10 Pius Augustine Surface tension

1
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Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara
Surface Tension
we will
overcome

Surface Tension
•Due to intermolecular
attraction (cohesive force)
•Liquid surface behaves
like stretched membrane.
•To minimise surface area
and surface energy.
Dr. Pius Augustine, S H College, Kochi

Some effects
i. Drop of water remains suspended from a tap
before it falls.
ii. Sewing needle (R.D =8) float on water
surface.
iii. Insects walk on water surface.
iv. Drop takes spherical shape.
v. Hairs of a brush taken out of water stick
together.
vi. Layer of water between glass plates
vii. Sweat sticks dress on the body
viii. Ends of glass rod becomes rounded on
heating .

Depression below the
needle on water surface.
ie. surface behaves like
elastic skin or membrane

Surface tension – definition
It is a property of a liquid by virtue
of which the free surface of a
liquid at rest behaves like a
stretched membrane.
It is the tangential force acting per
unit length of an imaginary line
drawn on the liquid surface.
S.T is numerically equal to
S.E (PE/unit area) Dr. Pius Augustine, S H College, Kochi

Does ST depend on area of
liquid surface?
No.
Measured as the force per
unit length and is
independent of area of
surface.

Calculate the work done to break up a drop
of mercury of diameter 1*10-2m into eight
drops , all of the same size. S.T = 0.035N/m
Tot. volume of 8 drops = volume of big drop
Solving, r = R/2
surface area of big drop = 4πR2.
Tot. surfac area of 8 drops = 8 * 4πr2.= 8 πR2
Increase in surface area = 8 πR2 - 4πR2 = πD2.
Work done = S.T * increase in area
= 1.1 * 10-5J

Calculate the work done in blowing a soap
bubble of radius 5cm.S.T= 3*10-2N/m
Radius of bubble = 0.05 m ( from zero to r)
Total surface area of bubble = 2*4πr2.
( two surfaces for bubble ) = increase in area
Work done = S.T * increase in area
= 3*10-2 x 8 πr2
= 1.88 x 10-3 J

A bigger drop is
broken in to a large
number of smaller
drops. Is the process
exo thermic or
endothermic?Dr. Pius Augustine, S H College, Kochi

Endothermic. As area increases , Surface energy
increases. So energy will be absorbed.
If big drop of radius R splits into n3 small drops of
radius r.
R = nr.
A1 =4πR2 = n2 4πr2.
A2 = n3 4πr2 ie: A2 > A1.
Energy absorbed = T * ∆A
= T [n3 4πr2 – n2 4πr2]
= T n3 4πr2 [1– 1/n]

The ends of glass tubes becomes
round on heating.Explain.
On heating glass melts.
Molten glass tends to
have minimum area due
to S.T.
Hence molten end takes
spherical shape.Dr. Pius Augustine, S H College, Kochi

Laplace’s theory – liquid meniscus
• Young–Laplace equation
• a nonlinear partial differential equation
• describes the capillary pressure difference
sustained across the interface between
two static fluids (say water and air)
Search for better understanding

How does duck float on the surface
of water ?
Feathers of duck secrete an
oil, S.T of water at that
point decreases.
Duck is pulled in the direction
of greater S.T and floats.

Sphere of influence
Range around a molecule, within
which it can feel the influence
of its neighbours is called range
of influence.
Sphere with molecule as center
and range of influence as
radius is called sphere of
influence. Dr. Pius Augustine, S H College, Kochi

Liquid enclosed in the region above
dotted line is called surface film.
Molecules below surface film do not
experience any net force.
Molecules inside the surface film
experience a net inward force, and
hence to pull a molecule in this film
,work has to be done.
ie. surface molecules have more
potential energy and this energy is
called surface energy.

Oil spreads over the surface of water
while water does not do so on oil
surface. Explain.
S.T of oil is less than that
of water.
Oil spreads due to higher
force of surface tension
of water.

Hot soup is more tasty than cold
soup?
Spreads over large
area of the tongue
due to its lower
surface tension.

Antiseptics used for cuts
and wounds in human
flesh have low S.T.
Spread over the
wound easily

Molecules near surface and
close to glass, major portion
of sphere of influence is out
side.
Net cohesive force (yellow )
Adhesive force ( green )
Resultant force (brown )
Liquid surface takes shape in
such way that, resultant force
should be perpendicular to
the surface for eqbm.Dr. Pius Augustine, S H College, Kochi

Angle of contact
Angle between the tangent
plane to the liquid surface at
the point of contact and the
solid surface inside the
liquid.
Depends on the nature of
surfaces in contact.Dr. Pius Augustine, S H College, Kochi

Factors on which angle of contact
depends
i. nature of surfaces in
contact.
ii. Cleanliness of surfaces
iii.Medium above free
surface of liquid

Experimental determination of
angle of contact .
Slanting glass is inserted into mercury .
Adjust the angle of inclination until mercury
meets glass without curvature.
Tanφ = AC/ BC
AC can be measured with the help of a
plumb line.
Angle of contact = 180 -φ
A
C

Clean glass plate in contact with
pure water, angle of contact is
zero.
ordinary tap water it is acute (8o)
Liquids which wet glass angle of
contact is acute.
Do not wet glass it is obtuse
Mercury and glass – 130o
Silver and water - 90o.Dr. Pius Augustine, S H College, Kochi

Wetting agents: Used by dyers to
reduce angle of contact between
the fabric and dye so that dye may
penetrate well.
Water proofing agents: used to
increase the angle of contact
between fabric and water to
prevent water from penetrating the
cloth.

Practical applications of capillarity
i. Water absorbed by the roots of plants
reaches branches and leaves.
ii. Kerosene oil in lantern and melted wax in
the upper portion of a candle rise in the
capillarity formed in the cotton wick and
burns.
iii. If one edge of a towel is dipped in water ,
the water begins to rise in the
innumerable holes in the threads of the
towel and ultimately the entire towel is
wetted.

Practical applications of capillarity
iv. Action of blotting paper.
v.Writing nib is split in the middle
so that a fine capillary gets
formed in it.
vi. Farmers plough their fields so
that the capillaries formed in the
soil get broken down and the
water remains in the lower layers
of the soil .

Big bubbles are formed from the soap
solution than from water. Why ?
Bubbles from pure water break at a
very early stage due to surface
tension of water.
Soap solution has a comparatively
much lower surface tension and
so bibber bubbles of the solution
can be formed.

i. Ploughing of field ( dry farming )
ii. Wick of stove
iii. Plants
iv. Blotting paper soaks ink
v. water is retained in a piece of
sponge.
vi. Walls get damped in rainy
season due to capillarity in bricks
vii. Pen nib is split
Some effects of capillarity

What is dry farming ?
In porous soil , water rises to the
surface by capillary action.
Space between compact soil act
as capillary tubes.
To prevent this loss during
summer , soil is loosened to
increase the space between
pores. Dr. Pius Augustine, S H College, Kochi

Ascent formula balance force method
Vol.above meniscus = 1/3 πR3.neglected

Volume of liquid = πR2h + (πR2R – ½ 4/3 πR3)
= πR2 (h+ R / 3)
S.T = R ( h + R/3)ρg
2cosθ

Calculate the height to which water will rise
in a capillary tube of 1mm diameter. S.T of
water = 73.5 dyne /cm, angle of contact = 0
h = 2γcosθ/ Rρg.
= 2 * 73.5 * cos0
0.05 * 1* 980
= 3 cm Dr. Pius Augustine, S H College, Kochi

Ascent formula, h = 2γcosθ/ Rρg.
i. Inversely proportional to radius
ii. Inversely proportional to density
iii. Directly proportional to surface
tension
cosθ is +ve (acute angle) - ascent
cosθ is -ve (obtuse angle) - depression

Jurin’s law
ρ, γ, θ and g are constants.
h α 1/R
Smaller the radius of the tube,
greater is the rise or fall of
liquid in it. This is called
Jurin’s law (hR = constant)Dr. Pius Augustine, S H College, Kochi

Capillary tube of insufficient length
Radius of capillary tube = radius of meniscus( wrong assumption)
c be the centre of curvature, r (AC) - radius of
curvature of meniscus and AO – R, radius of tube,
Angle CAO = angle of contact.
From triangle CAO, Cosθ = R/r
= 2γcosθ/ rcosθρg.
= 2γ/ rρg
ie. rh = 2γ/ ρg = constant
h’ be the insufficient length and r’ new radius of
curvature, rh = r’h’ ie liquid spills and
adjust radius of curvature of meniscus.
Angle of contact remains same as it is
independent of manner in which the two are
brought in contact.
c
A o

Drops and bubbles pressure difference
Free surface of a liquid is curved.
There is a difference of pressure between the
liquid side and vapor side of the surface.
Plane liquid surface – T acts horizontally
and has no component normal to the
surface. ∆P=0
Convex – T have components acting inward
.P inside increases so that surface is in
eqbm.
Concave –resultant T will be outward to
vapor side . For eqbm P on vapor side
must be grater Dr. Pius Augustine, S H College, Kochi

Pressure inside a liqid drop and bubble

Consider a spherical drop of radius R having
excess pressure (∆P) inside ,due to which
radius of drop increases by ∆R (very small )
Increase in surface area = 4π(R+∆R)2 - 4πR2.
= 8πR ∆R
∆W = γ * ∆A = γ * 8πR ∆R
Work done - also given by excess force x distance
∆W = ∆F * ∆R
=∆P * 4πR2 * ∆R
γ * 8πR ∆R = ∆P * 4πR2 * ∆R
∆P = 2γ / R
For bubble 2 surfaces , ∆P = 4γ / R

Worth noting
Extremely small value of R,
∆P assume large value.
Tiny liquid drops becomes as rigid
as solids.
Skater runs along tiny water
droplets as if on ball bearings.
Easier to walk on wet sand than on
dry sand.

Why is small drop of mercury spherical
but bigger drops are oval in shape?
Small – force of surface tension
is very large as compared to its
weight and hence it is spherical
in shape.
Big – oval due to its large weight

Spraying results in cooling. Why ?
Large no. of droplets are
formed on spraying.
Surface area increases.
Internal energy has been
utilized to create new
surface area causing fall in
temperature. Dr. Pius Augustine, S H College, Kochi

Why does water rise in a glass
capillary tube?
Narrow bore( tube) – meniscus spherical(aprox)
Pressure just outside = Patm.
Pressure inside = P - 2γ/R
Pressure outside the tube ( tangential or
horizontal with meniscus ) = Patm
Inside ( above tangent to lower meniscus )
there is a pressure gradient which lifts.
Liquid rises until hydrostatic pressure =
excess pressure

Why Hg is depressed in glass tube ?
Angle of contact- obtuse (surface is convex)
Pressure just outside = Patm.
Pressure inside = P + 2γ/R
Pressure outside the tube ( tangential or
horizontal with meniscus) = Patm
Inside (above tangent to lower meniscus)
Pressure gradient which depress.
Liquid rises until hydrostatic pressure =
excess pressure

Factors affecting S.T.
i. Temperature
ii.Contamination
iii.Concentration
iv.Electrification
v.Surrounding.

Effect of temperature on S.T.
Inversely proportional to temp.
Due to increase in average
separation between molecules.
For some liquids vanishes at
critical temp.
No satisfactory expression.

Small drops of Hg are spherical but
large ones are flat. Explain.
Shape governed by two factors – S.T,
gravitational force.
Gravity tends to spread,S.T tries to collect in the
form of sphere to have minimum area.
Force of gravity (Vdg) is proportional to V (r3).
S.T proportional to area (r2)
Large volume gravity is prominent
To minimize c.g should be as low.
Small volume S.T is prominent
surface area should be minimumDr. Pius Augustine, S H College, Kochi

Concentration and S.T.
S.T depends on nature of solute.
If solute is highly soluble, S.T
increases and vice versa.
Eg. Dissolving salt in water –
S.T increases.
Soap or phenol in water –
S.T decreases.

Effect of electrification
S.T decreases on
electrification.
Surface experience
outward normal pressure
tending to increase
surface area.

Camphor dances on water surface.
Explain.
Camphor dissolves and reduces S.T. of
water.
Camphor is pulled by surrounding
uncontaminated water of higher S.T.
Due to irregular shapes and sizes,
dissolving is not uniform.
S.T is non uniform all around, which
causes dance.

Explain detergent action ?
Dirt is grease or oil stains.
Water does not wet grease.
Detergents reduce S.T of water,
hence wet grease.
Molecules of detergent attract
water at one end and grease at
other end, thus separates.

Controlling ST
i. Surfactants
ii. Hydrophilization
iii.Electrowetting
iv.Thermocapilary effect

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75
Appeal: Please Contribute to Prime Minister’s or Chief
Minister’s fund in the fight against COVID-19
Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara
we will
overcome
Thank You
http://piusaugustine.shcollege.ac.in
https://www.facebook.com/piustine
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10 Pius Augustine Surface tension

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