Wetting and adhesion
Lecture 2
ACS© 2007
Surface tension is a pull
ACS© 2007
Lecure 2 - Wetting and adhesion
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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 work
is the surface tension
times the change in
area.
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Lecure 2 - Wetting and adhesion
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Thermodynamics for surfaces
The free energy (work at constant temperature) to compress a gas is:
ΔF = pΔV
The free energy to stretch a surface is:
ΔF = σΔA
Where σ is the surface tension.
When ΔF is negative, the process is spontaneous.
When ΔF is positive, the process reverses.
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Coalescence of Droplets
+
ΔF = Ffinal − Finitial
The change in energy is:
= σ ( Afinal − Ainitial )
= σΔA
<0
Therefore the drops coalesce spontaneously.
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Lecure 2 - Wetting and adhesion
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Coalescence of Droplets with Emulsifier
When droplets covered with
emulsifier coalesce, some
emulsifier must be desorbed.
This requires work.
+
Δ F = σ Δ A + work of desorption
If the emulsifier is strongly adsorbed, the work to
remove it is large, and the drops do not coalesce.
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Spreading
The energy change per unit area for liquid 2 (top) to spread
across the surface 1 (bottom) is:
Δ F = (σ 2 + σ 12 − σ 1 )
Surfactants reduce the two terms positive terms
allowing the drop to spread.
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Detergency
Requires only that the
energy of surfactant
adsorption is greater than the
energy of the new liquid
surface created.
Also requires that the
surfactant lower the new
solid/liquid interface to be less
than the previous solid/oil
interface.
Requires spontaneous
absorption of oil into
micelles.
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Lecure 2 - Wetting and adhesion
Holmberg et al. pp 474-5.
7
Liquids have different contact angles on different solids
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Contact angles: Liquids on solids
Mercury drops on glass.*
Drops vary in size from 4 to 24
grains (1 grain = 64.8 mg)
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.
* Bashforth and Adams, 1883.
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The equation for contact angles
The Young-Dupré introduces the idea of a solid surface/vapor surface
tension, σsv and a solid/liquid interfacial tension, σsl. The contact angle,
q, is independent of the geometry.
σlv
A sessile liquid drop on a solid:
σsv
θ
σsl
The idea is that the three tensions are balanced:
σ sv = σ lv cosθ + σ sl
or
σ sv − σ sl = σ lv cosθ
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Works of Cohesion and Adhesion
σsl
σlv
σsv
σ
σ
The work of adhesion is the
separation to create two new
surfaces from one interface:
W adh = σ sv + σ lv − σ sl
The work of cohesion is the
separation to create two new
surfaces.
W
Using the Young-Dupré equation:
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coh
= 2σ
W adh = σ lv cosθ + σ lv
Lecure 2 - Wetting and adhesion
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Large surface heterogeneities - contact angle
hysteresis
High energy spots –
low contact angles.
Low energy spots –
high contact angles.
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.
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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 in
surface tension.
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Pressure drops across a curved surface
The Laplace equation:
x+dx
x
dz
R
1
⎛ 1
1 ⎞
Δp = σ L ⎜
+
⎟
R
R
2 ⎠
⎝ 1
R
2
y
y+dy
R1 and R2 are the radii of curvature.
The pressure is larger on the concave (inside) of the curved surface.
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Capillary rise
2σ
L
cosθ
= ρ gh
R
The final position is determined by 2 principles:
(1) The pressure drops across curved interfaces.
(2) The pressure in the liquid must be the same
at the same depth.
In the final state the pressure drop across the AC
interface equals the hydrostatic pressure from C to B.
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Capillary rise is another example of Laplace pressure
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Bubbles are difficult to nucleate
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“Controlled” nucleation of bubbles
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Ostwald Ripening
The pressure inside > pressure outside
Δp =
2σ
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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The Kelvin Equation
The curvature of small drops changes the vapor pressure:
⎛ P ⎞ 2σ Vm
ln ⎜ ⎟ =
⎝ Po ⎠ rRT
Similarly, the “curvature” of small particles changes
the solubility:
⎛ c ⎞ 2σ Vm
ln ⎜ ⎟ =
⎝ c0 ⎠ rRT
Both these effects cause Ostwald ripening.
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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”
σ
+
σ
EthOH/H O
2
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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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