Surface Tension is defined as 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.
It is due to the phenomena of surface tension that the drops of water tend to assume a spherical shape to attain minimum surface area. the presentation gives a brief description of the methods to measue this important property of the interface of two fluid.
1. SURFACE TENSION
SEMINAR PRESENTATION ON
GROUP GUIDE:
Mr. PANKAJ DUMKA
COMPILED BY: GROUP NO. 21
GAURAV UPADHYAY (121739)
MAYANK TRIVEDI (121751)
MOHIT SINGH (121752)
PANKAJ SHARMA (121755)
PIYUSH SINGH (121756)
2. TABLE OF CONTENTS
1. INTRODUCTION TO SURFACE TENSION
2. FACTORS AFFECTING SURFACE TENSION
3. PHENOMENA OBSERVED DUE TO SURFACE TENSION
4. METHODS OF MEASUREMENT OF SURFACE TENSION
i. CAPILLARY RISE METHOD
ii. DROP ANALYSIS METHODS
a) STALAGMOMETER METHOD
b) SPINNING DROP METHOD
iii. MAXIMUM BUBBLE PRESSURE METHOD
iv. OSCILLATING JET METHOD
v. DU NOUY METHODS
a) RING TENSIOMETER
b) ROD PULL METHOD
3. WHAT IS SURFACE TENSION?
• Surface Tension is defined as
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.
• It is due to the phenomena
of surface tension that the
drops of water tend to
assume a spherical shape to
attain minimum surface
area.
4. The effect of surface tension on the interface area between two liquids may be
equivalently defined either through force or through energy.
1. In terms of force: surface tension γ of a liquid is one-half the force per unit length
required to keep still a movable side of a frame over which the liquid is stretched
(say, into a thin film).
γ=F/2L
2. In terms of energy: surface tension γ of a liquid is the ratio of 1) the change in
the energy of the liquid, and 2) the change in the surface area of the liquid (that led
to the change in energy).
γ= F/2L= F Δ x/2LΔ x= W/ΔA
6. PHENOMENA OBSERVED DUE TO SURFACE TENSION
1. Excess pressure in a soap bubble.
2. Formation of spherical droplets.
3. Capillarity.
4. Wetting and non-wetting properties of certain liquids
9. PRINCIPLE
• A consequence of the surface tension appearance
at the liquid/gas interface is moving up of the liquid
into a thin tube, that is capillary, which is usually
made of glass
• If the interaction forces of the liquid with the
capillary walls (adhesion) are stronger than those
between the liquid molecules (cohesion), the liquid
wets the walls and rises in the capillary to a defined
level and the meniscus is hemispherically concave
10. • In the opposite situation the forces
cause decrease of the liquid level in
the capillary below that in the
chamber and the meniscus is
hemispherically convex.
• If the cross-section area of the
capillary is circular and its radius is
sufficiently small, then the meniscus
is hemispherical. Along the
perimeter of the meniscus there acts
a force due to the surface tension
presence
Ref: http://zzm.umcs.lublin.pl/Wyklad/FGF-Ang/2A.F.G.F.%20Surface%20tension.pdf
11. f1=2πr𝛾cosθ
Where:
r – the capillary radius,
𝛾– the liquid surface tension,
θ– the wetting contact angle.
The force f1 in Eq.(1) is equilibrated by the mass of the liquid raised in the
capillary to the height h, that is the gravity force f2. In the case of non-
wetting liquid – it is lowered to a distance –h.
MATHEMATICAL ANALYSIS
12. f2 =πr2 hdg
where:
d : the liquid density (g/cm3) (actually the difference between the
liquid and the gas densities),
g : the acceleration of gravity
In equilibrium (the liquid does not moves in the capillary)
f1= f2
14. 1. DROP VOLUME METHOD
(STALAGMOMETER METHOD)
This method was first time described by Tate
in 1864 who formed an equation, which is
now called the Tate’s law.
𝑾 = 𝟐𝝅𝑹𝜸
W is the drop weight, r is the capillary radius,
and 𝛾 is the surface tension of the liquid.
Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
15. In the case of a liquid which wets the stalagmometer's tip the r value is that of the
outer radius of the capillary and if the liquid does not wet – the r value is that of
the inner radius of the capillary.
The drops wetting area corresponding to the
outer and inner radii of the stalagmometer's tip.
Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
16. CORRECTION FACTOR
Up to 40% of the drop volume may be left on the stalagmometer tip.
Therefore a correction f has to be introduced to the original Tate's equation.
𝑾′
= 𝟐𝝅𝒓𝜸𝒇
the weight of the falling drop W' is lower than W. This is a result of drop
formation, as shown
Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
17. f expresses the ratio of W’/ W.
Harkins and Brown found that the factor f is a function of the stalagmometer tip
radius, volume of the drop v, and a constant, which is characteristic of a given
stalagmometer, f = f (r, a, v)
𝒇 = 𝝋
𝒓
𝒂
= 𝝋
𝒓
𝒗 𝟏/𝟑
The f values for different tip radii were determined experimentally using water and
benzene, whose surface tensions were determined by the capillary rise method.
EXPERIMENTAL ANALYSIS OF THE CORRECTION FACTOR
Ref: C. E. Stauffer, “Measurement of surface tension by pendant
drop technique”, The journal of physical chemistry (1965) 1933.
18. Values of the factor f
Ref: C. E. Stauffer, “Measurement of surface tension by pendant
drop technique”, The journal of physical chemistry (1965) 1933.
19. PROCEDURE FOR MATHEMATICAL
CALCULATIONS
The factor f changes the least if:
0.6 < 𝑟
𝑣1/3 < 1.2
After having determined the mean weight m of the liquid drop
calculated from several drops weighed, one can calculate its volume at
the measurement temperature if the liquid density is known, and then
the value of 𝒓
𝒗 𝟏/𝟑.
Next the f value can be found in the table.
Finally, the surface tension can be calculated from
𝜸 =
𝒎𝒈
𝟐𝝅𝒓𝒇
Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
20. RELATIVE SURFACE TENSION MEASUREMENT USING
STALAGMOMETER
The f value depends also on the kind of
liquid tested.
Therefore the relative measurements (in
comparison to another liquid of known
surface tension) can not be applied here.
However, such measurement can be done
with 0.1 % accuracy if the shape of the
stalagmometer tip is like that shown in
figure.
Shape of the stalagmometer tip for relative
surface tension measurements.
Ref: Method and apparatus for detecting relative dynamic liquid surface
activity, Miller Brewing , citing patent, US4646562
21. MATHEMATICAL ANALYSIS
The relative surface tension is given by:
𝛾1
𝛾2
=
𝑚1
𝑚2
2/3
=
𝑑1
𝑑2
2/3
Having known the drop volume the surface tension can be calculated from :
𝛾 =
𝑚𝑔
2𝜋𝑟𝑓
=
𝑚𝑔
𝑘
=
𝑉𝑑𝑔
𝑘
𝜸 =
𝑽𝒅𝒈
𝒌
Ref: Method and apparatus for detecting relative dynamic liquid surface
activity, Miller Brewing , citing patent, US4646562
22. 2. SPINNING DROP METHOD
The spinning drop method (rotating drop method) is one of the
methods used to measure interfacial tension.
Measurements are carried out in a rotating horizontal tube which
contains a dense fluid. A drop of a less dense liquid or a gas bubble
is placed inside the fluid.
Ref: en.wikipedia.org/wiki/Spinning_drop_method
23. MATHEMATICAL ANALYSIS
A fluid drop of mass density ρ1 is
suspended in a liquid with the density ρ2 >
ρ1 .
The drop and the liquid are contained in a
horizontal tube cell.
At low rotational velocities ω, the drop will
take on an ellipsoidal shape, but when ω is
sufficiently large, it will become cylindrical.
𝛾 =
1
4
𝜌2 − 𝜌1 𝜔2 𝑟3
Ref:On two direct methods for measurement of interfacial tension
at microdroplet surfaces, J. Tothova, M. Richterova and V. Lisy
Institute of Physics, P.J. Safarik University, Jesenna 5, 041 54 Kosice, Slovakia
The Vonnegut’s equation
25. PRINCIPLE
• One of the useful methods to determine the
dynamic surface tension is measuring the
"maximum bubble pressure method
• Bubble pressure tensiometer produces gas bubbles
(ex. air) at constant rate and blows them through a
capillary which is submerged in the sample liquid
and its radius is already known
26. • The pressure (P) inside of the gas bubble continues
to increase and the maximum value is obtained
when the bubble has the completely hemispherical
shape whose radius is exactly corresponding to the
radius of the capillary.
• Applying Young–Laplace equation in the reduced
form
𝛾 = 𝑝 𝑚𝑎𝑥 ∗ 𝑟𝑐𝑎𝑝 2
27. • A, B: As the size increases, the radius of
curvature of the bubble decreases
• At the point of the maximum bubble pressure,
the bubble has a complete hemispherical shape
whose radius is identical to the radius of the
capillary denoted by Rcap
Fig.1
http://en.wikipedia.org/wiki/Maximum_bubble_pressure_method
28. Fig.2
• The measured value corresponds to
the surface tension at a certain
surface age, the time from the start
of the bubble formation to the
occurrence of the pressure
maximum
• The dependence of surface tension
on surface age can be measured by
varying the speed at which bubbles
are produced.
http://www.kruss.de/services/education-theory/glossary/bubble-pressure-
tensiometer/
29. APPARATUS
The capillary of radius r is immersed in the liquid
of density ρ and surface tension γ, such that the
bottom of capillary is at the depth of h bellow the
water level (Figure 2. The additional pressure ph
𝑝ℎ = ℎ ⋅ 𝜌 ⋅ 𝑔 ……..2
The pressure equal or greater than
p = 𝑝ℎ+ 𝑝 𝑘 ……………3
30. would push the air all the way through the capillary and will create a
bubble at its end. The combination of equations [1] and [2] with the
equation [3] yields
p= 2σ/t+hρg …………… 5
Pressure at knob c1
p=ℎ 𝑣*ρ 𝑣 ∗ 𝑔………. 6
The combination of the equation [6] and [5] determines the surface
tension
𝛾 =
𝑟
2
ℎ 𝑣 ∗ 𝜌 𝑣 − ℎ ∗ 𝜌
32. Measures “Dynamic Surface Tension”
Dynamic surface tension is the tension per
unit length developed at a specified point in
a surface and observed as a function of time.
The oscillating jet method consists of forcing
a stream of liquid under constant pressure
through an orifice.
Ref: link.springer.com/content/pdf/10.1007/978-1-4615-7972-4_4.pdf
33. The jet flows out from an elliptic orifice and therefore it
oscillates as shown in Figure
(Figure -1):
http://www.thermopedia.com/content/4740/SURFACE_AND_INTERFACIAL_TENSION_FIG15.gif
(Figure -1)
34. The oscillating crests and troughs are the result of
surface tension forces in the liquid .
Bohr (1909) presented the theory and relationship
between surface tension and measurable physical
properties such as the flow rate of the liquid,
wavelength and major and minor axes radii.
Wavelengths are frequently measured by passing
parallel light waves perpendicular to the jet stream.
Ref: http://www.seas.ucla.edu/stenstro/r/r18.pdf
38. Where
t = the oscillation period time
λ = the wave length
v = the jet flow rate
r = the radius of the jet at its spherical place
= surface tension
Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
40. Du Nouy ring method
• The du nuoy method is one technique by which the surface
tension of a liquid can be measured
• The method involves slowly lifting a ring, often made of platinum,
from the surface of a liquid.
• The force, F, required to raise the ring from the liquid's surface is
measured and related to the liquid's surface tension.
Ref :http://en.wikipedia.org/wiki/Du_No%C3%BCy_ring_method
42. 𝐹 = 2𝜋 𝑟𝑖 + 𝑟𝑎 𝛾
Where:
ri = the radius of the inner ring of the liquid film pulled
ra= the radius of the outer ring of the liquid film.
GOVERNING EQUATION FOR RING TENSIOMETER
43. Ref :http://en.wikipedia.org/wiki/Du_No%C3%BCy_ring_method
• This type of Tensiometer uses a platinum ring which is
submersed in a liquid. As the ring is pulled out of the liquid,
the tension required is precisely measured in order to
determine the surface tension of the liquid.
• This method requires that the platinum ring be nearly
perfect; even small blemish or scratch can greatly
alter the accuracy of the results.
• This method requires that the platinum ring be nearly
perfect; even small blemish or scratch can greatly alter the
accuracy of the results.
44. Du Nouy–Padday method
• This method uses a rod which is lowered into a test
liquid. The rod is then pulled out of the liquid and the
force required to pull the rod is precisely measured
• This is a rather novel method which is accurate and
repeatable. The Du Nouy-Padday Rod Pull Tensiometer
will take measurements quickly and unlike the ring and
plate methods, will work with liquids with a wide range
of viscosities
45. • The Du Noüy Padday rod consists of a rod usually on the
order of a few millimeters square making a small ring. The
rod is often made from a composite metal material that may
be roughened to ensure complete wetting at the interface.
• The rod is cleaned with water, alcohol and a flame or with
strong acid to ensure complete removal of surfactants. The
rod is attached to a scale or balance via a thin metal hook.
• The Padday method uses the maximum pull force method,
i.e. the maximum force due to the surface tension is
recorded as the probe is first immersed ca. one mm into the
solution and then slowly withdrawn from the interface.
46. • The main forces acting on a probe are the buoyancy
(due to the volume of liquid displaced by the probe)
and the mass of the meniscus adhering to the probe.
This is an old, reliable, and well-documented technique
• An important advantage of the maximum pull force
technique is that the receding contact angle on the
probe is effectively zero. The maximum pull force is
obtained when the buoyancy force reaches its
minimum.
