surface tension part 2

Khalifa M.Asif Yunus
M.Pharm (Pharmaceutics)
J I I U ’ S
Ali-Allana College of Pharmacy Akkalkuwa
NBAAccredited
Asst. Prof.
Pharmaceutics Department
Ali-Allana college of pharmacy Akkalkuwa
E-mail: khalifa4517@gmail.com Mob. No. +91 9925064346

By: Khalifa M Asif Y Asst. Professor Pharmaceutics Dept. AACOP Akkalkuwa
Determination of Surface & Interfacial Tension
1.Capillary rise method,
2.Drop formation method
a.Drop number method
b.Drop weight method
3.Du Nouy ring method,
4.Sessile drop method
5.Bubble Pressure method

Capillary-rise Method
A capillary tube of radius ‘r’ is vertically inserted
into a liquid. The liquid rises to a height ‘h’ and
forms a concave meniscus.
The surface tension (γ) acting along the
inner circumference of the tube exactly
supports the weight of the liquid column.

By definition, surface tension is force per 1cm acting at a tangent
(curve or line) to the meniscus surface.
If the angle between the tangent and the tube wall is θ, the vertical
component of surface tension is γ cosθ.
The total surface tension along the circular contact line of meniscus
is 2πr times. Therefore,
Upward force = 2πr γ cos θ

Upward force = 2πr γ cosθ
where ‘r’ is the radius of the capillary.
For most liquids, θ is essentially zero, and cos 0 = 1.
Then ; Upward force = 2πr γ
The Downward force on the liquid column is due to its weight which
is mass × gravity. Thus, Downward force
= volume × density × gravity
= Cross section area × height × density × gravity
= πr2 × h × 𝝆 × g

𝜸 =
𝟏
𝟐
r 𝝆gh
In order to know the value of ‘ 𝜸’, the value of ‘h’ & ‘r’ is found with the
help of a travelling microscope and density (𝝆) with a pycnometer.
But, at equilibrium,
Upward force = Downward force
2πr γ = πr2 × h × 𝝆 × g

 A clean & dry capillary tube is selected and the internal diameter is
determined by travelling microscope.
 About 50ml of water is placed in 100 ml beaker.
 The capillary tube is dipped in water in a manner that the point touches
the liquid surface. The liquid rise in the tube up to particular hight.
 The hight of lower meniscus is measured by travelling microscope.
 Density of liquid is measured by pycnometer.
 The surface tension is calculated by following formula; 𝛄 =
𝟏
𝟐
r 𝛒gh
Procedure

Drop Formation Method
 A drop of liquid is allowed to form at the
lower end of a capillary tube.
 The drop is supported by the upward force of
surface tension acting at the outer
circumference of the tube.
 The weight of the drop (mg) pulls it
downward. When the two forces are
balanced, the drop breaks.

Thus at the point of breaking,
mg = 2πr γ ...........................(1)
where
m = mass of the drop
g = acceleration due to gravity
r = outer radius of the tube
 The apparatus employed is Stalagmometer or Drop pipette. The
surface tension is determined by one of the two methods given
below.
a. Drop-weight Method
b. Drop-number Method.

Drop-weight Method
Stalagmometer is cleaned, dried and filled with the
experimental liquid, up to mark A.
About 20 drops of the given liquid are received from
the drop-pipette in a weighing bottle and weighed.
Thus weight of one drop is found.
The drop-pipette is again cleaned and dried.
It is filled with a second reference liquid (water) and
weight of one drop determined as before.
Stalagmometer

m1g =2 πr γ1 ……………..(2)
m2g =2 πr γ2 ……………..(3)
Dividing (2) by (3)
....................(4)
Then from equation (1)
𝛄 𝟏
𝛄 𝟐
=
𝐦 𝟏
𝐦 𝟐

Drop-number Method.
 The drop-pipette is filled up to the mark A with the
experimental liquid (No. 1).
 The number of drops is counted as the meniscus
travels from A to B.
 Similarly, the pipette is filled with the reference
liquid (No. 2) as the meniscus passes from A to B.
 Let n1 and n2 be the number of drops produced by
the same volume V of the two liquids. Stalagmometer

Thus,
The volume of one drop of liquid 1 = V/n1
The mass of one drop of liquid 1 (m1) = (V/n1)d1
Where, d1 is the density of liquid 1.
Similarly, The mass of one drop of liquid 2 (m2) = (V/n2)d2
Then from equation (4)

Ring-detachment Method
 In this method the force required to detach a platinum ring
(du Nouy ring) from the liquid surface is measured.
 This force (F) is exactly equal to the downward pull due to
surface tension acting along the circumference of the ring.
 Twice the length of the circumference (2 × 2 πr) is taken
since the liquid is in contact with both the inside and the
outside of ring.
𝛄 =
𝐅
𝟒𝛑𝐫

 One end of the torsion wire is fixed while the other is attached to a knob
carrying a pointer.
 The pointer moves on a fixed scale. The scale is calibrated.
 The liquid whose surface tension is to be determined is placed in a watch
glass so that the Pt ring just touches its surface.
 The knob of the torsion wire is then Slowly turned till the ring is just
detached from the surface.
 The reading shown by the pointer on the scale gives the force F. The
surface tension is then calculated from equation (1).

Surface Free Energy

A
B C
D
L
A’ D’
d
f
Upward
component
relate to γ
Downward
component,
applied force

 When the applied force is less than that is required to breaking,
the film would react on account of surface tension.
 If force ‘f’ is applied on AD (downward component), it shifts the
movable wire to a distance ‘d’ to A’D’;
The work done ‘W’ is given by;
work done (W) = force x distance moved
W = f x d ……………….. (1)

The above force acts against the surface tension (Upward
component), γ of liquid, Since surface tension tries to contract the
liquid.
 there are two surface of each length ‘L’ on either side of wire.
The force acting on the surface is;
f = γ x 2L ………………………….. (2)
 Substituting both equation;
W = γ x 2L x d ………..…………….. (3)

 Since, 2L x d is equal to increase in surface area ‘∆A’ produced by
extending the soap film, equation (3) changes to;
W = γ x ∆A ……………………………….. (3)
Or ∆G = γ x ∆A
In which, ‘W’ is the work done or surface free energy increase
(∆G) expressed in ergs (or mJm-2)

 When a drop of a liquid is in equilibrium with is vapor, it takes
the forms of sphere, as it occupies minimum surface area per
unit volume. In this state the system possess minimum free
energy. Therefore, molecules at the surface must posses higher
free energy then those in the bulk.

When a drop of an insoluble oil is placed on a clean water surface,
it may behave in one of three ways:
1. Remain as a lens, (non-spreading).
2. Spread as a thin film, which uniformly distributed over the
surface as a 'duplex' film.
(A Duplex film is a film which is thick enough for the two
interfaces.)
3. Spread as a monolayer, leaving excess oil as lenses in
equilibrium.
Spreading Coefficient

The work of cohesion; which is the energy
required to separate the molecules of the
spreading liquid so as it can flow over the
sub-layer
 Hypothetical cylinder (cross section area
of 1 sq. cm) is divided, two new surfaces
are created. Where 2 surfaces each with
a surface tension = γL
Wc = 2γL
L
L
L
γL
γL
The spreading of liquid can be analysed by considering the
Cohesive & Adhesive forces between the molecules.

The work of adhesion; which is the energy required to break
the attraction between the unlike molecules.
Consider, the hypothetical cylinder of sublayer liquid, ‘S’
present below the similar section of spreading liquid ‘L’
s
L
s
L
γL
γs

Work done is equal to Work of adhesion
Where: γL =the surface tension of the spreading liquid
γS =the surface tension of the sublayer liquid
γLS =the interfacial tension between the two liquids.
 Spreading occurs if the work of adhesion is greater than the
work of cohesion, i.e. Wa > Wc
Wa = γL + γS - γ LS

Spreading Coefficient (S) is The difference between the work of
adhesion and the work of cohesion
S = Wa - Wc
S = (γL + γS - γLS ) - 2γL
S = γS - γL - γLS
S = γS – (γL + γ LS )

 Spreading occurs (S is positive) i.e. when the surface tension of
the sub-layer liquid is greater than the sum of the surface tension
of the spreading liquid and the interfacial tension between the
sub-layer and the spreading liquid.
 If (γL + γLS ) is larger than γS , (S is negative) the substance forms
globules or a floating lens and fails to spread over the surface.
S = γS – (γL + γ LS )

Relation between molecular structures & spreading coefficients
 The greater the polarity of the molecule the more positive [S] as
ethyl alcohol and propionic acid.
 Non polar substances have negative [S], fail to spread on water
 For organic acids, as Oleic acid, the longer the carbon chain,
decrease in polar character decrease [S]
 Some oils can spread over water because they contain polar
groups as COOH and OH

Application of Spreading coefficient in pharmacy
 Absorption of medicaments: when cream or lotion is applied on
the skin, it has to spread on affected area. Normally surfactants
are added to formulation to increase the polarity & spreading
coefficient.
 Stabilization of emulsion: A blend of surfactants are mixed with
an oil and its spreading on the water surface layer is evaluated.
Based on the results, a blend of surfactants is selected for the
preparation of stable emulsion.

surface tension part 2

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