At equilibrium,
2π𝑟𝜎 = π𝑟2
𝜎
𝑟
+ 𝑚𝑔
2π𝑟𝜎 = π𝑟𝜎 + 𝑚𝑔
2π𝑟𝜎 − π𝑟𝜎 = 𝑚𝑔
π𝑟𝜎 = 𝑚𝑔
𝜎 =
𝑚𝑔
π𝑟
But equilibrium of the drop at the time of detachment is
dynamic hence 𝜎 =
𝑚𝑔
3.8𝑟
24

Link ST
Surface Tension-Click to learn
25

Properties of Matter - U4 - Surface Tension -PPT 1

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