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Colloidal Dispersions 2005
Surface and Interfacial Tensions
Lecture 1
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Surfaces and Interfaces 1Colloidal Dispersions 2005
Surface tension is a pull
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Thermodynamics for Interfacial Systems
F A =
Work must be done to increase surface area just as work must be done
to compress a gas.
At constant temperature (T), volume (V) and composition (n), the
energy, F, necessary to increase the surface area by an amount, A,is:
Where is the surface tension.
When Fis negative, the process is spontaneous.When Fis positive, the process reverses.
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Surfaces and Interfaces 3Colloidal Dispersions 2005
Coalescence of Droplets
The change in energy is:
+
( )
0
final initial
final initial
F F F
A A
A
=
=
=
+
This is not the common assertion.
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Surfaces and Interfaces 6Colloidal Dispersions 2005
Works of Cohesion and Adhesion
12 1
2
11
1 2 12
adhW = +
12
coh
W =
The work of adhesion is the
separation to create two new
surfaces from one interface:
The work of cohesion is theseparation to create two new
surfaces.
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Surfaces and Interfaces 7Colloidal Dispersions 2005
Liquids have different contact angles on different solids
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Surfaces and Interfaces 8Colloidal Dispersions 2005
Contact angles: Liquids on solids
The contact angle of 140o is the same for each drop, independent of
drop size.
The observation is that the contact angle depends on the materials but
not the particular geometry.
Mercury drops on glass.*
Drops vary in size from 4 to 24grains (1 grain = 64.8 mg)
* Bashforth and Adams, 1883.
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Surfaces and Interfaces 9Colloidal Dispersions 2005
The interaction of a liquid and a solid
= +cossv lv sl
The Young-Dupr introduces the idea of a solid surface/vapor surface
tension, sv and a solid/liquid interfacial tension, sl.
sv
lv
sl
The idea is that the three
tensions are balanced:
A sessile liquid drop on a
solid:
The contact angle is and is assumed to be independent of the geometry.
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Surfaces and Interfaces 10Colloidal Dispersions 2005
The Molecular Origin of Surface Tension
The molecules at the
liquid surface are pulled
towards the bulk liquid.
To expand the surface
requires work. The workis the surface tension
times the change in
area.
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Surfaces and Interfaces 11Colloidal Dispersions 2005
The Molecular Origin of Interfacial Tension
= + 1 2 12adhW
The stronger the interfacial
interactions, the lower the
interfacial tension!
But the greater the work of
adhesion:
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Surfaces and Interfaces 12Colloidal Dispersions 2005
A theory for interfacial tensions
Liquid 1
Liquid 2
1
2
1 2
d d
1 2
d d
12 1 2 1 22d d = +
Fowkes, in Ross, ed. 1965, p. x
The adhesion between the
liquids is approximated by the
root-mean-square of the
surface tensions:
1 22adh d d
W =
hence
The superscript d refers to the dispersion or van der Waals types of attraction.
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Surfaces and Interfaces 13Colloidal Dispersions 2005
Large surface heterogeneities - contact angle
hysteresis
Advancing liquids are held up by low energy spots and
show high contact angles.
Receding liquids are held by high energy spots and
show low contact angles.
High energy spots
low contact angles.
Low energy spots
high contact angles.
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Surfaces and Interfaces 14Colloidal Dispersions 2005
Small heterogeneities - contact angle changes
Coverage
0.0 0.2 0.4 0.6 0.8 1.0
cos
w
0.0
0.2
0.4
0.6
0.8
1.0
The cosine of the static contact angle of water on varioussubsaturated monolayers plotted versus the surface coverage
measured directly using the atomic force microscope.
Text, p. 220.
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Surfaces and Interfaces 15Colloidal Dispersions 2005
Motion of liquids due to surface energies
Capillary flow
Motion as a consequence of shape.
Key idea: pressure drop across a curved
surface
Marangoni flow
Motion as a consequence of variation insurface tension.
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Pressure drops across a curved surface
R1
R2
x x+dx
dz
y
y+dy
1 2
1 1Lp
R R
= +
The pressure is larger on the concave (inside) of the curved surface.
The Laplace equation:
R1 and R2 are the radii of curvature.
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Surfaces and Interfaces 17Colloidal Dispersions 2005
Bubbles are difficult to nucleate
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Surfaces and Interfaces 18Colloidal Dispersions 2005
Ostwald Ripening
The pressure inside > pressure outside
2p
r
=
This equation implies that in an emulsion with a range of drop sizes or
a foam with a range of bubble sizes, material diffuses from small
drops to large drops.
Also, this equation implies that bubbles are difficult to nucleate.
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Surfaces and Interfaces 19Colloidal Dispersions 2005
The Kelvin Equation
2ln m
o
P V
P rRT
=
0
2ln m
c V
c rRT
=
Similarly for small particles in suspension. If the particles have any
solubility, the small particles become smaller and the large particles
become larger. The effect is described by the Kelvin equation.
All these processes are called Ostwald ripening.
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Capillary rise is another example of Laplace pressure
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Capillary rise
The final position is determined by 2 principles:
(1) The pressure drops across curved interfaces.
(2) The pressure in the liquid must be the sameat the same depth.
In the final state the pressure drop across the ACinterface equals the hydrostatic pressure from C to B.
2 co sLg hR
=
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Marangoni Flow
Marangoni flow
flow resulting from local differences in
surface tension.
Causes of Variation in Surface Tension
Local temperature differences.
Local differences in composition due to
differential evaporation.
Electric charges at surfaces.
Local compression or dilatation of
adsorbed films.
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Liquid will flow away from a low surface tension region
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Liquid flows to the higher surface tension
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Tears of Wine
+
EthOH/H O2
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Flow due to surface tension differences
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Liquid flows away from a hot spot
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Liquid flows to a cold spot
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Equations of Capillarity
, , iT V n
F
A
=
= +cosSV LV SL
1 2
1 1pR R
= +
( )grad = +
Surface Free Energy
Young-Dupr Equation
LaPlace Equation
Marangoni Flow